Investigation on the Use of a Multiphase Eulerian CFD solver to simulate breaking waves
DEFF Research Database (Denmark)
Tomaselli, Pietro D.; Christensen, Erik Damgaard
2015-01-01
investigation on a CFD model capable of handling this problem. The model is based on a solver, available in the open-source CFD toolkit OpenFOAM, which combines the Eulerian multi-fluid approach for dispersed flows with a numerical interface sharpening method. The solver, enhanced with additional formulations...
An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry
International Nuclear Information System (INIS)
Bernard-Champmartin, Aude; Ghidaglia, Jean-Michel; Braeunig, Jean-Philippe
2013-01-01
In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable h), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific up-winding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uh. (authors)
International Nuclear Information System (INIS)
Wilde, Juray de; Vierendeels, Jan; Heynderickx, Geraldine J.; Marin, Guy B.
2005-01-01
Simultaneous solution algorithms for Eulerian-Eulerian gas-solid flow models are presented and their stability analyzed. The integration algorithms are based on dual-time stepping with fourth-order Runge-Kutta in pseudo-time. The domain is solved point or plane wise. The discretization of the inviscid terms is based on a low-Mach limit of the multi-phase preconditioned advection upstream splitting method (MP-AUSMP). The numerical stability of the simultaneous solution algorithms is analyzed in 2D with the Fourier method. Stability results are compared with the convergence behaviour of 3D riser simulations. The impact of the grid aspect ratio, preconditioning, artificial dissipation, and the treatment of the source terms is investigated. A particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the Eulerian-Eulerian gas-solid flow models and their solution. The numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas-solid slip velocities. Furthermore, the effect of the grid resolution on the convergence behaviour and the simulation results is investigated. Finally, simulations of the bottom zone of a pilot-scale riser with a side solids inlet are experimentally validated
Pathak, Ashish; Raessi, Mehdi
2016-04-01
We present a three-dimensional (3D) and fully Eulerian approach to capturing the interaction between two fluids and moving rigid structures by using the fictitious domain and volume-of-fluid (VOF) methods. The solid bodies can have arbitrarily complex geometry and can pierce the fluid-fluid interface, forming contact lines. The three-phase interfaces are resolved and reconstructed by using a VOF-based methodology. Then, a consistent scheme is employed for transporting mass and momentum, allowing for simulations of three-phase flows of large density ratios. The Eulerian approach significantly simplifies numerical resolution of the kinematics of rigid bodies of complex geometry and with six degrees of freedom. The fluid-structure interaction (FSI) is computed using the fictitious domain method. The methodology was developed in a message passing interface (MPI) parallel framework accelerated with graphics processing units (GPUs). The computationally intensive solution of the pressure Poisson equation is ported to GPUs, while the remaining calculations are performed on CPUs. The performance and accuracy of the methodology are assessed using an array of test cases, focusing individually on the flow solver and the FSI in surface-piercing configurations. Finally, an application of the proposed methodology in simulations of the ocean wave energy converters is presented.
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
Felici, Helene M.; Drela, Mark
1993-01-01
A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.
Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates
International Nuclear Information System (INIS)
Brizard, A.
1988-09-01
A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs
Graphs with Eulerian unit spheres
Knill, Oliver
2015-01-01
d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...
Eulerian Graphs and Related Topics
Fleischner, Herbert
1990-01-01
The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a
Combinatorial Interpretation of General Eulerian Numbers
Tingyao Xiong; Jonathan I. Hall; Hung-Ping Tsao
2014-01-01
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions { a, a+d, a+2d,...}.
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Improvements to SOIL: An Eulerian hydrodynamics code
International Nuclear Information System (INIS)
Davis, C.G.
1988-04-01
Possible improvements to SOIL, an Eulerian hydrodynamics code that can do coupled radiation diffusion and strength of materials, are presented in this report. Our research is based on the inspection of other Eulerian codes and theoretical reports on hydrodynamics. Several conclusions from the present study suggest that some improvements are in order, such as second-order advection, adaptive meshes, and speedup of the code by vectorization and/or multitasking. 29 refs., 2 figs
International Nuclear Information System (INIS)
Fox, R.O.; Laurent, F.; Massot, M.
2008-01-01
The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS
International Nuclear Information System (INIS)
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.
2011-01-01
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.
Eulerian Method for Ice Crystal Icing
Norde, Ellen; van der Weide, Edwin Theodorus Antonius; Hoeijmakers, Hendrik Willem Marie
In this study, an ice accretion method aimed at ice crystal icing in turbofan engines is developed and demonstrated for glaciated as well as mixed-phase icing conditions. The particle trajectories are computed by an Eulerian trajectory method. The effects of heat transfer and phase change on the
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Brouwer-Janse, M.D.
1991-01-01
Most formal problem-solving studies use verbal protocol and observational data of problem solvers working on a task. In user-centred product-design projects, observational studies of users are frequently used too. In the latter case, however, systematic control of conditions, indepth analysis and
Eulerian fluid-structure analysis of BWR
International Nuclear Information System (INIS)
McMaster, W.H.
1979-05-01
A fluid-structure-interaction algorithm is developed for the analysis of the dynamic response of a BWR pressure-suppression pool and containment structure. The method is incorporated into a two-dimensional semi-implicit Eulerian hydrodynamics code, PELE-IC, for the solution of incompressible flow coupled to flexible structures. The fluid, structure, and coupling algorithms have been verified by calculation of solved problems from the literature and by comparison with air and steam blowdown experiments
High performance simplex solver
Huangfu, Qi
2013-01-01
The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-sparse linear system solution technique, efficient approaches to updating LU factors and...
International Nuclear Information System (INIS)
Chang, Y.W.; Chu, H.Y.; Gvildys, J.; Wang, C.Y.
1979-01-01
The analysis of fluid-structure interaction involves the calculation of both fluid transient and structure dynamics. In the structural analysis, Lagrangian meshes have been used exclusively, whereas for the fluid transient, Lagrangian, Eulerian, and arbitrary Lagrangian-Eulerian (quasi-Eulerian) meshes have been used. This paper performs an evaluation on these three types of meshes. The emphasis is placed on the applicability of the method in analyzing fluid-structure interaction problems in HCDA analysis
Electric circuits problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av
Advanced calculus problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av
A permutations representation that knows what " Eulerian" means
Directory of Open Access Journals (Sweden)
Roberto Mantaci
2001-12-01
Full Text Available Eulerian numbers (and ``Alternate Eulerian numbers'' are often interpreted as distributions of statistics defined over the Symmetric group. The main purpose of this paper is to define a way to represent permutations that provides some other combinatorial interpretations of these numbers. This representation uses a one-to-one correspondence between permutations and the so-called subexceedant functions.
An Eulerian-Eulerian CFD Simulation of Air-Water Flow in a Pipe Separator
Directory of Open Access Journals (Sweden)
E.A. Afolabi
2014-06-01
Full Text Available This paper presents a three dimensional Computational Fluid Dynamics (CFD of air-water flow using Eulerian –Eulerian multiphase model and RSM mixture turbulence model to investigate its hydrodynamic flow behaviour in a 30 mm pipe separator. The simulated results are then compared with the stereoscopic PIV measurements at different axial positions. The comparison shows that the velocity distribution can be predicted with high accuracy using CFD. The numerical velocity profiles are also found to be in good qualitative agreement with the experimental measurements. However, there were some discrepancies between the CFD results and the SPIV measurements at some axial positions away from the inlet section. Therefore, the CFD model could provide good physical understanding on the hydrodynamics flow behaviour for air-water in a pipe separator.
Prediction of subcooled flow boiling characteristics using two-fluid Eulerian CFD model
Energy Technology Data Exchange (ETDEWEB)
Braz Filho, Francisco A.; Ribeiro, Guilherme B., E-mail: gbribeiro@ieav.cta.br; Caldeira, Alexandre D.
2016-11-15
Highlights: • CFD multiphase model is used to predict subcooled flow boiling characteristics. • Better agreement is achieved for higher saturation pressures. • Onset of nucleate boiling and saturated boiling are well predicted. • CFD multiphase model tends to underestimate the void fraction. • Factors were adjusted in order to improve the void fraction results. - Abstract: The present study concerns a detailed analysis of flow boiling phenomena under high pressure systems using a two-fluid Eulerian approach provided by a Computational Fluid Dynamics (CFD) solver. For this purpose, a vertical heated pipe made of stainless steel with an internal diameter of 15.4 mm was considered as the modeled domain. Two different uniform heat fluxes and three saturation pressures were applied to the channel wall, whereas water mass flux of 900 kg/m{sup 2} s was considered for all simulation cases. The model was validated against a set of experimental data and results have indicated a promising use of the CFD technique for estimation of the wall temperature, the liquid bulk temperature and the location of the departure of nucleate boiling. Changes in factors applied in the modeling of the interfacial heat transfer coefficient and bubble departure frequency were suggested, allowing a better prediction of the void fraction along the heated channel. The commercial CFD solver FLUENT 14.5 was used for the model implementation.
Prediction of subcooled flow boiling characteristics using two-fluid Eulerian CFD model
International Nuclear Information System (INIS)
Braz Filho, Francisco A.; Ribeiro, Guilherme B.; Caldeira, Alexandre D.
2016-01-01
Highlights: • CFD multiphase model is used to predict subcooled flow boiling characteristics. • Better agreement is achieved for higher saturation pressures. • Onset of nucleate boiling and saturated boiling are well predicted. • CFD multiphase model tends to underestimate the void fraction. • Factors were adjusted in order to improve the void fraction results. - Abstract: The present study concerns a detailed analysis of flow boiling phenomena under high pressure systems using a two-fluid Eulerian approach provided by a Computational Fluid Dynamics (CFD) solver. For this purpose, a vertical heated pipe made of stainless steel with an internal diameter of 15.4 mm was considered as the modeled domain. Two different uniform heat fluxes and three saturation pressures were applied to the channel wall, whereas water mass flux of 900 kg/m"2 s was considered for all simulation cases. The model was validated against a set of experimental data and results have indicated a promising use of the CFD technique for estimation of the wall temperature, the liquid bulk temperature and the location of the departure of nucleate boiling. Changes in factors applied in the modeling of the interfacial heat transfer coefficient and bubble departure frequency were suggested, allowing a better prediction of the void fraction along the heated channel. The commercial CFD solver FLUENT 14.5 was used for the model implementation.
Investigation of erosion behavior in different pipe-fitting using Eulerian-Lagrangian approach
Kulkarni, Harshwardhan; Khadamkar, Hrushikesh; Mathpati, Channamallikarjun
2017-11-01
Erosion is a wear mechanism of piping system in which wall thinning occurs because of turbulent flow along with along with impact of solid particle on the pipe wall, because of this pipe ruptures causes costly repair of plant and personal injuries. In this study two way coupled Eulerian-Lagrangian approach is used to solve the liquid solid (water-ferrous suspension) flow in the different pipe fitting namely elbow, t-junction, reducer, orifice and 50% open gate valve. Simulations carried out using incomressible transient solver in OpenFOAM for different Reynolds's number (10k, 25k, 50k) and using WenYu drag model to find out possible higher erosion region in pipe fitting. Used transient solver is a hybrid in nature which is combination of Lagrangian library and pimpleFoam. Result obtained from simulation shows that exit region of elbow specially downstream of straight, extradose of the bend section more affected by erosion. Centrifugal force on solid particle at bend affect the erosion behavior. In case of t-junction erosion occurs below the locus of the projection of branch pipe on the wall. For the case of reducer, orifice and a gate valve reduction area as well as downstream is getting more affected by erosion because of increase in velocities.
Solution of the stellar structure equations in Eulerian coordinates
International Nuclear Information System (INIS)
Deupree, R.G.
1976-01-01
The equations of hydrostatic and thermal equilibrium, assuming only radiative energy transport and spherical symmetry, are solved in Eulerian coordinates by a suitable modification of the Henyey method. An Eulerian approach may possibly be more suitably extended to more spatial dimensions than the usual Lagrangian procedure. The principle advantage of this method is that the equations of hydrostatic and thermal equilibrium and Poisson's equation may be solved simultaneously
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
2015-09-30
Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Estimating Eulerian spectra from pairs of drifters
LaCasce, Joe
2017-04-01
GPS-tracked surface drifters offer the possibility of sampling energetic variations at the ocean surface on scales of only 10s of meters, much less than that resolved by satellite. Here we investigate whether velocity differences between pairs of drifters can be used to estimate kinetic energy spectra. Theoretical relations between the spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived. The structure function is a natural statistic for particle pairs and is easily calculated. However it integrates contributions across wavenumber, and this tends to obscure the spectral dependencies when turbulent inertial ranges are of finite extent. Nevertheless, the transform from spectrum to structure function is robust, as illustrated with Eulerian data collected from aircraft. The inverse transform, from structure function to spectrum, is much less robust, yielding poor results in particular at large wavenumbers. This occurs because the transform involves a filter function which magnifies contributions from large pair separations, which tend to be noisy. Fitting the structure function to a polynomial improves the spectral estimate, but not sufficiently to distinguish correct inertial range dependencies. Thus with Lagrangian data, it is appears preferable to focus on structure functions, despite their shortcomings.
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS
International Nuclear Information System (INIS)
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.; Dolence, J.
2013-01-01
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
Nitrogen injection in stagnant liquid metal. Eulerian-Eulerian and VOF calculations by fluent
International Nuclear Information System (INIS)
Pena, A.; Esteban, G.A.
2004-01-01
High power spallation sources are devices that can be very useful in different fields, as medicine, material science, and also in the Accelerator Driven Systems (ADS). This devices use Heavy Liquid Metals (HLM) as the spallation target. Furthermore, HLM are thought to be the coolant of those big energy sources produced by the process. Fast breeder reactors, advanced nuclear reactors, as well as the future designs of fusion reactors, also consider HLM as targets or coolants. Gas injection in liquid metal flows allows the enhancement of this coolant circulation. The difference in densities between the gas and the liquid metal is a big challenge for the multiphase models implemented in the Computational Fluid Dynamics (CFD) codes. Also the changing shape of the bubbles involves extra difficulties in the calculations. A N 2 flow in stagnant Lead-Bismuth eutectic (Pb-Bi), experiment available at Forschungszentrum Rossendorf e.V (FZR) in Germany, was used in one of the work-packages of the ASCHLIM project (EU contract number FIKW-CT-2001-80121). In this paper, calculations made by the UPV/EHU (University of the Basque Country) show measuring data compared with numerical results using the CFD (Computational Fluid Dynamics) code FLUENT and two multiphase models: the Eulerian-Eulerian and the Volume of Fluid (VOF). The interpretation of the experimental resulting velocities was difficult, because some parameters were not known, bubble trajectory and bubble shape, for example, as direct optical methods cannot be used, like it is done with water experiments. (author)
Eulerian graph embeddings and trails confined to lattice tubes
International Nuclear Information System (INIS)
Soteros, C E
2006-01-01
Embeddings of graphs in sublattices of the square and simple cubic lattice known as tubes (or prisms) are considered. For such sublattices, two combinatorial bounds are obtained which each relate the number of embeddings of all closed eulerian graphs with k branch points (vertices of degree greater than two) to the number of self-avoiding polygons. From these bounds it is proved that the entropic critical exponent for the number of embeddings of closed eulerian graphs with k branch points is equal to k, and the entropic critical exponent for the number of closed trails with k branch points is equal to k + 1. One of the required combinatorial bounds is obtained via Madras' 1999 lattice cluster pattern theorem, which yields a bound on the number of ways to convert a self-avoiding polygon into a closed eulerian graph embedding with k branch points. The other combinatorial bound is established by constructing a method for sequentially removing branch points from a closed eulerian graph embedding; this yields a bound on the number of ways to convert a closed eulerian graph embedding into a self-avoiding polygon
Modern solvers for Helmholtz problems
Tang, Jok; Vuik, Kees
2017-01-01
This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...
International Nuclear Information System (INIS)
Kalteh, Mohammad; Abbassi, Abbas; Saffar-Avval, Majid; Harting, Jens
2011-01-01
In this paper, laminar forced convection heat transfer of a copper-water nanofluid inside an isothermally heated microchannel is studied numerically. An Eulerian two-fluid model is considered to simulate the nanofluid flow inside the microchannel and the governing mass, momentum and energy equations for both phases are solved using the finite volume method. For the first time, the detailed study of the relative velocity and temperature of the phases are presented and it has been observed that the relative velocity and temperature between the phases is very small and negligible and the nanoparticle concentration distribution is uniform. However, the two-phase modeling results show higher heat transfer enhancement in comparison to the homogeneous single-phase model. Also, the heat transfer enhancement increases with increase in Reynolds number and nanoparticle volume concentration as well as with decrease in the nanoparticle diameter, while the pressure drop increases only slightly.
Self-correcting Multigrid Solver
International Nuclear Information System (INIS)
Lewandowski, Jerome L.V.
2004-01-01
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work
Eulerian Time-Domain Filtering for Spatial LES
Pruett, C. David
1997-01-01
Eulerian time-domain filtering seems to be appropriate for LES (large eddy simulation) of flows whose large coherent structures convect approximately at a common characteristic velocity; e.g., mixing layers, jets, and wakes. For these flows, we develop an approach to LES based on an explicit second-order digital Butterworth filter, which is applied in,the time domain in an Eulerian context. The approach is validated through a priori and a posteriori analyses of the simulated flow of a heated, subsonic, axisymmetric jet.
Iterative solvers in forming process simulations
van den Boogaard, Antonius H.; Rietman, Bert; Huetink, Han
1998-01-01
The use of iterative solvers in implicit forming process simulations is studied. The time and memory requirements are compared with direct solvers and assessed in relation with the rest of the Newton-Raphson iteration process. It is shown that conjugate gradient{like solvers with a proper
GPU acceleration of Eulerian-Lagrangian particle-laden turbulent flow simulations
Richter, David; Sweet, James; Thain, Douglas
2017-11-01
The Lagrangian point-particle approximation is a popular numerical technique for representing dispersed phases whose properties can substantially deviate from the local fluid. In many cases, particularly in the limit of one-way coupled systems, large numbers of particles are desired; this may be either because many physical particles are present (e.g. LES of an entire cloud), or because the use of many particles increases statistical convergence (e.g. high-order statistics). Solving the trajectories of very large numbers of particles can be problematic in traditional MPI implementations, however, and this study reports the benefits of using graphical processing units (GPUs) to integrate the particle equations of motion while preserving the original MPI version of the Eulerian flow solver. It is found that GPU acceleration becomes cost effective around one million particles, and performance enhancements of up to 15x can be achieved when O(108) particles are computed on the GPU rather than the CPU cluster. Optimizations and limitations will be discussed, as will prospects for expanding to two- and four-way coupled systems. ONR Grant No. N00014-16-1-2472.
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
Energy Technology Data Exchange (ETDEWEB)
Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel [Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/Dr. Moliner 50, E-46100 Burjassot (Spain); Müller, Ewald, E-mail: tomasz.rembiasz@uv.es [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
2017-06-01
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.
QUANTIFYING SUBGRID POLLUTANT VARIABILITY IN EULERIAN AIR QUALITY MODELS
In order to properly assess human risk due to exposure to hazardous air pollutants or air toxics, detailed information is needed on the location and magnitude of ambient air toxic concentrations. Regional scale Eulerian air quality models are typically limited to relatively coar...
Eulerian derivations of non-inertial Navier-Stokes equations
CSIR Research Space (South Africa)
Combrinck, MA
2014-09-01
Full Text Available The paper presents an Eulerian derivation of the non-inertial Navier-Stokes equations as an alternative to the Lagrangian fluid parcel approach. This work expands on the work of Kageyama and Hyodo [1] who derived the incompressible momentum equation...
A generalized gyrokinetic Poisson solver
International Nuclear Information System (INIS)
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms
Directory of Open Access Journals (Sweden)
Alessandra M Bavo
Full Text Available In recent years the role of FSI (fluid-structure interaction simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations' outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results.
Asymptotic shape of the region visited by an Eulerian walker.
Kapri, Rajeev; Dhar, Deepak
2009-11-01
We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the boundary region grows as Nalpha/3, with alpha=0.40+/-0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, approximately approximately N2nu, shows a crossover from the Eulerian (nu=1/3) to a simple random-walk (nu=1/2) behavior.
Eulerian Multiphase Population Balance Model of Atomizing, Swirling Flows
Directory of Open Access Journals (Sweden)
Narayana P. Rayapati
2011-06-01
Full Text Available An Eulerian/Eulerian multiphase flow model coupled with a population balance model is used as the basis for numerical simulation of atomization in swirling flows. The objective of this exercise is to develop a methodology capable of predicting the local point-wise drop size distribution in a spray, such as would be measured by the Phase Doppler Particle Analyzer (PDA. Model predictions are compared to experimental measurements of particle size distributions in an air-blast atomizer spray to demonstrate good qualitative and quantitative agreement. It is observed that the dependence of velocity on drop size inherent in a multiphase description of the drop cloud appears necessary to capture some features of the experimental data. Using this model, we demonstrate the relative contributions of secondary atomization and transport to the variation observed in the downstream spray drop size distribution.
An arbitrary Lagrangian-Eulerian method for interfacial flows with insoluble surfactants
Yang, Xiaofeng
Interfacial flows, fluid flows involving two or more fluids that do not mix, are common in many natural and industrial processes such as rain drop formation, crude oil recovery, polymer blending, fuel spray formation, and so on. Surfactants (surface active substances) play an important role in such processes because they significantly change the interfacial dynamics. In this thesis, an arbitrary Lagrangian-Eulerian (ALE) method has been developed to numerically simulate interfacial flows with insoluble surfactants. The interface is captured using a coupled level set and volume of fluid method. To evolve the surfactant concentration, the method directly tracks the surfactant mass and the interfacial area. The surfactant concentration, which determines the local surface tension through an equation of state, is then computed as surfactant mass per interfacial area. By directly tracking the surfactant mass, the method conserves the surfactant mass exactly. To accurately approximate the interfacial area, the fluid interface is reconstructed using piecewise parabolas. The evolution of the level set function, volume fraction, interfacial area, and the surfactant mass is performed using an ALE approach. The fluid flow is governed by Stokes equations, which are solved using a finite element method. The surface forces are included in the momentum equation using a continuum surface stress formulation. To efficiently resolve the complex interfacial dynamics, interfacial regions of high surface curvature, and near contact regions between two interacting interfaces, the grid near the interface is adaptively refined. The method is extendible to axisymmetric and 3D spaces, and can be coupled with other flow solvers, such as Navier-Stokes and viscoelastic flow solvers, as well. The method has been applied to study the effect of surfactants on drop deformation and breakup in an extensional flow. Drop deformation results are compared with available experimental and theoretical
An Eulerian two-phase flow model for sediment transport under realistic surface waves
Hsu, T. J.; Kim, Y.; Cheng, Z.; Chauchat, J.
2017-12-01
Wave-driven sediment transport is of major importance in driving beach morphology. However, the complex mechanisms associated with unsteadiness, free-surface effects, and wave-breaking turbulence have not been fully understood. Particularly, most existing models for sediment transport adopt bottom boundary layer approximation that mimics the flow condition in oscillating water tunnel (U-tube). However, it is well-known that there are key differences in sediment transport when comparing to large wave flume datasets, although the number of wave flume experiments are relatively limited regardless of its importance. Thus, a numerical model which can resolve the entire water column from the bottom boundary layer to the free surface can be a powerful tool. This study reports an on-going effort to better understand and quantify sediment transport under shoaling and breaking surface waves through the creation of open-source numerical models in the OpenFOAM framework. An Eulerian two-phase flow model, SedFoam (Cheng et al., 2017, Coastal Eng.) is fully coupled with a volume-of-fluid solver, interFoam/waves2Foam (Jacobsen et al., 2011, Int. J. Num. Fluid). The fully coupled model, named SedWaveFoam, regards the air and water phases as two immiscible fluids with the interfaces evolution resolved, and the sediment particles as dispersed phase. We carried out model-data comparisons with the large wave flume sheet flow data for nonbreaking waves reported by Dohmen-Janssen and Hanes (2002, J. Geophysical Res.) and good agreements were obtained for sediment concentration and net transport rate. By further simulating a case without free-surface (mimic U-tube condition), the effects of free-surface, most notably the boundary layer streaming effect on total transport, can be quantified.
Test set for initial value problem solvers
W.M. Lioen (Walter); J.J.B. de Swart (Jacques)
1998-01-01
textabstractThe CWI test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit differential equations. This test set can both decrease the effort for the code developer to test his software in a reliable way, and cross the bridge between the application
Iterative linear solvers in a 2D radiation-hydrodynamics code: Methods and performance
International Nuclear Information System (INIS)
Baldwin, C.; Brown, P.N.; Falgout, R.; Graziani, F.; Jones, J.
1999-01-01
Computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations. The authors present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation-hydrodynamics problems. The linear solvers used are diagonally scaled conjugate gradient, GMRES with incomplete LU preconditioning, conjugate gradient with incomplete Cholesky preconditioning, multigrid, and multigrid-preconditioned conjugate gradient. These problems involve shock propagation, opacities varying over 5--6 orders of magnitude, tabular equations of state, and dynamic ALE (Arbitrary Lagrangian Eulerian) meshes. They perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1,000 to 100,000 zones. The fundamental question they address in this paper is: Is it more efficient to invert the matrix in many inexpensive steps (like diagonally scaled conjugate gradient) or in fewer expensive steps (like multigrid)? In addition, what is the answer to this question as a function of problem size and is the answer problem dependent? They find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size, increasing in both iteration count and overall CPU time with the size of the problem and also increasing for larger time steps. For all problems considered, the multigrid algorithms scale almost perfectly (i.e., the iteration count is approximately independent of problem size and problem time step). For pure radiation flow problems (i.e., no hydrodynamics), they see speedups in CPU time of factors of ∼15--30 for the largest problems, when comparing the multigrid solvers relative to diagonal scaled conjugate gradient
Quasi-Eulerian formulation for fluid-structure interaction
International Nuclear Information System (INIS)
Kennedy, J.M.; Belytschko, T.B.
1979-01-01
In this paper, recent developments of a quasi-Eulerian finite element formulation for the treatment of the fluid in fluid-structure interaction problems are described. The present formulation is applicable both to plane two-dimensional and axisymmetric three-dimensional problems. In order to reduce the noise associated with the convection terms, an amplification factor is used to implement an up-winding type scheme. The application of the method is illustrated in two problems which are of importance in nuclear reactor safety: 1. A two-dimensional model of a cross section of a subassembly configuration, where the quasi-Eulerian formulation is used to model the fluid adjacent to the structures and in the channel between the subassemblies. 2. Pressure transients in a straight pipe, where the axisymmetric formulation is used to model the fluid in the pipe. These results are compared to experimental results for these problems and compare quite well. The major problem in the application of these methods appears to be the automation of the scheme for moving the fluid nodes. Several alternative schemes are used in the problems described here, and a more general scheme which appears to offer a reasonable (orig.)
Numerical modelling of diesel spray using the Eulerian multiphase approach
International Nuclear Information System (INIS)
Vujanović, Milan; Petranović, Zvonimir; Edelbauer, Wilfried; Baleta, Jakov; Duić, Neven
2015-01-01
Highlights: • Numerical model for fuel disintegration was presented. • Fuel liquid and vapour were calculated. • Good agreement with experimental data was shown for various combinations of injection and chamber pressure. - Abstract: This research investigates high pressure diesel fuel injection into the combustion chamber by performing computational simulations using the Euler–Eulerian multiphase approach. Six diesel-like conditions were simulated for which the liquid fuel jet was injected into a pressurised inert environment (100% N 2 ) through a 205 μm nozzle hole. The analysis was focused on the liquid jet and vapour penetration, describing spatial and temporal spray evolution. For this purpose, an Eulerian multiphase model was implemented, variations of the sub-model coefficients were performed, and their impact on the spray formation was investigated. The final set of sub-model coefficients was applied to all operating points. Several simulations of high pressure diesel injections (50, 80, and 120 MPa) combined with different chamber pressures (5.4 and 7.2 MPa) were carried out and results were compared to the experimental data. The predicted results share a similar spray cloud shape for all conditions with the different vapour and liquid penetration length. The liquid penetration is shortened with the increase in chamber pressure, whilst the vapour penetration is more pronounced by elevating the injection pressure. Finally, the results showed good agreement when compared to the measured data, and yielded the correct trends for both the liquid and vapour penetrations under different operating conditions
A cavitation model based on Eulerian stochastic fields
Magagnato, F.; Dumond, J.
2013-12-01
Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
ALPS - A LINEAR PROGRAM SOLVER
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
Benzi, R.; Biferale, L.; Fisher, R.T.; Lamb, D.Q.; Toschi, F.
2009-01-01
We report a detailed study of Eulerian and Lagrangian statistics from high resolution Direct Numerical Simulations of isotropic weakly compressible turbulence. Reynolds number at the Taylor microscale is estimated to be around 600. Eulerian and Lagrangian statistics is evaluated over a huge data
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Numerical methods for Eulerian and Lagrangian conservation laws
Després, Bruno
2017-01-01
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.
A model relating Eulerian spatial and temporal velocity correlations
Cholemari, Murali R.; Arakeri, Jaywant H.
2006-03-01
In this paper we propose a model to relate Eulerian spatial and temporal velocity autocorrelations in homogeneous, isotropic and stationary turbulence. We model the decorrelation as the eddies of various scales becoming decorrelated. This enables us to connect the spatial and temporal separations required for a certain decorrelation through the ‘eddy scale’. Given either the spatial or the temporal velocity correlation, we obtain the ‘eddy scale’ and the rate at which the decorrelation proceeds. This leads to a spatial separation from the temporal correlation and a temporal separation from the spatial correlation, at any given value of the correlation relating the two correlations. We test the model using experimental data from a stationary axisymmetric turbulent flow with homogeneity along the axis.
Development and deployment of constitutive softening routines in Eulerian hydrocodes.
Energy Technology Data Exchange (ETDEWEB)
Fuller, Timothy Jesse; Dewers, Thomas A.; Swan, Matthew Scot
2013-03-01
The state of the art in failure modeling enables assessment of crack nucleation, propagation, and progression to fragmentation due to high velocity impact. Vulnerability assessments suggest a need to track material behavior through failure, to the point of fragmentation and beyond. This eld of research is particularly challenging for structures made of porous quasi-brittle materials, such as ceramics used in modern armor systems, due to the complex material response when loading exceeds the quasi-brittle material's elastic limit. Further complications arise when incorporating the quasi-brittle material response in multi-material Eulerian hydrocode simulations. In this report, recent e orts in coupling a ceramic materials response in the post-failure regime with an Eulerian hydro code are described. Material behavior is modeled by the Kayenta material model [2] and Alegra as the host nite element code [14]. Kayenta, a three invariant phenomenological plasticity model originally developed for modeling the stress response of geologic materials, has in recent years been used with some success in the modeling of ceramic and other quasi-brittle materials to high velocity impact. Due to the granular nature of ceramic materials, Kayenta allows for signi cant pressures to develop due to dilatant plastic ow, even in shear dominated loading where traditional equations of state predict little or no pressure response. When a material's ability to carry further load is compromised, Kayenta allows the material's strength and sti ness to progressively degrade through the evolution of damage to the point of material failure. As material dilatation and damage progress, accommodations are made within Alegra to treat in a consistent manner the evolving state.
Energy Technology Data Exchange (ETDEWEB)
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.
Using SPARK as a Solver for Modelica
Energy Technology Data Exchange (ETDEWEB)
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK solver has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
New iterative solvers for the NAG Libraries
Energy Technology Data Exchange (ETDEWEB)
Salvini, S.; Shaw, G. [Numerical Algorithms Group Ltd., Oxford (United Kingdom)
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Cafesat: A modern sat solver for scala
Blanc Régis
2013-01-01
We present CafeSat a SAT solver written in the Scala programming language. CafeSat is a modern solver based on DPLL and featuring many state of the art techniques and heuristics. It uses two watched literals for Boolean constraint propagation conict driven learning along with clause deletion a restarting strategy and the VSIDS heuristics for choosing the branching literal. CafeSat is both sound and complete. In order to achieve reasonable performance low level and hand tuned data structures a...
International Nuclear Information System (INIS)
Leung Shingyu; Qian Jianliang
2010-01-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
IMPOSING A LAGRANGIAN PARTICLE FRAMEWORK ON AN EULERIAN HYDRODYNAMICS INFRASTRUCTURE IN FLASH
International Nuclear Information System (INIS)
Dubey, A.; Daley, C.; Weide, K.; Graziani, C.; ZuHone, J.; Ricker, P. M.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.
Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco
2017-08-25
We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.
Micro Expression Recognition Using the Eulerian Video Magnification Method
Directory of Open Access Journals (Sweden)
Elham Zarezadeh
2016-08-01
Full Text Available In this paper we propose a new approach for facial micro expressions recognition. For this purpose the Eulerian Video Magnification (EVM method is used to retrieve the subtle motions of the face. The results of this method are obtained as in the magnified images sequence. In this study the numerical tests are performed on two databases: Spontaneous Micro expression (SMIC and Category and Sourcing Managers Executive (CASME. We evaluate our proposed method in two phases using the eigenface method. In phase 1 we recognize the type of a micro expression, for example emotional versus unemotional in SMIC database. Phase 2 classifies the recognized micro expression as negative versus positive in SMIC database and happiness versus disgust in CASME database. The results show that the eigenface method by the EVM method for the retrieval of subtle motions of the face increases the performance of micro expression recognition. Moreover, the proposed approach is more accurate and promising than the previous works in micro expressions recognition.
Directory of Open Access Journals (Sweden)
Milosz Ciznicki
2015-01-01
Full Text Available The recent advent of novel multi- and many-core architectures forces application programmers to deal with hardware-specific implementation details and to be familiar with software optimisation techniques to benefit from new high-performance computing machines. Extra care must be taken for communication-intensive algorithms, which may be a bottleneck for forthcoming era of exascale computing. This paper aims to present a high-level stencil framework implemented for the EULerian or LAGrangian model (EULAG that efficiently utilises multi- and many-cores architectures. Only an efficient usage of both many-core processors (CPUs and graphics processing units (GPUs with the flexible data decomposition method can lead to the maximum performance that scales the communication-intensive Generalized Conjugate Residual (GCR elliptic solver with preconditioner.
An entropic solver for ideal Lagrangian magnetohydrodynamics
International Nuclear Information System (INIS)
Bezard, F.; Despres, B.
1999-01-01
In this paper, the authors adapt to the ideal 1D lagrangian MHD equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system. They use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions. These numerical schemes satisfy an entropy inequality under CFL conditions. In the last section, they describe a particular scheme for the MHD equations and show with some numerical applications its robustness and accuracy. The generalization to full Eulerian multidimensional MHD will be the subject of a forthcoming paper
An Eulerian-Eulerian Approach to CFD Simulation of Two-Phase Bubble Column using ANSYS CFX Code
International Nuclear Information System (INIS)
Mohd Amirul Syafiq Mohd Yunos; Nur Khairunnisa Abd Halim; Siti Aslina Hussain
2016-01-01
Bubble columns are widely used as gas-liquid contactors and reactors in chemical, biochemical and petrochemical industries. Effective mixing, high interfacial area between phases, cheap to install and lack of moving parts are the main factors bubble column is chosen for the described processes. Understanding the complexity of the fluid dynamics of gas-liquid flow in bubble column is important due to its unsteady complex processes as well as application in the chemical and bioprocess industries. The gas-liquid of two-phase fluid flow system has been carried out to investigate the hydrodynamics parameters. An Eulerian-Eulerian approach was used to model air as the dispersed phase within a continuous phase of water using the commercial software ANSYSTM CFD software (CFX 14.0). The turbulence in the gas-liquid simulation is described by using the k-e model. This process occurs under the atmospheric pressure. The configuration of model consists of 0.2 m width, 0.2 m depth and 0.5 m height of rectangular bubble column equipped with a sparger at the bottom. Two different sparger designs, Sparger A with 4 holes and 2.6 mm diameter each and Sparger B with 81 holes and 0.5 mm diameter each are tested for three different value of superficial gas velocity of 0.0125 m/s, 0.0501 m/s and 0.0627 m/s. The volume fraction of model is described the behavior of bubble which is represented by the parameters of gas holdup, contact surface area and gas superficial velocity. The simulation was verified by comparing the two different model results. Comparison of simulation results with the experimental work data has provided a successful validation of the model. Results shows the contact surface area increasing with behavior of bubble and gas holdup increases with increasing superficial gas velocity but independent of the sparger design at high superficial velocity (>0.05 m/s). The highest value obtained which is represented of water superficial velocity, gas holdup and superficial gas
Benchmarking optimization solvers for structural topology optimization
DEFF Research Database (Denmark)
Rojas Labanda, Susana; Stolpe, Mathias
2015-01-01
solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance...
On a construction of fast direct solvers
Czech Academy of Sciences Publication Activity Database
Práger, Milan
2003-01-01
Roč. 48, č. 3 (2003), s. 225-236 ISSN 0862-7940 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : Poisson equation * boundary value problem * fast direct solver Subject RIV: BA - General Mathematics
DEFF Research Database (Denmark)
Bjørner, Nikolaj; Dung, Phan Anh; Fleckenstein, Lars
2015-01-01
vZ is a part of the SMT solver Z3. It allows users to pose and solve optimization problems modulo theories. Many SMT applications use models to provide satisfying assignments, and a growing number of these build on top of Z3 to get optimal assignments with respect to objective functions. vZ provi...
Extending the Finite Domain Solver of GNU Prolog
Bloemen, Vincent; Diaz, Daniel; van der Bijl, Machiel; Abreu, Salvador; Ströder, Thomas; Swift, Terrance
This paper describes three significant extensions for the Finite Domain solver of GNU Prolog. First, the solver now supports negative integers. Second, the solver detects and prevents integer overflows from occurring. Third, the internal representation of sparse domains has been redesigned to
Star formation, using 3-D explicit Eulerian hydrodynamics
International Nuclear Information System (INIS)
Williams, H.A.
1988-01-01
Evolutions of rapidly rotating, self-gravitating objects initially in axisymmetric equilibrium have been studied using a 3-D Newtonian hydrodynamic computer code with an eye toward understanding angular momentum transport in dynamically evolving protostars. First, a number of evolutions have been modeled using an existing explicit, Eulerian, finite difference code that is accurate to first-order in its spatial differences. The bar-mode dynamic instability has been explored by considering several models with different degrees of compressibility. This instability occurs in models with different degrees of comprresibility. This instability occurs in models having β > β d ≡ 0.27, where β is the ratio of the rotational to the gravitational potential energy. A two-armed spiral, with a well-defined pattern speed and growth rate that match the pattern speed and growth rate predicted by linear theory, develops from each of the axisymmetric equilibria. The models with greater compressibility exhibit spirals which are more tightly wound. As the nonaxisymmetric distortion become large in an extended evolution, the object does not undergo binary fission as had been thought earlier. Instead, the spiral elongates and then wraps up on itself, forming a central pulsating triaxial object surrounded by a more diffuse ring-like disk. Angular momentum and mass are dynamically redistributed by gravitational torques during the evolution, and β is reduced below β d . Since this gravitational-rotational dynamic instability is a general feature of gaseous systems, this study may have application to theta galaxies and to rapidly rotating neutron stars, as well as to protostars
Fostering Creative Problem Solvers in Higher Education
DEFF Research Database (Denmark)
Zhou, Chunfang
2016-01-01
to meet such challenges. This chapter aims to illustrate how to understand: 1) complexity as the nature of professional practice; 2) creative problem solving as the core skill in professional practice; 3) creativity as interplay between persons and their environment; 4) higher education as the context......Recent studies have emphasized issues of social emergence based on thinking of societies as complex systems. The complexity of professional practice has been recognized as the root of challenges for higher education. To foster creative problem solvers is a key response of higher education in order...... of fostering creative problem solvers; and 5) some innovative strategies such as Problem-Based Learning (PBL) and building a learning environment by Information Communication Technology (ICT) as potential strategies of creativity development. Accordingly, this chapter contributes to bridge the complexity...
Mathematical programming solver based on local search
Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain
2014-01-01
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...
Aleph Field Solver Challenge Problem Results Summary
Energy Technology Data Exchange (ETDEWEB)
Hooper, Russell [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.
Evolving effective incremental SAT solvers with GP
Bader, Mohamed; Poli, R.
2008-01-01
Hyper-Heuristics could simply be defined as heuristics to choose other heuristics, and it is a way of combining existing heuristics to generate new ones. In a Hyper-Heuristic framework, the framework is used for evolving effective incremental (Inc*) solvers for SAT. We test the evolved heuristics (IncHH) against other known local search heuristics on a variety of benchmark SAT problems.
Asynchronous Parallelization of a CFD Solver
Abdi, Daniel S.; Bitsuamlak, Girma T.
2015-01-01
The article of record as published may be found at http://dx.doi.org/10.1155/2015/295393 A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used inCFDcodes; however, it has a potential to alleviate scaling bottlenecks incurred due to process...
Chemical Mechanism Solvers in Air Quality Models
Directory of Open Access Journals (Sweden)
John C. Linford
2011-09-01
Full Text Available The solution of chemical kinetics is one of the most computationally intensivetasks in atmospheric chemical transport simulations. Due to the stiff nature of the system,implicit time stepping algorithms which repeatedly solve linear systems of equations arenecessary. This paper reviews the issues and challenges associated with the construction ofefficient chemical solvers, discusses several families of algorithms, presents strategies forincreasing computational efficiency, and gives insight into implementing chemical solverson accelerated computer architectures.
Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays
International Nuclear Information System (INIS)
Wocjan, Pawel
2006-01-01
The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to effect sequences of instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To overcome the shortcomings of bang-bang control, Viola and Knill proposed a method called 'Eulerian decoupling' that allows the use of bounded-strength controls for decoupling. However, their method was not directly designed to take advantage of the local structure of internal couplings and couplings to an environment that typically occur in multipartite quantum systems. In this paper we define a combinatorial structure called Eulerian orthogonal array. It merges the desirable properties of orthogonal arrays and Eulerian cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show that this structure gives rise to decoupling schemes with bounded-strength control Hamiltonians that can be used to remove both internal couplings and couplings to an environment of a multipartite quantum system. Furthermore, we show how to construct Eulerian orthogonal arrays having good parameters in order to obtain efficient decoupling schemes
Efficient Eulerian gyrokinetic simulations with block-structured grids
International Nuclear Information System (INIS)
Jarema, Denis
2017-01-01
applied to different Eulerian gyrokinetic simulation codes, as the technique relies on a general approach. We implemented and tested our block-structured grids in GENE (http://genecode.org), a highly parallel and heavily used gyrokinetic code, for which it is crucial to keep the good parallel characteristic of the implementation and allow developers to easily port the code written for the original grid to the block-structured counterpart. The presented scenarios clearly demonstrate benefits of the block-structured grids: a high speedup, a tremendously reduced memory footprint and size of diagnostic output data, and the capability to significantly advance the frontier of feasible simulations.
Efficient Eulerian gyrokinetic simulations with block-structured grids
Energy Technology Data Exchange (ETDEWEB)
Jarema, Denis
2017-01-20
applied to different Eulerian gyrokinetic simulation codes, as the technique relies on a general approach. We implemented and tested our block-structured grids in GENE (http://genecode.org), a highly parallel and heavily used gyrokinetic code, for which it is crucial to keep the good parallel characteristic of the implementation and allow developers to easily port the code written for the original grid to the block-structured counterpart. The presented scenarios clearly demonstrate benefits of the block-structured grids: a high speedup, a tremendously reduced memory footprint and size of diagnostic output data, and the capability to significantly advance the frontier of feasible simulations.
Statistics of a mixed Eulerian-Lagrangian velocity increment in fully developed turbulence
International Nuclear Information System (INIS)
Friedrich, R; Kamps, O; Grauer, R; Homann, H
2009-01-01
We investigate the relationship between Eulerian and Lagrangian probability density functions obtained from numerical simulations of two-dimensional as well as three-dimensional turbulence. We show that in contrast to the structure functions of the Lagrangian velocity increment δ τ v(y)=u(x(y, τ), τ)- u(y, 0), where u(x, t) denotes the Eulerian velocity and x(y, t) the particle path initially starting at x(y, 0)=y, the structure functions of the velocity increment δ τ w(y)=u(x(y, τ), τ)- u(y, τ) exhibit a wide range of scaling behavior. Similar scaling indices are detected for the structure functions for particles diffusing in frozen turbulent fields. Furthermore, we discuss a connection to the scaling of Eulerian transversal structure functions.
Hybrid Multiphase CFD Solver for Coupled Dispersed/Segregated Flows in Liquid-Liquid Extraction
Directory of Open Access Journals (Sweden)
Kent E. Wardle
2013-01-01
Full Text Available The flows in stage-wise liquid-liquid extraction devices include both phase segregated and dispersed flow regimes. As a additional layer of complexity, for extraction equipment such as the annular centrifugal contactor, free-surface flows also play a critical role in both the mixing and separation regions of the device and cannot be neglected. Traditionally, computional fluid dynamics (CFD of multiphase systems is regime dependent—different methods are used for segregated and dispersed flows. A hybrid multiphase method based on the combination of an Eulerian multifluid solution framework (per-phase momentum equations and sharp interface capturing using Volume of Fluid (VOF on selected phase pairs has been developed using the open-source CFD toolkit OpenFOAM. Demonstration of the solver capability is presented through various examples relevant to liquid-liquid extraction device flows including three-phase, liquid-liquid-air simulations in which a sharp interface is maintained between each liquid and air, but dispersed phase modeling is used for the liquid-liquid interactions.
A coupled PFEM-Eulerian approach for the solution of porous FSI problems
Larese, A.; Rossi, R.; Oñate, E.; Idelsohn, S. R.
2012-12-01
This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a Lagrangian model for the structural behavior and an Eulerian approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an Eulerian fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.
Development of a multimaterial, two-dimensional, arbitrary Lagrangian-Eulerian mesh computer program
International Nuclear Information System (INIS)
Barton, R.T.
1982-01-01
We have developed a large, multimaterial, two-dimensional Arbitrary Lagrangian-Eulerian (ALE) computer program. The special feature of an ALE mesh is that it can be either an embedded Lagrangian mesh, a fixed Eulerian mesh, or a partially embedded, partially remapped mesh. Remapping is used to remove Lagrangian mesh distortion. This general purpose program has been used for astrophysical modeling, under the guidance of James R. Wilson. The rationale behind the development of this program will be used to highlight several important issues in program design
Energy Technology Data Exchange (ETDEWEB)
Kaufmann, A.
2004-03-15
Particle laden flows occur in industrial applications ranging from droplets in gas turbines to fluidized bed in chemical industry. Prediction of the dispersed phase properties such as concentration and dynamics are crucial for the design of more efficient devices that meet the new pollutant regulations of the European community. Numerical simulation coupling Lagrangian tracking of discrete particles with DNS or LES of the carrier phase provide a well established powerful tool to investigate particle laden flows. Such numerical methods have the drawback of being numerically very expensive for practical applications. Numerical simulations based on separate Eulerian balance equations for both phases, coupled through inter-phase exchange terms might be an effective alternative approach. This approach has been validated for the case of tracer particles with very low inertia that follow the carrier phase almost instantaneously due to their small response time compared with the micro-scale time scales of the carrier phase. Objective of this thesis is to extend this approach to more inertial particles that occur in practical applications such as fuel droplets in gas turbine combustors. Existing results suggest a separation of the dispersed phase velocity into a correlated and an uncorrelated component. The energy related to the uncorrelated component is about 30% of the total particle kinetic energy when the particle relaxation time is comparable to the Lagrangian integral time scale. The presence of this uncorrelated motion leads to stress terms in the Eulerian balance equation for the particle momentum. Models for this stress terms are proposed and tested. Numerical simulations in the Eulerian framework are validated by comparison with simulations using Lagrangian particle tracking. Additionally coupling of the Eulerian transport equations for the particles to combustion models is tested. (author)
The Openpipeflow Navier–Stokes solver
Directory of Open Access Journals (Sweden)
Ashley P. Willis
2017-01-01
Full Text Available Pipelines are used in a huge range of industrial processes involving fluids, and the ability to accurately predict properties of the flow through a pipe is of fundamental engineering importance. Armed with parallel MPI, Arnoldi and Newton–Krylov solvers, the Openpipeflow code can be used in a range of settings, from large-scale simulation of highly turbulent flow, to the detailed analysis of nonlinear invariant solutions (equilibria and periodic orbits and their influence on the dynamics of the flow.
New multigrid solver advances in TOPS
International Nuclear Information System (INIS)
Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S
2005-01-01
In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (αSA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The αSA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG
Metaheuristics progress as real problem solvers
Nonobe, Koji; Yagiura, Mutsunori
2005-01-01
Metaheuristics: Progress as Real Problem Solvers is a peer-reviewed volume of eighteen current, cutting-edge papers by leading researchers in the field. Included are an invited paper by F. Glover and G. Kochenberger, which discusses the concept of Metaheuristic agent processes, and a tutorial paper by M.G.C. Resende and C.C. Ribeiro discussing GRASP with path-relinking. Other papers discuss problem-solving approaches to timetabling, automated planograms, elevators, space allocation, shift design, cutting stock, flexible shop scheduling, colorectal cancer and cartography. A final group of methodology papers clarify various aspects of Metaheuristics from the computational view point.
A finite different field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-08-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL
A finite element field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-01-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL. (author). 7 refs., 4 figs
International Nuclear Information System (INIS)
Park, Chan Wook; Lee, Sung Su
2008-01-01
Two-phase compressible flow fields of air-water are investigated numerically in the fixed Eulerian grid framework. The phase interface is captured via volume fractions of ech phase. A way to model two phase compressible flows as a single phase one is found based on an equivalent equation of states of Tait's type for a multiphase cell. The equivalent single phase field is discretized using the Roe's approximate Riemann solver. Two approaches are tried to suppress the pressure oscillation phenomena at the phase interface, a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. In discretizing the compressible form of volume fraction equation, phase interfaces are geometrically reconstructed to minimize the numerical diffusion of volume fraction and relevant variables. The motion of a projectile in a water-filled tube which is fired by the release of highly pressurized air is simulated presuming the flow field as a two dimensional one, and several design factors affecting the projectile movement are investigated
Eulerian short-time statistics of turbulent flow at large Reynolds number
Brouwers, J.J.H.
2004-01-01
An asymptotic analysis is presented of the short-time behavior of second-order temporal velocity structure functions and Eulerian acceleration correlations in a frame that moves with the local mean velocity of the turbulent flow field. Expressions in closed-form are derived which cover the viscous
A New Eulerian Model for Turbulent Evaporating Sprays in Recirculating Flows
Wittig, S.; Hallmann, M.; Scheurlen, M.; Schmehl, R.
1993-01-01
A new Eulerian model for the computation of turbulent evaporating sprays in recirculating flows is derived. It comprises droplet heating and evaporation processes by solving separate transport equations for the droplet's temperature and diameter. Full coupling of the droplet and the gaseous phase is
Dynamic Load Balancing for PIC code using Eulerian/Lagrangian partitioning
Sauget, Marc; Latu, Guillaume
2017-01-01
This document presents an analysis of different load balance strategies for a Plasma physics code that models high energy particle beams with PIC method. A comparison of different load balancing algorithms is given: static or dynamic ones. Lagrangian and Eulerian partitioning techniques have been investigated.
Simulation of Steady Laser Hardening by an Arbitrary Lagrangian Eulerian Method
Geijselaers, Hubertus J.M.; Huetink, Han
2004-01-01
One of the most practical methods for simulation of steady state thermal processing is the Arbitrary Lagrangian- Eulerian method. Each calculation step is split into two phases. In the first phase, the Lagrangian phase, the element mesh remains attached to the material. The evolution of the state
PCX, Interior-Point Linear Programming Solver
International Nuclear Information System (INIS)
Czyzyk, J.
2004-01-01
1 - Description of program or function: PCX solves linear programming problems using the Mehrota predictor-corrector interior-point algorithm. PCX can be called as a subroutine or used in stand-alone mode, with data supplied from an MPS file. The software incorporates modules that can be used separately from the linear programming solver, including a pre-solve routine and data structure definitions. 2 - Methods: The Mehrota predictor-corrector method is a primal-dual interior-point method for linear programming. The starting point is determined from a modified least squares heuristic. Linear systems of equations are solved at each interior-point iteration via a sparse Cholesky algorithm native to the code. A pre-solver is incorporated in the code to eliminate inefficiencies in the user's formulation of the problem. 3 - Restriction on the complexity of the problem: There are no size limitations built into the program. The size of problem solved is limited by RAM and swap space on the user's computer
Directory of Open Access Journals (Sweden)
Sánchez Álvarez , I.
1998-01-01
Full Text Available La relevancia de los problemas de optimización en el mundo empresarial ha generado la introducción de herramientas de optimización cada vez más sofisticadas en las últimas versiones de las hojas de cálculo de utilización generalizada. Estas utilidades, conocidas habitualmente como «solvers», constituyen una alternativa a los programas especializados de optimización cuando no se trata de problemas de gran escala, presentado la ventaja de su facilidad de uso y de comunicación con el usuario final. Frontline Systems Inc es la empresa que desarrolla el «solver» de Excel, si bien existen asimismo versiones para Lotus y Quattro Pro con ligeras diferencias de uso. En su dirección de internet (www.frontsys.com se puede obtener información técnica sobre las diferentes versiones de dicha utilidad y diversos aspectos operativos del programa, algunos de los cuales se comentan en este trabajo.
A sparse-grid isogeometric solver
Beck, Joakim
2018-02-28
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse version of IGA solvers
Beck, Joakim
2017-07-30
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse-grid isogeometric solver
Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo
2018-01-01
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A sparse version of IGA solvers
Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo
2017-01-01
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.
A Novel Interactive MINLP Solver for CAPE Applications
DEFF Research Database (Denmark)
Henriksen, Jens Peter; Støy, S.; Russel, Boris Mariboe
2000-01-01
This paper presents an interactive MINLP solver that is particularly suitable for solution of process synthesis, design and analysis problems. The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master pr...
Experiences with linear solvers for oil reservoir simulation problems
Energy Technology Data Exchange (ETDEWEB)
Joubert, W.; Janardhan, R. [Los Alamos National Lab., NM (United States); Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Parallel sparse direct solver for integrated circuit simulation
Chen, Xiaoming; Yang, Huazhong
2017-01-01
This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...
High order Poisson Solver for unbounded flows
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2015-01-01
This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field....... The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel...... the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing...
Optimising a parallel conjugate gradient solver
Energy Technology Data Exchange (ETDEWEB)
Field, M.R. [O`Reilly Institute, Dublin (Ireland)
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
Finegold, M.; Mass, R.
1985-01-01
Good problem solvers and poor problem solvers in advanced physics (N=8) were significantly different in their ability in translating, planning, and physical reasoning, as well as in problem solving time; no differences in reliance on algebraic solutions and checking problems were noted. Implications for physics teaching are discussed. (DH)
Boscheri, Walter; Dumbser, Michael
2017-10-01
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total
Comparison of open-source linear programming solvers.
Energy Technology Data Exchange (ETDEWEB)
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Scalable Methods for Eulerian-Lagrangian Simulation Applied to Compressible Multiphase Flows
Zwick, David; Hackl, Jason; Balachandar, S.
2017-11-01
Multiphase flows can be found in countless areas of physics and engineering. Many of these flows can be classified as dispersed two-phase flows, meaning that there are solid particles dispersed in a continuous fluid phase. A common technique for simulating such flow is the Eulerian-Lagrangian method. While useful, this method can suffer from scaling issues on larger problem sizes that are typical of many realistic geometries. Here we present scalable techniques for Eulerian-Lagrangian simulations and apply it to the simulation of a particle bed subjected to expansion waves in a shock tube. The results show that the methods presented here are viable for simulation of larger problems on modern supercomputers. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138. This work was supported in part by the U.S. Department of Energy under Contract No. DE-NA0002378.
Large deformation analysis of adhesive by Eulerian method with new material model
International Nuclear Information System (INIS)
Maeda, K; Nishiguchi, K; Iwamoto, T; Okazawa, S
2010-01-01
The material model to describe large deformation of a pressure sensitive adhesive (PSA) is presented. A relationship between stress and strain of PSA includes viscoelasticity and rubber-elasticity. Therefore, we propose the material model for describing viscoelasticity and rubber-elasticity, and extend the presented material model to the rate form for three dimensional finite element analysis. After proposing the material model for PSA, we formulate the Eulerian method to simulate large deformation behavior. In the Eulerian calculation, the Piecewise Linear Interface Calculation (PLIC) method for capturing material surface is employed. By using PLIC method, we can impose dynamic and kinematic boundary conditions on captured material surface. The representative two computational examples are calculated to check validity of the present methods.
Udaykumar, H S; Belk, D M; Vanden, K J
2003-01-01
A technique is presented for the numerical simulation of high-speed multimaterial impact. Of particular interest is the interaction of solid impactors with targets. The computations are performed on a fixed Cartesian mesh by casting the equations governing material deformation in Eulerian conservation law form. The advantage of the Eulerian setting is the disconnection of the mesh from the boundary deformation allowing for large distortions of the interfaces. Eigenvalue analysis reveals that the system of equations is hyperbolic for the range of materials and impact velocities of interest. High-order accurate ENO shock-capturing schemes are used along with interface tracking techniques to evolve sharp immersed boundaries. The numerical technique is designed to tackle the following physical phenomena encountered during impact: (1) high velocities of impact leading to large deformations of the impactor as well as targets; (2) nonlinear wave-propagation and the development of shocks in the materials; (3) modelin...
SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method
International Nuclear Information System (INIS)
Amsden, A.A.; Ruppel, H.M.
1991-01-01
1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which
Influence of Diesel Nozzle Geometry on Cavitation Using Eulerian Multi-Fluid Method
Institute of Scientific and Technical Information of China (English)
张军; 杜青; 杨延相
2010-01-01
Dependent on automatically generated unstructured grids, a comprehensive computational fluid dynamics(CFD)numerical simulation is performed to analyze the influence of nozzle geometry on the internal flow characteristics of a multi-hole diesel injector with the multi-phase flow model based on Eulerian multi-fluid method.The diesel components in nozzle are considered as two continuous phases, diesel liquid and diesel vapor respectively.Considering that both of them are fully coupled and interpenetrated, sepa...
Tsang, Yue-Kin; Vallis, Geoffrey K.
2018-01-01
In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation---in which condensation occurs---that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will ...
Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence
Schmitt , François G
2005-01-01
Intermittency is a basic feature of fully developed turbulence, for both velocity and passive scalars. Intermittency is classically characterized by Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework to characterize the temporal intermittency of the velocity and passive scalar concentration of a an element of fluid advected by a turbulent intermittent field. Here we focus on Lagrangian passive scalar scaling exponents, and discuss their p...
Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems
International Nuclear Information System (INIS)
Donea, J.; Fasoli-Stella, P.; Giuliani, S.
1977-01-01
The basic finite element equations for transient compressible fluid flow are presented in a form that allows the elements to be moved with the fluid in normal Lagrangian fashion, to be held fixed in a Eulerian manner, or to be moved in some arbitrarily specified way. The co-existence of Lagrangian and Eulerian regions within the finite element mesh will permit to handle greater distortions in the fluid motion than would be allowed by a purely Lagrangian method, with more resolution than is afforded by a purely Eulerian method. To achieve a mixed formulation, the conservation statements of mass, momentum and energy are expressed in integral form over a reference volume whose surface may be moving with an arbitrarily prescribed velocity. Direct use can be made of the integral forms of the mass and energy equations to adjust the element density and specific internal energy. The Galerkin process is employed to formulate a variational statement associated with the momentum equation. The difficulties associated with the presence of convective terms in the conservation equations are handled by expressing transports of mass, momentum and energy terms of intermediate velocities derived at each cycle from the previous cycle velocities and accelerations. The hydrodynamic elements presented are triangles, quadrilaterals with constant pressure and density. The finite element equations associated with these elements are described in the necessary detail. Numerical results are presented based on purely Lagrangian, purely Eulerian and mixed formulations. Simple problems with analytic solution are solved first to show the validity and accuracy of the proposed mixed finite element formulation. Then, practical problems are illustrated in the field of fast reactor safety analysis
Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie
2016-01-01
The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.
Learning Domain-Specific Heuristics for Answer Set Solvers
Balduccini, Marcello
2010-01-01
In spite of the recent improvements in the performance of Answer Set Programming (ASP) solvers, when the search space is sufficiently large, it is still possible for the search algorithm to mistakenly focus on areas of the search space that contain no solutions or very few. When that happens, performance degrades substantially, even to the point that the solver may need to be terminated before returning an answer. This prospect is a concern when one is considering using such a solver in an in...
A non-conforming 3D spherical harmonic transport solver
Energy Technology Data Exchange (ETDEWEB)
Van Criekingen, S. [Commissariat a l' Energie Atomique CEA-Saclay, DEN/DM2S/SERMA/LENR Bat 470, 91191 Gif-sur-Yvette, Cedex (France)
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
A non-conforming 3D spherical harmonic transport solver
International Nuclear Information System (INIS)
Van Criekingen, S.
2006-01-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
Unit physics performance of a mix model in Eulerian fluid computations
Energy Technology Data Exchange (ETDEWEB)
Vold, Erik [Los Alamos National Laboratory; Douglass, Rod [Los Alamos National Laboratory
2011-01-25
In this report, we evaluate the performance of a K-L drag-buoyancy mix model, described in a reference study by Dimonte-Tipton [1] hereafter denoted as [D-T]. The model was implemented in an Eulerian multi-material AMR code, and the results are discussed here for a series of unit physics tests. The tests were chosen to calibrate the model coefficients against empirical data, principally from RT (Rayleigh-Taylor) and RM (Richtmyer-Meshkov) experiments, and the present results are compared to experiments and to results reported in [D-T]. Results show the Eulerian implementation of the mix model agrees well with expectations for test problems in which there is no convective flow of the mass averaged fluid, i.e., in RT mix or in the decay of homogeneous isotropic turbulence (HIT). In RM shock-driven mix, the mix layer moves through the Eulerian computational grid, and there are differences with the previous results computed in a Lagrange frame [D-T]. The differences are attributed to the mass averaged fluid motion and examined in detail. Shock and re-shock mix are not well matched simultaneously. Results are also presented and discussed regarding model sensitivity to coefficient values and to initial conditions (IC), grid convergence, and the generation of atomically mixed volume fractions.
Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments
Chitta, Subhashini; Steinhoff, John
2015-11-01
In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.
Flow Modeling in Pelton Turbines by an Accurate Eulerian and a Fast Lagrangian Evaluation Method
Directory of Open Access Journals (Sweden)
A. Panagiotopoulos
2015-01-01
Full Text Available The recent development of CFD has allowed the flow modeling in impulse hydro turbines that includes complex phenomena like free surface flow, multifluid interaction, and unsteady, time dependent flow. Some commercial and open-source CFD codes, which implement Eulerian methods, have been validated against experimental results showing satisfactory accuracy. Nevertheless, further improvement of accuracy is still a challenge, while the computational cost is very high and unaffordable for multiparametric design optimization of the turbine’s runner. In the present work a CFD Eulerian approach is applied at first, in order to simulate the flow in the runner of a Pelton turbine model installed at the laboratory. Then, a particulate method, the Fast Lagrangian Simulation (FLS, is used for the same case, which is much faster and hence potentially suitable for numerical design optimization, providing that it can achieve adequate accuracy. The results of both methods for various turbine operation conditions, as also for modified runner and bucket designs, are presented and discussed in the paper. In all examined cases the FLS method shows very good accuracy in predicting the hydraulic efficiency of the runner, although the computed flow evolution and the torque curve exhibit some systematic differences from the Eulerian results.
Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates
Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil
1984-01-01
The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.
International Nuclear Information System (INIS)
Thompson, S.L.; Herrmann, W.
1977-01-01
Calculations, using the two-dimensional Eulerian finite-difference code CSQ, were performed for the problem of a small spherical high-explosive charge detonated in a closed heavy-walled cylindrical container partially filled with water. Data from corresponding experiments, specifically performed to validate codes used for hypothetical core disruptive accidents of liquid metal fast breeder reactors, are available in the literature. The calculations were performed specifically to test whether Eulerian methods could handle this type of problem, to determine whether water cavitation, which plays a large role in the loadings on the roof of the containment vessel, could be described adequately by an equilibrium liquid-vapor mixed phase model, and to investigate the trade-off between accuracy and cost of the calculations by using different sizes of computational meshes. Comparison of the experimental and computational data shows that the Eulerian method can handle the problem with ease, giving good predictions of wall and floor loadings. While roof loadings are qualitatively correct, peak impulse appears to be affected by numerical resolution and is underestimated somewhat
Gupta, Puneet; Bhowmick, Brojeshwar; Pal, Arpan
2017-07-01
Camera-equipped devices are ubiquitous and proliferating in the day-to-day life. Accurate heart rate (HR) estimation from the face videos acquired from the low cost cameras in a non-contact manner, can be used in many real-world scenarios and hence, require rigorous exploration. This paper has presented an accurate and near real-time HR estimation system using these face videos. It is based on the phenomenon that the color and motion variations in the face video are closely related to the heart beat. The variations also contain the noise due to facial expressions, respiration, eye blinking and environmental factors which are handled by the proposed system. Neither Eulerian nor Lagrangian temporal signals can provide accurate HR in all the cases. The cases where Eulerian temporal signals perform spuriously are determined using a novel poorness measure and then both the Eulerian and Lagrangian temporal signals are employed for better HR estimation. Such a fusion is referred as serial fusion. Experimental results reveal that the error introduced in the proposed algorithm is 1.8±3.6 which is significantly lower than the existing well known systems.
A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.
Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu
2017-10-01
The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel; Pardo, D.; Dalcin, Lisandro; Calo, Victor M.
2018-01-01
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Resolving Neighbourhood Relations in a Parallel Fluid Dynamic Solver
Frisch, Jerome; Mundani, Ralf-Peter; Rank, Ernst
2012-01-01
solver with a special aspect on the hierarchical data structure, unique cell and grid identification, and the neighbourhood relations in-between grids on different processes. A special server concept keeps track of every grid over all processes while
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo; Sun, Shuyu; Salama, Amgad
2015-01-01
and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Energy Technology Data Exchange (ETDEWEB)
Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
A Python interface to Diffpack-based classes and solvers
Munthe-Kaas, Heidi Vikki
2013-01-01
Python is a programming language that has gained a lot of popularity during the last 15 years, and as a very easy-to-learn and flexible scripting language it is very well suited for computa- tional science, both in mathematics and in physics. Diffpack is a PDE library written in C++, made for easier implementation of both smaller PDE solvers and for larger libraries of simu- lators. It contains large class hierarchies for different solvers, grids, arrays, parallel computing and almost everyth...
International Nuclear Information System (INIS)
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
Comparing direct and iterative equation solvers in a large structural analysis software system
Poole, E. L.
1991-01-01
Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.
A robust multilevel simultaneous eigenvalue solver
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
Pang, Kar Mun; Jangi, Mehdi; Bai, X.-S.; Schramm, Jesper; Walther, Jens Honore
2016-01-01
The use of transported Probability Density Function(PDF) methods allows a single model to compute the autoignition, premixed mode and diffusion flame of diesel combustion under engine-like conditions [1,2]. The Lagrangian particle based transported PDF models have been validated across a wide range of conditions [2,3]. Alternatively, the transported PDF model can also be formulated in the Eulerian framework[4]. The Eulerian PDF is commonly known as the Eulerian Stochastic Fields (ESF) model. ...
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel
2018-02-12
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost required to solve the corresponding system of equations using a direct LU factorization solver dramatically reduces (up to a factor of 55) Garcia et al. (2017). At the same time, rIGA enriches the IGA spaces, thus improving the best approximation error. In this work, we extend the complexity analysis of rIGA to the case of iterative solvers. We build an iterative solver as follows: we first construct the Schur complements using a direct solver over small subdomains (macro-elements). We then assemble those Schur complements into a global skeleton system. Subsequently, we solve this system iteratively using Conjugate Gradients (CG) with an incomplete LU (ILU) preconditioner. For a 2D Poisson model problem with a structured mesh and a uniform polynomial degree of approximation, rIGA achieves moderate savings with respect to IGA in terms of the number of Floating Point Operations (FLOPs) and computational time (in seconds) required to solve the resulting system of linear equations. For instance, for a mesh with four million elements and polynomial degree p=3, the iterative solver is approximately 2.6 times faster (in time) when applied to the rIGA system than to the IGA one. These savings occur because the skeleton rIGA system contains fewer non-zero entries than the IGA one. The opposite situation occurs for 3D problems, and as a result, 3D rIGA discretizations provide no gains with respect to their IGA counterparts when considering iterative solvers.
International Nuclear Information System (INIS)
Bott, E.; Frepoli, C.; Monti, R.; Notini, V.; Carcassi, M.; Fineschi, F.; Heitsch, M.
1999-01-01
Large amounts of hydrogen can be generated in the containment of a nuclear power plant following a postulated accident with significant fuel damage. Different strategies have been proposed and implemented to prevent violent hydrogen combustion. An attractive one aims to eliminate hydrogen without burning processes; it is based on the use of catalytic hydrogen recombiners. This paper describes a simulation methodology which is being developed by Ansaldo, to support the application of the above strategy, in the frame of two projects sponsored by the Commission of the European Communities within the IV Framework Program on Reactor Safety. Involved organizations also include the DCMN of Pisa University (Italy), Battelle Institute and GRS (Germany), Politechnical University of Madrid (Spain). The aims to make available a simulation approach, suitable for use for containment design at industrial level (i.e. with reasonable computer running time) and capable to correctly capture the relevant phenomenologies (e.g. multiflow convective flow patterns, hydrogen, air and steam distribution in the containment atmosphere as determined by containment structures and geometries as well as by heat and mass sources and sinks). Eulerian algorithms provide the capability of three dimensional modelling with a fairly accurate prediction, however lower than CFD codes with a full Navier Stokes formulation. Open linking of an Eulerian code as GOTHIC to a full Navier Stokes CFD code as CFX 4.1 allows to dynamically tune the solving strategies of the Eulerian code itself. The effort in progress is an application of this innovative methodology to detailed hydrogen recombination simulation and a validation of the approach itself by reproducing experimental data. (author)
Analysis of primary containment response using an arbitrary Langrangian-Eulerian method
Energy Technology Data Exchange (ETDEWEB)
Chungyi, Wang
1988-02-01
This paper describes an advanced arbitrary Lagrangian-Eulerian method and its associated computer program, ALICE-II, for calculating the response of liquid metal reactor containment to core energetics. It is a versatile numerical algorithm with more flexibility and efficiency than other methods used to treat reactor containment with complex internals such as internal thin shells, upper internal structures, perforated plates, core-support diagrid, shield baffles, and deflector plates. The algorithm uses a two-dimensional, hybrid Lagrangian-Eulerian finite-difference technique to calculate the hydrodynamics and fluid-structure interactions, together with a purely Eulerian finite-difference approach to analyze the free-surface and material interface motions. It has significant advantages in treating complex phenomena such as flow through perforated structures, large material distortions, multi-dimensional sliding interfaces, flow around corners, highly contorted fluid boundaries, outflow boundary conditions, and coolant spillage. Numerical calculations for the hydrodynamic solutions are separated into three phases. The first phase consists of an explicit Lagrangian calculation. The second phase, which is options, contains an implicit iteration. The third phase, which is also optional, rezones the mesh vertices to prescribed positions. The structural response is computed by a library of elastic-plastic elements formulated in corotational coordinates in conjunction with an explicit time-integration scheme. Interaction between fluid and structure is accounted for by rigorously enforcing the interface boundary conditions. Many sample problems are given to illustrate the code effectiveness. Results demonstrate that these complex fluid-structure interaction problems can be analyzed with the ALICE-II code in a relatively natural and straightforward manner.
Grid studies for the simulation of resolved structures in an Eulerian two-fluid framework
Energy Technology Data Exchange (ETDEWEB)
Gauss, Friederike, E-mail: f.gauss@hzdr.de; Lucas, Dirk; Krepper, Eckhard
2016-08-15
Highlights: • Elaborated Eulerian two-fluid methods may predict multiphase flow with large differences in interfacial length scales. • A study on the grid requirements of resolved structures in such two-fluid methods is presented. • The two-fluid results are only little dependent on the grid size. • The results justify the resolved treatment of flow structures covering only few grid cells. • A grid-dependent limit between resolved an modeled structures may be established. - Abstract: The influence of the grid size on the rise velocity of a single bubble simulated with an Eulerian two-fluid method is investigated. This study is part of the development of an elaborated Eulerian two-fluid framework, which is able to predict complex flow phenomena as arising in nuclear reactor safety research issues. Such flow phenomena cover a wide range of interfacial length scales. An important aspect of the simulation method is the distinction into small flow structures, which are modeled, and large structures, which are resolved. To investigate the requirements on the numerical grid for the simulation of such resolved structures the velocity of rising gas bubbles is a good example since theoretical values are available. It is well known that the rise velocity of resolved bubbles is clearly underestimated in a one-fluid approach if they span over only few numerical cells. In the present paper it is shown that in the case of the two-fluid model the bubble rise velocity depends only slightly on the grid size. This is explained with the use of models for the gas–liquid interfacial forces. Good approximations of the rise velocity and the bubble shape are obtained with only few grid points per bubble diameter. This result justifies the resolved treatment of flow structures, which cover only few grid cells. Thus, a limit for the distinction into resolved and modeled structures in the two-fluid context may be established.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
International Nuclear Information System (INIS)
Pyun, J.J.
1981-01-01
As part of an effort to incorporate the variable Eulerian mesh into the second-order PIC computational method, a truncation error analysis was performed to calculate the second-order error terms for the variable Eulerian mesh system. The results that the maximum mesh size increment/decrement is limited to be α(Δr/sub i/) 2 where Δr/sub i/ is a non-dimensional mesh size of the ith cell, and α is a constant of order one. The numerical solutions of Burgers' equation by the second-order PIC method in the variable Eulerian mesh system wer compared with its exact solution. It was found that the second-order accuracy in the PIC method was maintained under the above condition. Additional problems were analyzed using the second-order PIC methods in both variable and uniform Eulerian mesh systems. The results indicate that the second-order PIC method in the variable Eulerian mesh system can provide substantial computational time saving with no loss in accuracy
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
Energy Technology Data Exchange (ETDEWEB)
Noble, Charles R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Anderson, Andrew T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Barton, Nathan R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bramwell, Jamie A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Capps, Arlie [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chang, Michael H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chou, Jin J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dawson, David M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Diana, Emily R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dunn, Timothy A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Faux, Douglas R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Fisher, Aaron C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Heinz, Ines [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kanarska, Yuliya [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Khairallah, Saad A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Liu, Benjamin T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Margraf, Jon D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nichols, Albert L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Puso, Michael A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Reus, James F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Robinson, Peter B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Shestakov, Alek I. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Solberg, Jerome M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Taller, Daniel [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Tsuji, Paul H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); White, Christopher A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); White, Jeremy L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-23
ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.
International Nuclear Information System (INIS)
Boman, R.; Papeleux, L.; Ponthot, J. P.
2007-01-01
In this paper, the Arbitrary Lagrangian Eulerian formalism is used to compute the steady state of a 2D metal cutting operation and a 3D U-shaped cold roll forming process. Compared to the Lagrangian case, this method allows the use of a refined mesh near the tools, leading to an accurate representation of the chip formation (metal cutting) and the bending of the sheet (roll forming) with a limited computational time. The main problem of this kind of simulation is the rezoning of the nodes on the free surfaces of the sheet. A modified iterative isoparametric smoother is used to manage this geometrically complex and CPU expensive task
General Eulerian formulation of the comoving-frame equation of radiative transfer
International Nuclear Information System (INIS)
Riffert, H.
1986-01-01
For a wide range of problems in radiation hydrodynamics the motion of the matter is best described in an Eulerian coordinate system, and here a comoving-frame equation of radiation transfer in such fixed coordinates is derived, using the radiation quantities measured in the comoving frame. The choice of coordinates is arbitrary, and the equation is given explicitly for an arbitrary diagonal metric, correct to all orders in v/c. All comoving frame equations derived earlier are included as special cases. An example is given for the case of a spherically symmetric flow in a Schwarzschild metric. 9 references
A Coupled VOF-Eulerian Multiphase CFD Model to Simulate Breaking Wave Impacts on Offshore Structures
DEFF Research Database (Denmark)
Tomaselli, Pietro; Christensen, Erik Damgaard
2016-01-01
Breaking wave-induced loads on offshore structures can be extremely severe. The air entrainment mechanism during the breaking process plays a not well-known role in the exerted forces. This paper present a CFD solver, developed in the Open-FOAM environment, capable of simulating the wave breaking...
Parallel linear solvers for simulations of reactor thermal hydraulics
International Nuclear Information System (INIS)
Yan, Y.; Antal, S.P.; Edge, B.; Keyes, D.E.; Shaver, D.; Bolotnov, I.A.; Podowski, M.Z.
2011-01-01
The state-of-the-art multiphase fluid dynamics code, NPHASE-CMFD, performs multiphase flow simulations in complex domains using implicit nonlinear treatment of the governing equations and in parallel, which is a very challenging environment for the linear solver. The present work illustrates how the Portable, Extensible Toolkit for Scientific Computation (PETSc) and scalable Algebraic Multigrid (AMG) preconditioner from Hypre can be utilized to construct robust and scalable linear solvers for the Newton correction equation obtained from the discretized system of governing conservation equations in NPHASE-CMFD. The overall long-tem objective of this work is to extend the NPHASE-CMFD code into a fully-scalable solver of multiphase flow and heat transfer problems, applicable to both steady-state and stiff time-dependent phenomena in complete fuel assemblies of nuclear reactors and, eventually, the entire reactor core (such as the Virtual Reactor concept envisioned by CASL). This campaign appropriately begins with the linear algebraic equation solver, which is traditionally a bottleneck to scalability in PDE-based codes. The computational complexity of the solver is usually superlinear in problem size, whereas the rest of the code, the “physics” portion, usually has its complexity linear in the problem size. (author)
BCYCLIC: A parallel block tridiagonal matrix cyclic solver
Hirshman, S. P.; Perumalla, K. S.; Lynch, V. E.; Sanchez, R.
2010-09-01
A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.
MINOS: A simplified Pn solver for core calculation
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.
2007-01-01
This paper describes a new generation of the neutronic core solver MINOS resulting from developments done in the DESCARTES project. For performance reasons, the numerical method of the existing MINOS solver in the SAPHYR system has been reused in the new system. It is based on the mixed-dual finite element approximation of the simplified transport equation. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals, allowing us to treat geometries where fuel pins are exactly represented. For Cartesian geometries, the solver takes into account assembly discontinuity coefficients in the simplified P n context. The solver has been rewritten in C + + programming language using an object-oriented design. Its general architecture was reconsidered in order to improve its capability of evolution and its maintainability. Moreover, the performance of the previous version has been improved mainly regarding the matrix construction time; this result improves significantly the performance of the solver in the context of industrial application requiring thermal-hydraulic feedback and depletion calculations. (authors)
EVA – a non-linear Eulerian approach for assessment of health-cost externalities of air pollution
DEFF Research Database (Denmark)
Andersen, Mikael Skou; Frohn, Lise Marie; Nielsen, Jytte Seested
2006-01-01
of the emissions. External cost estimates based on the Eulerian approach, on the other hand, are in mutual conformity. The existence of non-linear dynamics and possible thresholds, both in the atmospheric modelling and in the dose-response functions for health effects, need further attention and should......Integrated models which are used to account for the external costs of air pollution have to a considerable extent ignored the non-linear dynamics of atmospheric science. In order to bridge the gap between economic analysis and environmental modelling an integrated model EVA, based on a Eulerian...... for the final external cost estimates of the Eulerian approach is explored. Uncertainties in the health costs estimates are endemic in particular for mortality, but in order to achieve a common baseline the approach recommended by the OECD has been employed for the valuation part. This approach implies the use...
A pure Eulerian method for multi-material fluid flows in dimension 1,2 and 3
International Nuclear Information System (INIS)
Braeunig, J.Ph.
2007-12-01
The method described in this report is designed to simulate multi-material fluid flows, by solving compressible Euler equations with sharp interface capturing, in dimension 2 and 3. Materials are supposed to be non-miscible and to follow different equations of state. The main purpose of this work is to design an interface reconstruction method with no diffusion at all between materials of any Eulerian quantity. One novelty of our approach is the use of a pure Eulerian finite volume scheme in an interface reconstruction method. A new concept is introduced, the 'condensate', which allows to handle mixed cells containing two or more materials and to calculate the evolution of the interface on the fixed Eulerian grid. Moreover, this method allows a free sliding of materials on each others. The accuracy of the method is evaluated on academic 1D benchmarks and its robustness is tested with severe 2D benchmarks. (author)
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
Chen, Meng-Huo
2015-09-13
In this research we are particularly interested in extending the robustness of multigrid solvers to encounter complex systems related to subsurface reservoir applications for flow problems in porous media. In many cases, the step for solving the pressure filed in subsurface flow simulation becomes a bottleneck for the performance of the simulator. For solving large sparse linear system arising from MPFA discretization, we choose multigrid methods as the linear solver. The possible difficulties and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately goal which we desire to achieve.
Integrating Problem Solvers from Analogous Markets in New Product Ideation
DEFF Research Database (Denmark)
Franke, Nikolaus; Poetz, Marion; Schreier, Martin
2014-01-01
Who provides better inputs to new product ideation tasks, problem solvers with expertise in the area for which new products are to be developed or problem solvers from “analogous” markets that are distant but share an analogous problem or need? Conventional wisdom appears to suggest that target...... market expertise is indispensable, which is why most managers searching for new ideas tend to stay within their own market context even when they do search outside their firms' boundaries. However, in a unique symmetric experiment that isolates the effect of market origin, we find evidence...... for the opposite: Although solutions provided by problem solvers from analogous markets show lower potential for immediate use, they demonstrate substantially higher levels of novelty. Also, compared to established novelty drivers, this effect appears highly relevant from a managerial perspective: we find...
An efficient spectral crystal plasticity solver for GPU architectures
Malahe, Michael
2018-03-01
We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.
Equilibrium-eulerian les model for turbulent poly-dispersed particle-laden flow
Icardi, Matteo
2013-04-01
An efficient Eulerian method for poly-dispersed particles in turbulent flows is implemented, verified and validated for a channel flow. The approach couples a mixture model with a quadrature-based moment method for the particle size distribution in a LES framework, augmented by an approximate deconvolution method to reconstructs the unfiltered velocity. The particle velocity conditioned on particle size is calculated with an equilibrium model, valid for low Stokes numbers. A population balance equation is solved with the direct quadrature method of moments, that efficiently represents the continuous particle size distribution. In this first study particulate processes are not considered and the capability of the model to properly describe particle transport is investigated for a turbulent channel flow. First, single-phase LES are validated through comparison with DNS. Then predictions for the two-phase system, with particles characterised by Stokes numbers ranging from 0.2 to 5, are compared with Lagrangian DNS in terms of particle velocity and accumulation at the walls. Since this phenomenon (turbophoresis) is driven by turbulent fluctuations and depends strongly on the particle Stokes number, the approximation of the particle size distribution, the choice of the sub-grid scale model and the use of an approximate deconvolution method are important to obtain good results. Our method can be considered as a fast and efficient alternative to classical Lagrangian methods or Eulerian multi-fluid models in which poly-dispersity is usually neglected.
Comparison of HF radar measurements with Eulerian and Lagrangian surface currents
Röhrs, Johannes; Sperrevik, Ann Kristin; Christensen, Kai Håkon; Broström, Göran; Breivik, Øyvind
2015-05-01
High-frequency (HF) radar-derived ocean currents are compared with in situ measurements to conclude if the radar observations include effects of surface waves that are of second order in the wave amplitude. Eulerian current measurements from a high-resolution acoustic Doppler current profiler and Lagrangian measurements from surface drifters are used as references. Directional wave spectra are obtained from a combination of pressure sensor data and a wave model. Our analysis shows that the wave-induced Stokes drift is not included in the HF radar-derived currents, that is, HF radars measure the Eulerian current. A disputed nonlinear correction to the phase velocity of surface gravity waves, which may affect HF radar signals, has a magnitude of about half the Stokes drift at the surface. In our case, this contribution by nonlinear dispersion would be smaller than the accuracy of the HF radar currents, hence no conclusion can be made. Finally, the analysis confirms that the HF radar data represent an exponentially weighted vertical average where the decay scale is proportional to the wavelength of the transmitted signal.
2-D Eulerian hydrodynamics with fluid interfaces, self-gravity and rotation
International Nuclear Information System (INIS)
Norman, M.L.; Winkler, K.H.A.
1982-01-01
The purpose of this paper is to describe in detail the numerical approach we have developed over the past five years for solving 2-dimensional gas-dynamical problems in astrophysics involving inviscid compressible flow, self-gravitation, rotation, and fluid instabilities of the Rayleigh-Taylor and Kelvin-Helmholtz types. The computer code to be described has been applied most recently to modeling jets in radio galaxies (Norman et al. 1981, 1982) and is an outgrowth of a code developed for studying rotating protostellar collapse (Norman, Wilson and Barton 1980; Norman 1980). This basic methodology draws heavily on the techniques and experience of James R. Wilson and James M. LeBlanc of the Lawrence Livermore National Laboratory, and thus the code is designed to be a general purpose 2-D Eulerian hydrocode, and is characterized by a high degree of simplicity, robustness, modularity and speed. Particular emphases of this article are: (1) the recent improvements to the code's accuracy through the use of vanLeer's (1977) monotonic advection algorithm, (2) a discussion of the importance of what we term consistent advection, and (3) a description of a numerical techique for modeling dynamic fluid interfaces in multidimensional Eulerian calculations developed by LeBlanc. 23 refs., 14 figs
Comparisons of 'Identical' Simulations by the Eulerian Gyrokinetic Codes GS2 and GYRO
Bravenec, R. V.; Ross, D. W.; Candy, J.; Dorland, W.; McKee, G. R.
2003-10-01
A major goal of the fusion program is to be able to predict tokamak transport from first-principles theory. To this end, the Eulerian gyrokinetic code GS2 was developed years ago and continues to be improved [1]. Recently, the Eulerian code GYRO was developed [2]. These codes are not subject to the statistical noise inherent to particle-in-cell (PIC) codes, and have been very successful in treating electromagnetic fluctuations. GS2 is fully spectral in the radial coordinate while GYRO uses finite-differences and ``banded" spectral schemes. To gain confidence in nonlinear simulations of experiment with these codes, ``apples-to-apples" comparisons (identical profile inputs, flux-tube geometry, two species, etc.) are first performed. We report on a series of linear and nonlinear comparisons (with overall agreement) including kinetic electrons, collisions, and shaped flux surfaces. We also compare nonlinear simulations of a DIII-D discharge to measurements of not only the fluxes but also the turbulence parameters. [1] F. Jenko, et al., Phys. Plasmas 7, 1904 (2000) and refs. therein. [2] J. Candy, J. Comput. Phys. 186, 545 (2003).
Equilibrium-eulerian les model for turbulent poly-dispersed particle-laden flow
Icardi, Matteo; Marchisio, Daniele Luca; Chidambaram, Narayanan; Fox, Rodney O.
2013-01-01
An efficient Eulerian method for poly-dispersed particles in turbulent flows is implemented, verified and validated for a channel flow. The approach couples a mixture model with a quadrature-based moment method for the particle size distribution in a LES framework, augmented by an approximate deconvolution method to reconstructs the unfiltered velocity. The particle velocity conditioned on particle size is calculated with an equilibrium model, valid for low Stokes numbers. A population balance equation is solved with the direct quadrature method of moments, that efficiently represents the continuous particle size distribution. In this first study particulate processes are not considered and the capability of the model to properly describe particle transport is investigated for a turbulent channel flow. First, single-phase LES are validated through comparison with DNS. Then predictions for the two-phase system, with particles characterised by Stokes numbers ranging from 0.2 to 5, are compared with Lagrangian DNS in terms of particle velocity and accumulation at the walls. Since this phenomenon (turbophoresis) is driven by turbulent fluctuations and depends strongly on the particle Stokes number, the approximation of the particle size distribution, the choice of the sub-grid scale model and the use of an approximate deconvolution method are important to obtain good results. Our method can be considered as a fast and efficient alternative to classical Lagrangian methods or Eulerian multi-fluid models in which poly-dispersity is usually neglected.
Equilibrium Eulerian approach for predicting the thermal field of a dispersion of small particles
Energy Technology Data Exchange (ETDEWEB)
Ferry, J. [University of Illinois, Urbana-Champaign, IL (United States). Center for Simulation of Advanced Rockets; Balachandar, S. [University of Illinois, Urbana-Champaign, IL (United States). Dept. of Theoretical and Applied Mechanics
2005-02-01
The equilibrium Eulerian method [J. Ferry, S. Balachandar, A fast Eulerian method for disperse two-phase flow, Int. J. Multiphase Flow 27 (7) (2001) 1199-1226] provides an accurate approximation to the velocity field of sufficiently small dispersed particles in a turbulent fluid. In particular, it captures the important physics of particle response to turbulent flow, such as preferential concentration and turbophoresis. It is therefore employed as an efficient alternative to solving a PDE to determine the particle velocity field. Here we explore two possible extensions of this method to determine the particle temperature field accurately and efficiently, as functions of the underlying fluid velocity and temperature fields. Both extensions are theoretically shown to be highly accurate for asymptotically small particles. Their behavior for finite-size particles is assessed in a DNS of turbulent channel flow (Re{sub {tau}} = 150) with a passive temperature field (Pr = 1). Here it is found that although the order of accuracy of the two extensions is the same, the constant factor by which one is superior to the other can be quite large, so the less accurate extension is appropriate only in the case of a very small mechanical-to-thermal response time ratio. (Author)
Blender, R.
2009-04-01
An approach for the reconstruction of atmospheric flow is presented which uses space- and time-dependent fields of density ?, potential vorticity Q and potential temperature Î& cedil;[J. Phys. A, 38, 6419 (2005)]. The method is based on the fundamental equations without approximation. The basic idea is to consider the time-dependent continuity equation as a condition for zero divergence of momentum in four dimensions (time and space, with unit velocity in time). This continuity equation is solved by an ansatz for the four-dimensional momentum using three conserved stream functions, the potential vorticity, potential temperature and a third field, denoted as ?-potential. In zonal flows, the ?-potential identifies the initial longitude of particles, whereas potential vorticity and potential temperature identify mainly meridional and vertical positions. Since the Lagrangian tracers Q, Î&,cedil; and ? determine the Eulerian velocity field, the reconstruction combines the Eulerian and the Lagrangian view of hydrodynamics. In stationary flows, the ?-potential is related to the Bernoulli function. The approach requires that the gradients of the potential vorticity and potential temperature do not vanish when the velocity remains finite. This behavior indicates a possible interrelation with stability conditions. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flows.
Uncertainty quantification in Eulerian-Lagrangian models for particle-laden flows
Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs
2017-11-01
A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based Eulerian-Lagrangian model, which traces individual particles in their Lagrangian frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear Eulerian-Lagrangian systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.
On the Eulerian-Lagrangian Transform in the Statistical Theory of Turbulence
DEFF Research Database (Denmark)
Wandel, C. F:; Kofoed-Hansen, O.
1962-01-01
"Fundamental Problems in Turbulence" Conference Paper (see Abstr. 1962A024007). Two important types of probing of a turbulent velocity field droarr/dtoarr = voarr (voarr constant) and the Lagrangian probing defined by droarr/dtoarr = roarr (roarr t). Explicit expressions are derived for the trans......"Fundamental Problems in Turbulence" Conference Paper (see Abstr. 1962A024007). Two important types of probing of a turbulent velocity field droarr/dtoarr = voarr (voarr constant) and the Lagrangian probing defined by droarr/dtoarr = roarr (roarr t). Explicit expressions are derived...... for the transformation of autocorrelations and power spectra obtained by Eulerian and Lagrangian probing in the case of fully developed isotropic and homogeneous turbulence. The derivations are based on a statistical representation of the turbulent velocity field using the results of the equilibrium theory of turbulence....... The Taylor (1921) hypothesis is verified in the limit of high probing velocities. The Hay-Pasquill (1960) conjecture relating the Lagrangian and Eulerian power spectra results as an approximation to the transformation equations. Application of the results to the theory of turbulent diffusion is indicated....
International Nuclear Information System (INIS)
Bouttier, J; Francesco, P Di; Guitter, E
2007-01-01
We introduce Eulerian maps with blocked edges as a general way to implement statistical matter models on random maps by a modification of intrinsic distances. We show how to code these dressed maps by means of mobiles, i.e. decorated trees with labelled vertices, leading to a closed system of recursion relations for their generating functions. We discuss particular solvable cases in detail, as well as various applications of our method to several statistical systems such as spanning trees on quadrangulations, mutually excluding particles on Eulerian triangulations or the Ising model on quadrangulations
On Cafesat: A Modern SAT Solver for Scala
Blanc, Régis William
2013-01-01
We present CafeSat, a SAT solver written in the Scala programming language. CafeSat is a modern solver based on DPLL and featuring many state-of-the-art techniques and heuristics. It uses two-watched literals for Boolean constraint propagation, conflict-driven learning along with clause deletion, a restarting strategy, and the VSIDS heuristics for choosing the branching literal. CafeSat is both sound and complete. In order to achieve reasonnable performances, low level and hand-tuned data ...
MINARET: Towards a time-dependent neutron transport parallel solver
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.; Maday, Y.; Mula, O.
2013-01-01
We present the newly developed time-dependent 3D multigroup discrete ordinates neutron transport solver that has recently been implemented in the MINARET code. The solver is the support for a study about computing acceleration techniques that involve parallel architectures. In this work, we will focus on the parallelization of two of the variables involved in our equation: the angular directions and the time. This last variable has been parallelized by a (time) domain decomposition method called the para-real in time algorithm. (authors)
LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators
International Nuclear Information System (INIS)
Gonzalez, Juan; Nunez, Rafael C
2009-01-01
We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.
Fast Laplace solver approach to pore-scale permeability
Arns, C. H.; Adler, P. M.
2018-02-01
We introduce a powerful and easily implemented method to calculate the permeability of porous media at the pore scale using an approximation based on the Poiseulle equation to calculate permeability to fluid flow with a Laplace solver. The method consists of calculating the Euclidean distance map of the fluid phase to assign local conductivities and lends itself naturally to the treatment of multiscale problems. We compare with analytical solutions as well as experimental measurements and lattice Boltzmann calculations of permeability for Fontainebleau sandstone. The solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.
Energy Technology Data Exchange (ETDEWEB)
Zwick, D; Balachandar, S [Department of Mechanical and Aerospace Engineering, University of Florida, FL, United States of America (United States); Sakhaee, E; Entezari, A, E-mail: dpzwick@ufl.edu [Department of Computer and Information Science and Engineering, University of Florida, FL, United States of America (United States)
2017-10-15
Multiphase flow simulation serves a vital purpose in applications as diverse as engineering design, natural disaster prediction, and even study of astrophysical phenomena. In these scenarios, it can be very difficult, expensive, or even impossible to fully represent the physical system under consideration. Even still, many such real-world applications can be modeled as a two-phase flow containing both continuous and dispersed phases. Consequentially, the continuous phase is thought of as a fluid and the dispersed phase as particles. The continuous phase is typically treated in the Eulerian frame of reference and represented on a fixed grid, while the dispersed phase is treated in the Lagrangian frame and represented by a sample distribution of Lagrangian particles that approximate a cloud. Coupling between the phases requires interpolation of the continuous phase properties at the locations of the Lagrangian particles. This interpolation step is straightforward and can be performed at higher order accuracy. The reverse process of projecting the Lagrangian particle properties from the sample points to the Eulerian grid is complicated by the time-dependent non-uniform distribution of the Lagrangian particles. In this paper we numerically examine three reconstruction, or projection, methods: (i) direct summation (DS), (ii) least-squares, and (iii) sparse approximation. We choose a continuous representation of the dispersed phase property that is systematically varied from a simple single mode periodic signal to a more complex artificially constructed turbulent signal to see how each method performs in reconstruction. In these experiments, we show that there is a link between the number of dispersed Lagrangian sample points and the number of structured grid points to accurately represent the underlying functional representation to machine accuracy. The least-squares method outperforms the other methods in most cases, while the sparse approximation method is able to
Eulerian frequency analysis of structural vibrations from high-speed video
International Nuclear Information System (INIS)
Venanzoni, Andrea; De Ryck, Laurent; Cuenca, Jacques
2016-01-01
An approach for the analysis of the frequency content of structural vibrations from high-speed video recordings is proposed. The techniques and tools proposed rely on an Eulerian approach, that is, using the time history of pixels independently to analyse structural motion, as opposed to Lagrangian approaches, where the motion of the structure is tracked in time. The starting point is an existing Eulerian motion magnification method, which consists in decomposing the video frames into a set of spatial scales through a so-called Laplacian pyramid [1]. Each scale — or level — can be amplified independently to reconstruct a magnified motion of the observed structure. The approach proposed here provides two analysis tools or pre-amplification steps. The first tool provides a representation of the global frequency content of a video per pyramid level. This may be further enhanced by applying an angular filter in the spatial frequency domain to each frame of the video before the Laplacian pyramid decomposition, which allows for the identification of the frequency content of the structural vibrations in a particular direction of space. This proposed tool complements the existing Eulerian magnification method by amplifying selectively the levels containing relevant motion information with respect to their frequency content. This magnifies the displacement while limiting the noise contribution. The second tool is a holographic representation of the frequency content of a vibrating structure, yielding a map of the predominant frequency components across the structure. In contrast to the global frequency content representation of the video, this tool provides a local analysis of the periodic gray scale intensity changes of the frame in order to identify the vibrating parts of the structure and their main frequencies. Validation cases are provided and the advantages and limits of the approaches are discussed. The first validation case consists of the frequency content
A General Symbolic PDE Solver Generator: Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available A symbolic solver generator to deal with a system of partial differential equations (PDEs in functions of an arbitrary number of variables is presented; it can also handle arbitrary domains (geometries of the independent variables. Given a system of PDEs, the solver generates a set of explicit finite-difference methods to any specified order, and a Fourier stability criterion for each method. For a method that is stable, an iteration function is generated symbolically using the PDE and its initial and boundary conditions. This iteration function is dynamically generated for every PDE problem, and its evaluation provides a solution to the PDE problem. A C++/Fortran 90 code for the iteration function is generated using the MathCode system, which results in a performance gain of the order of a thousand over Mathematica, the language that has been used to code the solver generator. Examples of stability criteria are presented that agree with known criteria; examples that demonstrate the generality of the solver and the speed enhancement of the generated C++ and Fortran 90 codes are also presented.
Numerical solver for compressible two-fluid flow
J. Naber (Jorick)
2005-01-01
textabstractThis report treats the development of a numerical solver for the simulation of flows of two non-mixing fluids described by the two-dimensional Euler equations. A level-set equation in conservative form describes the interface. After each time step the deformed level-set function is
Parallel time domain solvers for electrically large transient scattering problems
Liu, Yang
2014-09-26
Marching on in time (MOT)-based integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. MOT integral equation solvers for analyzing electromagnetic scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary to finite difference and element competitors, these solvers apply to nonlinear and multi-scale structures comprising geometrically intricate and deep sub-wavelength features residing atop electrically large platforms. Moreover, they are high-order accurate, stable in the low- and high-frequency limits, and applicable to conducting and penetrable structures represented by highly irregular meshes. This presentation reviews some recent advances in the parallel implementations of time domain integral equation solvers, specifically those that leverage multilevel plane-wave time-domain algorithm (PWTD) on modern manycore computer architectures including graphics processing units (GPUs) and distributed memory supercomputers. The GPU-based implementation achieves at least one order of magnitude speedups compared to serial implementations while the distributed parallel implementation are highly scalable to thousands of compute-nodes. A distributed parallel PWTD kernel has been adopted to solve time domain surface/volume integral equations (TDSIE/TDVIE) for analyzing transient scattering from large and complex-shaped perfectly electrically conducting (PEC)/dielectric objects involving ten million/tens of millions of spatial unknowns.
Using a satisfiability solver to identify deterministic finite state automata
Heule, M.J.H.; Verwer, S.
2009-01-01
We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach seems to be competitive with alternative techniques. Our contributions are threefold: First, we
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-01-01
extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM
Implementation and testing of a multivariate inverse radiation transport solver
International Nuclear Information System (INIS)
Mattingly, John; Mitchell, Dean J.
2012-01-01
Detection, identification, and characterization of special nuclear materials (SNM) all face the same basic challenge: to varying degrees, each must infer the presence, composition, and configuration of the SNM by analyzing a set of measured radiation signatures. Solutions to this problem implement inverse radiation transport methods. Given a set of measured radiation signatures, inverse radiation transport estimates properties of the source terms and transport media that are consistent with those signatures. This paper describes one implementation of a multivariate inverse radiation transport solver. The solver simultaneously analyzes gamma spectrometry and neutron multiplicity measurements to fit a one-dimensional radiation transport model with variable layer thicknesses using nonlinear regression. The solver's essential components are described, and its performance is illustrated by application to benchmark experiments conducted with plutonium metal. - Highlights: ► Inverse problems, specifically applied to identifying and characterizing radiation sources . ► Radiation transport. ► Analysis of gamma spectroscopy and neutron multiplicity counting measurements. ► Experimental testing of the inverse solver against measurements of plutonium.
A High Performance QDWH-SVD Solver using Hardware Accelerators
Sukkari, Dalal E.; Ltaief, Hatem; Keyes, David E.
2015-01-01
few digits of accuracy, compared to the full double precision floating point arithmetic. We further leverage the single GPU QDWH-SVD implementation by introducing the first multi-GPU SVD solver to study the scalability of the QDWH-SVD framework.
Hypersonic simulations using open-source CFD and DSMC solvers
Casseau, V.; Scanlon, T. J.; John, B.; Emerson, D. R.; Brown, R. E.
2016-11-01
Hypersonic hybrid hydrodynamic-molecular gas flow solvers are required to satisfy the two essential requirements of any high-speed reacting code, these being physical accuracy and computational efficiency. The James Weir Fluids Laboratory at the University of Strathclyde is currently developing an open-source hybrid code which will eventually reconcile the direct simulation Monte-Carlo method, making use of the OpenFOAM application called dsmcFoam, and the newly coded open-source two-temperature computational fluid dynamics solver named hy2Foam. In conjunction with employing the CVDV chemistry-vibration model in hy2Foam, novel use is made of the QK rates in a CFD solver. In this paper, further testing is performed, in particular with the CFD solver, to ensure its efficacy before considering more advanced test cases. The hy2Foam and dsmcFoam codes have shown to compare reasonably well, thus providing a useful basis for other codes to compare against.
Implementing parallel elliptic solver on a Beowulf cluster
Directory of Open Access Journals (Sweden)
Marcin Paprzycki
1999-12-01
Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.
Implementation of Generalized Adjoint Equation Solver for DeCART
International Nuclear Information System (INIS)
Han, Tae Young; Cho, Jin Young; Lee, Hyun Chul; Noh, Jae Man
2013-01-01
In this paper, the generalized adjoint solver based on the generalized perturbation theory is implemented on DeCART and the verification calculations were carried out. As the results, the adjoint flux for the general response coincides with the reference solution and it is expected that the solver could produce the parameters for the sensitivity and uncertainty analysis. Recently, MUSAD (Modules of Uncertainty and Sensitivity Analysis for DeCART) was developed for the uncertainty analysis of PMR200 core and the fundamental adjoint solver was implemented into DeCART. However, the application of the code was limited to the uncertainty to the multiplication factor, k eff , because it was based on the classical perturbation theory. For the uncertainty analysis to the general response as like the power density, it is necessary to develop the analysis module based on the generalized perturbation theory and it needs the generalized adjoint solutions from DeCART. In this paper, the generalized adjoint solver is implemented on DeCART and the calculation results are compared with the results by TSUNAMI of SCALE 6.1
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
for optimization problems, (2) an extensible infrastructure for integrating different solvers, and (3) query optimization techniques to achieve the best execution performance and/or result quality. Extensive experiments with the PostgreSQL-based implementation show that SolveDB is a versatile tool offering much...
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf; Liebmann, Manfred; Douglas, Craig C.; Plank, Gernot
2010-01-01
-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster
Analysis of transient plasmonic interactions using an MOT-PMCHWT integral equation solver
Uysal, Ismail Enes; Ulku, Huseyin Arda; Bagci, Hakan
2014-01-01
that discretize only on the interfaces. Additionally, IE solvers implicitly enforce the radiation condition and consequently do not need (approximate) absorbing boundary conditions. Despite these advantages, IE solvers, especially in time domain, have not been
Parallel Solver for H(div) Problems Using Hybridization and AMG
Energy Technology Data Exchange (ETDEWEB)
Lee, Chak S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-15
In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.
Norde, E.; van der Weide, E. T.A.; Hoeijmakers, H. W.M.
2017-01-01
The aim of this study is to show the application of an Eulerian method for ice crystal icing to a three-element airfoil in high-lift configuration. The ice crystals have been modeled as non-spherical particles which are subject to convection and/or phase change along their trajectories. On impact
International Nuclear Information System (INIS)
Carter, H.H.; Okubo, A.; Wilson, R.E.; Sanderson, B.; Pritchard, D.W.
1980-07-01
This research project addresses a fundamental problem in turbulence theory, the relation between Lagrangian and Eulerian statistics, by carrying out, analyzing, and interpreting a set of field experiments in the coastal waters off the south shore of Long Island. The study will not only provide information on the relation between the Lagrangian and Eulerian autocorrelations but also between the various experimental methods for quantitatively estimating turbulent diffusion. Two experiments, one in summer and one in winter, consisting of simultaneous measurements of dye diffusion, drogue dispersion, and Eulerian current velocities in a typical coastal locale were planned. In order to ensure a match between the Lagrangian (drogues, dye) scales of motion and the Eulerian (current meters) scales, however, a preliminary experiment, consisting of a 6 mooring current meter array and a short (approx. 3 hours) drogue experiment, was conducted during March 1980. Results of this preliminary experiment and their implications to the experimental program are discussed. The principal results were an improved design of our current meter array, and a wider variety of drogue experiments, i.e., multi-level, multi-scale, and continuous source simulation
A High Performance QDWH-SVD Solver using Hardware Accelerators
Sukkari, Dalal E.
2015-04-08
This paper describes a new high performance implementation of the QR-based Dynamically Weighted Halley Singular Value Decomposition (QDWH-SVD) solver on multicore architecture enhanced with multiple GPUs. The standard QDWH-SVD algorithm was introduced by Nakatsukasa and Higham (SIAM SISC, 2013) and combines three successive computational stages: (1) the polar decomposition calculation of the original matrix using the QDWH algorithm, (2) the symmetric eigendecomposition of the resulting polar factor to obtain the singular values and the right singular vectors and (3) the matrix-matrix multiplication to get the associated left singular vectors. A comprehensive test suite highlights the numerical robustness of the QDWH-SVD solver. Although it performs up to two times more flops when computing all singular vectors compared to the standard SVD solver algorithm, our new high performance implementation on single GPU results in up to 3.8x improvements for asymptotic matrix sizes, compared to the equivalent routines from existing state-of-the-art open-source and commercial libraries. However, when only singular values are needed, QDWH-SVD is penalized by performing up to 14 times more flops. The singular value only implementation of QDWH-SVD on single GPU can still run up to 18% faster than the best existing equivalent routines. Integrating mixed precision techniques in the solver can additionally provide up to 40% improvement at the price of losing few digits of accuracy, compared to the full double precision floating point arithmetic. We further leverage the single GPU QDWH-SVD implementation by introducing the first multi-GPU SVD solver to study the scalability of the QDWH-SVD framework.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Energy Technology Data Exchange (ETDEWEB)
Tang, Yu-Hang, E-mail: yuhang_tang@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Kudo, Shuhei, E-mail: shuhei-kudo@outlook.jp [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501 (Japan); Bian, Xin, E-mail: xin_bian@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Li, Zhen, E-mail: zhen_li@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI (United States); Collaboratory on Mathematics for Mesoscopic Modeling of Materials, Pacific Northwest National Laboratory, Richland, WA 99354 (United States)
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
Migration of vectorized iterative solvers to distributed memory architectures
Energy Technology Data Exchange (ETDEWEB)
Pommerell, C. [AT& T Bell Labs., Murray Hill, NJ (United States); Ruehl, R. [CSCS-ETH, Manno (Switzerland)
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
Transport equations, Level Set and Eulerian mechanics. Application to fluid-structure coupling
International Nuclear Information System (INIS)
Maitre, E.
2008-11-01
My works were devoted to numerical analysis of non-linear elliptic-parabolic equations, to neutron transport equation and to the simulation of fabrics draping. More recently I developed an Eulerian method based on a level set formulation of the immersed boundary method to deal with fluid-structure coupling problems arising in bio-mechanics. Some of the more efficient algorithms to solve the neutron transport equation make use of the splitting of the transport operator taking into account its characteristics. In the present work we introduced a new algorithm based on this splitting and an adaptation of minimal residual methods to infinite dimensional case. We present the case where the velocity space is of dimension 1 (slab geometry) and 2 (plane geometry) because the splitting is simpler in the former
A mechanistic Eulerian-Lagrangian model for dispersed flow film boiling
International Nuclear Information System (INIS)
Andreani, M.; Yadigaroglu, G.
1991-01-01
In this paper a new mechanistic model of heat transfer in the dispersed flow regime is presented. The usual assumptions that render most of the available models unsuitable for the analysis of the reflooding phase of the LOCA are discussed, and a two-dimensional time-independent numerical model is developed. The gas temperature field is solved in a fixed-grid (Eulerian) mesh, with the droplets behaving as mass and energy sources. The histories of a large number of computational droplets are followed in a Lagrangian frame, considering evaporation, break-up and interactions with the vapor and with the wall. comparisons of calculated wall and vapor temperatures with experimental data are shown for two reflooding tests
An Eulerian transport-dispersion model of passive effluents: the Difeul code
International Nuclear Information System (INIS)
Wendum, D.
1994-11-01
R and D has decided to develop an Eulerian diffusion model easy to adapt to meteorological data coming from different sources: for instance the ARPEGE code of Meteo-France or the MERCURE code of EDF. We demand this in order to be able to apply the code in independent cases: a posteriori studies of accidental releases from nuclear power plants ar large or medium scale, simulation of urban pollution episodes within the ''Reactive Atmospheric Flows'' research project. For simplicity reasons, the numerical formulation of our code is the same as the one used in Meteo-France's MEDIA model. The numerical tests presented in this report show the good performance of those schemes. In order to illustrate the method by a concrete example a fictitious release from Saint-Laurent has been simulated at national scale: the results of this simulation agree quite well with those of the trajectory model DIFTRA. (author). 6 figs., 4 tabs
Schroeder, Craig
2012-02-01
We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels. © 2011.
Analysis of LMFBR containment response to an HCDA using a multifield Eulerian code
International Nuclear Information System (INIS)
Chu, H.Y.; Chang, Y.W.
1977-01-01
This paper describes a computer code, MICE (Multifield Implicit Continuous-fluid Eulerian Containment Code), which is being developed at Argonne National Laboratory (ANL) for the analysis of containment response to a hypothetical core distruptive accident (HCDA). The code is applicable to multifield flow problems where material fields are allowed to have penetrations. Reactor structures are treated as axisymmetrical shells and solved by the large-displacement and small-strain theory. Two sample problems have been performed using the MICE code. The first illustrates the relative motions of the material fields after the initiation of a core disassembly accident. Core support structure and core barrel are modelled as rigid obstacles. The second demonstrates the interactions between fluid and structures. Core expansion and reactor wall deformation at several instants are shown by the computer-generated film plots. (Auth.)
An Eulerian description of the streaming process in the lattice Boltzmann equation
Lee Tae Hun
2003-01-01
This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...
DEFF Research Database (Denmark)
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver.We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matr...
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Benchmarking ICRF Full-wave Solvers for ITER
International Nuclear Information System (INIS)
Budny, R.V.; Berry, L.; Bilato, R.; Bonoli, P.; Brambilla, M.; Dumont, R.J.; Fukuyama, A.; Harvey, R.; Jaeger, E.F.; Indireshkumar, K.; Lerche, E.; McCune, D.; Phillips, C.K.; Vdovin, V.; Wright, J.
2011-01-01
Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.
Minaret, a deterministic neutron transport solver for nuclear core calculations
International Nuclear Information System (INIS)
Moller, J-Y.; Lautard, J-J.
2011-01-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
Comparison of Einstein-Boltzmann solvers for testing general relativity
Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.
2018-01-01
We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.
Minaret, a deterministic neutron transport solver for nuclear core calculations
Energy Technology Data Exchange (ETDEWEB)
Moller, J-Y.; Lautard, J-J., E-mail: jean-yves.moller@cea.fr, E-mail: jean-jacques.lautard@cea.fr [CEA - Centre de Saclay , Gif sur Yvette (France)
2011-07-01
We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared. (author)
An alternative solver for the nodal expansion method equations - 106
International Nuclear Information System (INIS)
Carvalho da Silva, F.; Carlos Marques Alvim, A.; Senra Martinez, A.
2010-01-01
An automated procedure for nuclear reactor core design is accomplished by using a quick and accurate 3D nodal code, aiming at solving the diffusion equation, which describes the spatial neutron distribution in the reactor. This paper deals with an alternative solver for nodal expansion method (NEM), with only two inner iterations (mesh sweeps) per outer iteration, thus having the potential to reduce the time required to calculate the power distribution in nuclear reactors, but with accuracy similar to the ones found in conventional NEM. The proposed solver was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of the method for practical purposes. (authors)
A Nonlinear Modal Aeroelastic Solver for FUN3D
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Energy Technology Data Exchange (ETDEWEB)
Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter
The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...
Preston, L. A.
2017-12-01
Marine hydrokinetic (MHK) devices offer a clean, renewable alternative energy source for the future. Responsible utilization of MHK devices, however, requires that the effects of acoustic noise produced by these devices on marine life and marine-related human activities be well understood. Paracousti is a 3-D full waveform acoustic modeling suite that can accurately propagate MHK noise signals in the complex bathymetry found in the near-shore to open ocean environment and considers real properties of the seabed, water column, and air-surface interface. However, this is a deterministic simulation that assumes the environment and source are exactly known. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected noise levels within the marine environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. One method is to use Monte Carlo (MC) techniques where simulation results from a large number of deterministic solutions are aggregated to provide statistical properties of the output signal. However, MC methods can be computationally prohibitive since they can require tens of thousands or more simulations to build up an accurate representation of those statistical properties. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a small fraction of the computational cost of MC. We are developing a SPDE solver for the 3-D acoustic wave propagation problem called Paracousti-UQ to help regulators and operators assess the statistical properties of environmental noise produced by MHK devices. In this presentation, we present the SPDE method and compare statistical distributions of simulated acoustic signals in simple models to MC simulations to show the accuracy and efficiency of the SPDE method. Sandia National Laboratories
Matlab Geochemistry: An open source geochemistry solver based on MRST
McNeece, C. J.; Raynaud, X.; Nilsen, H.; Hesse, M. A.
2017-12-01
The study of geological systems often requires the solution of complex geochemical relations. To address this need we present an open source geochemical solver based on the Matlab Reservoir Simulation Toolbox (MRST) developed by SINTEF. The implementation supports non-isothermal multicomponent aqueous complexation, surface complexation, ion exchange, and dissolution/precipitation reactions. The suite of tools available in MRST allows for rapid model development, in particular the incorporation of geochemical calculations into transport simulations of multiple phases, complex domain geometry and geomechanics. Different numerical schemes and additional physics can be easily incorporated into the existing tools through the object-oriented framework employed by MRST. The solver leverages the automatic differentiation tools available in MRST to solve arbitrarily complex geochemical systems with any choice of species or element concentration as input. Four mathematical approaches enable the solver to be quite robust: 1) the choice of chemical elements as the basis components makes all entries in the composition matrix positive thus preserving convexity, 2) a log variable transformation is used which transfers the nonlinearity to the convex composition matrix, 3) a priori bounds on variables are calculated from the structure of the problem, constraining Netwon's path and 4) an initial guess is calculated implicitly by sequentially adding model complexity. As a benchmark we compare the model to experimental and semi-analytic solutions of the coupled salinity-acidity transport system. Together with the reservoir simulation capabilities of MRST the solver offers a promising tool for geochemical simulations in reservoir domains for applications in a diversity of fields from enhanced oil recovery to radionuclide storage.
Boltzmann Solver with Adaptive Mesh in Velocity Space
International Nuclear Information System (INIS)
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-01-01
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
Resolving Neighbourhood Relations in a Parallel Fluid Dynamic Solver
Frisch, Jerome
2012-06-01
Computational Fluid Dynamics simulations require an enormous computational effort if a physically reasonable accuracy should be reached. Therefore, a parallel implementation is inevitable. This paper describes the basics of our implemented fluid solver with a special aspect on the hierarchical data structure, unique cell and grid identification, and the neighbourhood relations in-between grids on different processes. A special server concept keeps track of every grid over all processes while minimising data transfer between the nodes. © 2012 IEEE.
Menu-Driven Solver Of Linear-Programming Problems
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
A contribution to the great Riemann solver debate
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
Applications of 3-D Maxwell solvers to accelerator design
International Nuclear Information System (INIS)
Chou, W.
1990-01-01
This paper gives a brief discussion on various applications of 3-D Maxwell solvers to accelerator design. The work is based on our experience gained during the design of the storage ring of the 7-GeV Advanced Photon Source (APS). It shows that 3-D codes are not replaceable in many cases, and that a lot of work remains to be done in order to establish a solid base for 3-D simulations
Scalable parallel prefix solvers for discrete ordinates transport
International Nuclear Information System (INIS)
Pautz, S.; Pandya, T.; Adams, M.
2009-01-01
The well-known 'sweep' algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations has some desirable numerical properties. However, it suffers from parallel scaling issues caused by a lack of concurrency. The maximum degree of concurrency, and thus the maximum parallelism, grows more slowly than the problem size for sweeps-based solvers. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in prefix form. We implement two variants of the algorithm within the radlib/SCEPTRE transport code library at Sandia National Laboratories and show results on two different massively parallel systems. Both the 'forward' and 'symmetric' solvers behave similarly, scaling well to larger degrees of parallelism then sweeps-based solvers. We do observe some issues at the highest levels of parallelism (relative to the system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems, but the parallel scalability will depend heavily on the architecture of the communication networks of these systems. (authors)
An immersed interface vortex particle-mesh solver
Marichal, Yves; Chatelain, Philippe; Winckelmans, Gregoire
2014-11-01
An immersed interface-enabled vortex particle-mesh (VPM) solver is presented for the simulation of 2-D incompressible viscous flows, in the framework of external aerodynamics. Considering the simulation of free vortical flows, such as wakes and jets, vortex particle-mesh methods already provide a valuable alternative to standard CFD methods, thanks to the interesting numerical properties arising from its Lagrangian nature. Yet, accounting for solid bodies remains challenging, despite the extensive research efforts that have been made for several decades. The present immersed interface approach aims at improving the consistency and the accuracy of one very common technique (based on Lighthill's model) for the enforcement of the no-slip condition at the wall in vortex methods. Targeting a sharp treatment of the wall calls for substantial modifications at all computational levels of the VPM solver. More specifically, the solution of the underlying Poisson equation, the computation of the diffusion term and the particle-mesh interpolation are adapted accordingly and the spatial accuracy is assessed. The immersed interface VPM solver is subsequently validated on the simulation of some challenging impulsively started flows, such as the flow past a cylinder and that past an airfoil. Research Fellow (PhD student) of the F.R.S.-FNRS of Belgium.
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.; Scacchi, S.; Zampini, Stefano
2015-01-01
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Direct solvers performance on h-adapted grids
Paszynski, Maciej; Pardo, David; Calo, Victor M.
2015-01-01
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
A Survey of Solver-Related Geometry and Meshing Issues
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Energy Technology Data Exchange (ETDEWEB)
Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Direct solvers performance on h-adapted grids
Paszynski, Maciej
2015-05-27
We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
IGA-ADS: Isogeometric analysis FEM using ADS solver
Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav
2017-08-01
In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).
NITSOL: A Newton iterative solver for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
Java Based Symbolic Circuit Solver For Electrical Engineering Curriculum
Directory of Open Access Journals (Sweden)
Ruba Akram Amarin
2012-11-01
Full Text Available The interactive technical electronic book, TechEBook, currently under development at the University of Central Florida (UCF, introduces a paradigm shift by replacing the traditional electrical engineering course with topic-driven modules that provide a useful tool for engineers and scientists. The TechEBook comprises the two worlds of classical circuit books and interactive operating platforms such as iPads, laptops and desktops. The TechEBook provides an interactive applets screen that holds many modules, each of which has a specific application in the self learning process. This paper describes one of the interactive techniques in the TechEBook known as Symbolic Circuit Solver (SymCirc. The SymCirc develops a versatile symbolic based linear circuit with a switches solver. The solver works by accepting a Netlist and the element that the user wants to find the voltage across or current on, as input parameters. Then it either produces the plot or the time domain expression of the output. Frequency domain plots or Symbolic Transfer Functions are also produced. The solver gets its input from a Web-based GUI circuit drawer developed at UCF. Typical simulation tools that electrical engineers encounter are numerical in nature, that is, when presented with an input circuit they iteratively solve the circuit across a set of small time steps. The result is represented as a data set of output versus time, which can be plotted for further inspection. Such results do not help users understand the ultimate nature of circuits as Linear Time Invariant systems with a finite dimensional basis in the solution space. SymCirc provides all simulation results as time domain expressions composed of the basic functions that exclusively include exponentials, sines, cosines and/or t raised to any power. This paper explains the motivation behind SymCirc, the Graphical User Interface front end and how the solver actually works. The paper also presents some examples and
Energy Technology Data Exchange (ETDEWEB)
Fisher, A. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bailey, D. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kaiser, T. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Eder, D. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gunney, B. T. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Masters, N. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Koniges, A. E. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Anderson, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-02-01
Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
Umeyama, Motohiko
2012-04-13
This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an Eulerian scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the Eulerian velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.
Arbogast, Todd; Huang, Chieh-Sen; Russell, Thomas F.
2012-01-01
Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna; Jopek, Konrad; Banaś, Krzysztof; Paszyński, Maciej; Gurgul, Piotr; Lenerth, Andrew; Nguyen, Donald; Pingali, Keshav; Dalcind, Lisandro; Calo, Victor M.
2015-01-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna
2015-06-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Energy Technology Data Exchange (ETDEWEB)
Van Roekel, Luke [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-01-30
We have conducted a suite of Large Eddy Simulation (LES) to form the basis of a multi-model comparison (left). The results have led to proposed model improvements. We have verified that Eulerian-Lagrangian effective diffusivity estimates of mesoscale mixing are consistent with traditional particle statistics metrics (right). LES and Lagrangian particles will be utilized to better represent the movement of water into and out of the mixed layer.
International Nuclear Information System (INIS)
Lapillonne, X.
2010-04-01
In magnetically confined fusion devices, the energy and particle transport is significantly larger than expected from purely collisional processes. This degraded confinement mostly results from small-scale turbulence and prevents from reaching self-sustained burning plasma conditions in present day experiments. A better understanding of these nonlinear phenomena is therefore of key importance on the way towards controlled fusion. The small-scale microinstabilities and associated turbulence are investigated for Tokamak plasmas by means of numerical simulations in the frame of the gyrokinetic theory. This model describes the evolution of the particle distribution functions in phase space together with self-consistent electromagnetic fields, while neglecting the fast motion associated with the Larmor orbit of particles around the magnetic field lines. In the course of this thesis work, substantial modifications to the existing Eulerian gyrokinetic code GENE have been carried out in collaboration with the Max-Planck- Institute f¨ur Plasmaphysik in Garching, Germany. The code has been extended from a local approximation, which only considers a reduced volume of a fusion plasma, to a global version which fully includes radial temperature and density profiles as well as radial magnetic equilibrium variations. To this end, the gyrokinetic equations have been formulated for general magnetic geometry, keeping radial variations of equilibrium quantities, and considering field aligned coordinates, suitable for their numerical implementation. The numerical treatment of the radial direction has been modified from a Fourier representation in the local approach to real space in the global code. This has in particular required to adapt the radial derivatives, the field solver, and to implement a real space dealiasing scheme for the treatment of the nonlinearity. A heat source was in addition introduced to allow for steady state global nonlinear simulations. An important part of
International Nuclear Information System (INIS)
Blanchet, Y.; Obry, P.; Louvet, J.; Graveleau, J.
1981-04-01
Two different numerical methods have been implemented in two computer codes developed in CEA/DRNR, Cadarache, to predict the dynamic response of the containment of Super-Phenix reactor after a hypothetical energy excursion. Both codes are 2D-axisymmetric and solve the time-dependent flow of compressible fluids in the presence of deformable thin structures. The first one, called SIRIUS, uses only Lagrangian meshes; in the second one, called CASSIOPEE, the thick elastic-plastic materials are calculated in Lagrangian coordinates while fluids can be calculated either in Lagrangian or in Eulerian coordinates. The treatment of hydrodynamic, elastic-plastic thick domains then the thin shells models and the fluid-structure couplings are described in parallel for both codes. The efficiency and the limits of the previous methods are finally illustrated by comparison of measured and predicted strains of a vessel issued from one of the MARA experiments which are being purposely performed in Cadarache for validation of these codes in Super-Phenix scale models. These comparisons are encouraging and justify that the Super-Phenix reactor vessel response can be determined using the SIRIUS and CASSIOPEE codes
Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations
International Nuclear Information System (INIS)
Atzberger, Paul J.
2011-01-01
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.
Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.
Energy Technology Data Exchange (ETDEWEB)
Staten, Matthew L.; Owen, Steven James
2010-09-01
Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.
Jiang, Jiming
2013-06-01
This paper presents a new wireless platform designed for an integrated traffic monitoring system based on combined Lagrangian (mobile) and Eulerian (fixed) sensing. The sensor platform is built around a 32-bit ARM Cortex M4 micro-controller and a 2.4GHz 802.15.4 ISM compliant radio module, and can be interfaced with fixed traffic sensors, or receive data from vehicle transponders. The platform is specially designed and optimized to be integrated in a solar-powered wireless sensor network in which traffic flow maps are computed by the nodes directly using distributed computing. A MPPT circuitry is proposed to increase the power output of the attached solar panel. A self-recovering unit is designed to increase reliability and allow periodic hard resets, an essential requirement for sensor networks. A radio monitoring circuitry is proposed to monitor incoming and outgoing transmissions, simplifying software debug. An ongoing implementation is briefly discussed, and compared with existing platforms used in wireless sensor networks. © 2013 IEEE.
Li, K. F.; Yao, K.; Taketa, C.; Zhang, X.; Liang, M. C.; Jiang, X.; Newman, C. E.; Tung, K. K.; Yung, Y. L.
2015-12-01
With the advance of modern computers, studies of planetary atmospheres have heavily relied on general circulation models (GCMs). Because these GCMs are usually very complicated, the simulations are sometimes difficult to understand. Here we develop a semi-analytic zonally averaged, cyclostrophic residual Eulerian model to illustrate how some of the large-scale structures of the middle atmospheric circulation can be explained qualitatively in terms of simple thermal (e.g. solar heating) and mechanical (the Eliassen-Palm flux divergence) forcings. This model is a generalization of that for fast rotating planets such as the Earth, where geostrophy dominates (Andrews and McIntyre 1987). The solution to this semi-analytic model consists of a set of modified Hough functions of the generalized Laplace's tidal equation with the cyclostrohpic terms. As examples, we apply this model to Titan and Venus. We show that the seasonal variations of the temperature and the circulation of these slowly-rotating planets can be well reproduced by adjusting only three parameters in the model: the Brunt-Väisälä bouyancy frequency, the Newtonian radiative cooling rate, and the Rayleigh friction damping rate. We will also discuss the application of this model to study the meridional transport of photochemically produced tracers that can be observed by space instruments.
Exploring the hole cleaning parameters of horizontal wellbore using two-phase Eulerian CFD approach
Directory of Open Access Journals (Sweden)
Satish K Dewangan
2016-03-01
Full Text Available The present investigation deals with the flow through concentric annulus with the inner cylinder in rotation. This work has got its importance in the petroleum industries in relation to the wellbore drilling. In wellbore drilling, the issue of the hole-cleaning is very serious problem especially in case of the horizontal drilling process. The effect of the various parameters like slurry flow velocity, inner cylinder rotational speed, inlet solid concentration which affect hole cleaning was discussed. Their effect on the pressure drop, wall shear stress, mixture turbulence kinetic energy, and solid-phase velocity and slip velocity were analyzed, which are responsible for solid-phase distribution. Flow was considered to be steady, incompressible and two-phase slurry flow with water as carrier fluid and silica sand as the secondary phase. Eulerian approach was used for modeling the slurry flow. Silica sand was considered of spherical shape with particle size of 180 µm. ANSYS FLUENT software was used for modeling and solution. Plotting was done using Tecplot software and Microsoft Office.
Simulation of shear plugging through thin plates using the GRIM Eulerian hydrocode
Church, P.; Cornish, R.; Cullis, I.; Lynch, N.
2000-03-01
Ballistic experiments have been performed using aluminum spheres against 10-mm rolled homogenous armour (RHA), MARS270, MARS300, and titanium alloy plates to investigate the influence of the plugging mechanism on material properties. The experiments have measured the threshold for plug mass and velocity as well as the recovered aluminum sphere mass over a range of velocities. Some of the experiments have been simulated using the in-house second generation Eulerian hydrocode GRIM. The calculations feature advanced material algorithms derived from interrupted tensile testing techniques and a triaxial failure model derived from notched tensile tests over a range of strain rates and temperatures. The effect of mesh resolution on the results has been investigated and understood. The simulation results illustrate the importance of the constitutive model in the shear localization process and the subsequent plugging phenomena. The stress triaxiality is seen as the dominant feature in controlling the onset and subsequent propagation of the crack leading to the shear plug. The simulations have demonstrated that accurate numerics coupled with accurate constitutive and fracture algorithms can successfully reproduce the observed experimental features. However, extrapolation of the fracture data leads to the simulations overpredicting the plug damage. The reasons for this are discussed.
Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.
2017-10-01
Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.
Monte Carlo sensitivity analysis of an Eulerian large-scale air pollution model
International Nuclear Information System (INIS)
Dimov, I.; Georgieva, R.; Ostromsky, Tz.
2012-01-01
Variance-based approaches for global sensitivity analysis have been applied and analyzed to study the sensitivity of air pollutant concentrations according to variations of rates of chemical reactions. The Unified Danish Eulerian Model has been used as a mathematical model simulating a remote transport of air pollutants. Various Monte Carlo algorithms for numerical integration have been applied to compute Sobol's global sensitivity indices. A newly developed Monte Carlo algorithm based on Sobol's quasi-random points MCA-MSS has been applied for numerical integration. It has been compared with some existing approaches, namely Sobol's ΛΠ τ sequences, an adaptive Monte Carlo algorithm, the plain Monte Carlo algorithm, as well as, eFAST and Sobol's sensitivity approaches both implemented in SIMLAB software. The analysis and numerical results show advantages of MCA-MSS for relatively small sensitivity indices in terms of accuracy and efficiency. Practical guidelines on the estimation of Sobol's global sensitivity indices in the presence of computational difficulties have been provided. - Highlights: ► Variance-based global sensitivity analysis is performed for the air pollution model UNI-DEM. ► The main effect of input parameters dominates over higher-order interactions. ► Ozone concentrations are influenced mostly by variability of three chemical reactions rates. ► The newly developed MCA-MSS for multidimensional integration is compared with other approaches. ► More precise approaches like MCA-MSS should be applied when the needed accuracy has not been achieved.
An Eulerian-Lagrangian finite-element method for modeling crack growth in creeping materials
International Nuclear Information System (INIS)
Lee Hae Sung.
1991-01-01
This study is concerned with the development of finite-element-solution methods for analysis of quasi-static, ductile crack growth in history-dependent materials. The mixed Eulerian-Langrangian description (ELD) kinematic model is shown to have several desirable properties for modeling inelastic crack growth. Accordingly, a variational statement based on the ELD for history-dependent materials is developed, and a new moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method is applied to the analysis of transient, quasi-static, mode-III crack growth in creeping materials. A generalized Petrov-Galerkin method (GPG) is developed that simultaneously stabilizes the statement to admit L 2 basis functions for the nonlinear strain field. Quasi-static, model-III crack growth in creeping materials under small-scale-yielding (SSY) conditions is considered. The GPG/ELD moving-grid finite-element formulation is used to model a transient crack-growth problem. The GPG/ELD results compare favorably with previously-published numerical results and the asymptotic solutions
Alver, Morten Omholt; Broch, Ole Jacob; Melle, Webjørn; Bagøien, Espen; Slagstad, Dag
2016-08-01
Calanus finmarchicus is an important zooplankton species in the Norwegian Sea, as a dominant food organism for pelagic fish larvae, and a potentially large source of marine lipids and proteins. Its position in the marine food web also makes it an important model species in assessing the risk posed by oil spills in the Norwegian and Arctic Seas. In this study, an Eulerian population model for C.finmarchicus, coupled to the physical and ecological model SINMOD, is presented. The model includes the full life cycle of C. finmarchicus with a representation of all developmental stages. The model has been validated against field measurements made in different areas of the Norwegian Sea in 1997 and 1998. The model displays geographical and temporal distributions of development stages that is in line with observed patterns. When comparing time series for selected regions, we see a high degree of variability both in the field samples and model output. On average, the model deviations are near half of the summed variability of the field data and model estimates. The model has applications within assessment of ecological production, and the potential for harvesting in the Norwegian and Arctic Seas, but in combination with other models, also for the assessment of ecological effects of oil spills and other types of pollution.
Simulation of atmospheric dispersion of radionuclides using an Eulerian-Lagrangian modelling system.
Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N
2008-12-01
In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a Lagrangian stochastic particle model (LSPM) coupled with an Eulerian regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS code. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a Lagrangian stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.
Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics
International Nuclear Information System (INIS)
Nazem, M; Carter, J P; Airey, D W
2010-01-01
In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.
Van Hillegondsberg, Ludo; Carr, Jonathan; Brey, Naeem; Henning, Franclo
2017-12-01
This study seeks to determine whether the use of Eulerian video magnification (EVM) increases the detection of muscle fasciculations in people with amyotrophic lateral sclerosis (PALS) compared with direct clinical observation (DCO). Thirty-second-long video recordings were taken of 9 body regions of 7 PALS and 7 controls, and fasciculations were counted by DCO during the same 30-s period. The video recordings were then motion magnified and reviewed by 2 independent assessors. In PALS, median fasciculation count per body region was 1 by DCO (range 0-10) and 3 in the EVM recordings (range 0-15; P < 0.0001). EVM revealed more fasciculations than DCO in 61% of recordings. In controls, median fasciculation count was 0 for both DCO and EVM. Compared with DCO, EVM significantly increased the detection of fasciculations in body regions of PALS. When it is used to supplement clinical examination, EVM has the potential to facilitate the diagnosis of ALS. Muscle Nerve 56: 1063-1067, 2017. © 2017 Wiley Periodicals, Inc.
ICECO-CEL: a coupled Eulerian-Lagrangian code for analyzing primary system response in fast reactors
International Nuclear Information System (INIS)
Wang, C.Y.
1981-02-01
This report describes a coupled Eulerian-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit Eulerian method is used to calculate the fluid motion so that large fluid distortion, two-dimensional sliding interface, flow around corners, flow through coolant passageways, and out-flow boundary conditions can be treated. The explicit Lagrangian formulation is employed to compute the response of the containment vessel and other elastic-plastic solids inside the reactor containment. Large displacements, as well as geometrical and material nonlinearities are considered in the analysis. Marker particles are utilized to define the free surface or the material interface and to visualize the fluid motion. The basic equations and numerical techniques used in the Eulerian hydrodynamics and Lagrangian structural dynamics are described. Treatment of the above-core hydrodynamics, sodium spillage, fluid cavitation, free-surface boundary conditions and heat transfer are also presented. Examples are given to illustrate the capabilities of the computer code. Comparisons of the code predictions with available experimental data are also made
Simplified Eigen-structure decomposition solver for the simulation of two-phase flow systems
International Nuclear Information System (INIS)
Kumbaro, Anela
2012-01-01
This paper discusses the development of a new solver for a system of first-order non-linear differential equations that model the dynamics of compressible two-phase flow. The solver presents a lower-complexity alternative to Roe-type solvers because it only makes use of a partial Eigen-structure information while maintaining its accuracy: the outcome is hence a good complexity-tractability trade-off to consider as relevant in a large number of situations in the scope of two-phase flow numerical simulation. A number of numerical and physical benchmarks are presented to assess the solver. Comparison between the computational results from the simplified Eigen-structure decomposition solver and the conventional Roe-type solver gives insight upon the issues of accuracy, robustness and efficiency. (authors)
Using Solver Interfaced Virtual Reality in PEACER Design Process
International Nuclear Information System (INIS)
Lee, Hyong Won; Nam, Won Chang; Jeong, Seung Ho; Hwang, Il Soon; Shin, Jong Gye; Kim, Chang Hyo
2006-01-01
The recent research progress in the area of plant design and simulation highlighted the importance of integrating design and analysis models on a unified environment. For currently developed advanced reactors, either for power production or research, this effort has embraced impressive state-of-the-art information and automation technology. The PEACER (Proliferation-resistant, Environment friendly, Accident-tolerant, Continual and Economical Reactor) is one of the conceptual fast reactor system cooled by LBE (Lead Bismuth Eutectic) for nuclear waste transmutation. This reactor system is composed of innovative combination between design process and analysis. To establish an integrated design process by coupling design, analysis, and post-processing technology while minimizing the repetitive and costly manual interactions for design changes, a solver interfaced virtual reality simulation system (SIVR) has been developed for a nuclear transmutation energy system as PEACER. The SIVR was developed using Virtual Reality Modeling Language (VRML) in order to interface a commercial 3D CAD tool with various engineering solvers and to implement virtual reality presentation of results in a neutral format. In this paper, we have shown the SIVR approach viable and effective in the life-cycle management of complex nuclear energy systems, including design, construction and operation. For instance, The HELIOS is a down scaled model of the PEACER prototype to demonstrate the operability and safety as well as preliminary test of PEACER PLM (Product Life-cycle Management) with SIVR (Solver Interfaced Virtual Reality) concepts. Most components are designed by CATIA, which is 3D CAD tool. During the construction, 3D drawing by CATIA was effective to handle and arrange the loop configuration, especially when we changed the design. Most of all, This system shows the transparency of design and operational status of an energy complex to operators and inspectors can help ensure accident
Application of Nearly Linear Solvers to Electric Power System Computation
Grant, Lisa L.
To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.
Computational aeroelasticity using a pressure-based solver
Kamakoti, Ramji
A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto
2017-01-01
discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...
Modeling Microbunching from Shot Noise Using Vlasov Solvers
International Nuclear Information System (INIS)
Venturini, Marco; Venturini, Marco; Zholents, Alexander
2008-01-01
Unlike macroparticle simulations, which are sensitive to unphysical statistical fluctuations when the number of macroparticles is smaller than the bunch population, direct methods for solving the Vlasov equation are free from sampling noise and are ideally suited for studying microbunching instabilities evolving from shot noise. We review a 2D (longitudinal dynamics) Vlasov solver we have recently developed to study the microbunching instability in the beam delivery systems for x-ray FELs and present an application to FERMI(at)Elettra. We discuss, in particular, the impact of the spreader design on microbunching
Parallel implementations of 2D explicit Euler solvers
International Nuclear Information System (INIS)
Giraud, L.; Manzini, G.
1996-01-01
In this work we present a subdomain partitioning strategy applied to an explicit high-resolution Euler solver. We describe the design of a portable parallel multi-domain code suitable for parallel environments. We present several implementations on a representative range of MlMD computers that include shared memory multiprocessors, distributed virtual shared memory computers, as well as networks of workstations. Computational results are given to illustrate the efficiency, the scalability, and the limitations of the different approaches. We discuss also the effect of the communication protocol on the optimal domain partitioning strategy for the distributed memory computers
Algorithms for parallel flow solvers on message passing architectures
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
Fast Multipole-Based Elliptic PDE Solver and Preconditioner
Ibeid, Huda
2016-12-07
Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf
2010-01-01
The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.
Modelo de selección de cartera con Solver
Directory of Open Access Journals (Sweden)
P. Fogués Zornoza
2012-04-01
Full Text Available In this paper, we present an example of linear optimization in the context of degrees in Economics or Business Administration and Management. We show techniques that enable students to go deep and investigate in real problems that have been modelled using the Excel platform. The model shown here has been developed by a student and it consists in minimizing the absolute deviations over the average expected return of a portfolio of securities, using the solver tool that it is included in this software.
Use of Tabu Search in a Solver to Map Complex Networks onto Emulab Testbeds
National Research Council Canada - National Science Library
MacDonald, Jason E
2007-01-01
The University of Utah's solver for the testbed mapping problem uses a simulated annealing metaheuristic algorithm to map a researcher's experimental network topology onto available testbed resources...
On the implicit density based OpenFOAM solver for turbulent compressible flows
Fürst, Jiří
The contribution deals with the development of coupled implicit density based solver for compressible flows in the framework of open source package OpenFOAM. However the standard distribution of OpenFOAM contains several ready-made segregated solvers for compressible flows, the performance of those solvers is rather week in the case of transonic flows. Therefore we extend the work of Shen [15] and we develop an implicit semi-coupled solver. The main flow field variables are updated using lower-upper symmetric Gauss-Seidel method (LU-SGS) whereas the turbulence model variables are updated using implicit Euler method.
Bridging the scales in a eulerian air quality model to assess megacity export of pollution
Siour, G.; Colette, A.; Menut, L.; Bessagnet, B.; Coll, I.; Meleux, F.
2013-08-01
In Chemistry Transport Models (CTMs), spatial scale interactions are often represented through off-line coupling between large and small scale models. However, those nested configurations cannot give account of the impact of the local scale on its surroundings. This issue can be critical in areas exposed to air mass recirculation (sea breeze cells) or around regions with sharp pollutant emission gradients (large cities). Such phenomena can still be captured by the mean of adaptive gridding, two-way nesting or using model nudging, but these approaches remain relatively costly. We present here the development and the results of a simple alternative multi-scale approach making use of a horizontal stretched grid, in the Eulerian CTM CHIMERE. This method, called "stretching" or "zooming", consists in the introduction of local zooms in a single chemistry-transport simulation. It allows bridging online the spatial scales from the city (∼1 km resolution) to the continental area (∼50 km resolution). The CHIMERE model was run over a continental European domain, zoomed over the BeNeLux (Belgium, Netherlands and Luxembourg) area. We demonstrate that, compared with one-way nesting, the zooming method allows the expression of a significant feedback of the refined domain towards the large scale: around the city cluster of BeNeLuX, NO2 and O3 scores are improved. NO2 variability around BeNeLux is also better accounted for, and the net primary pollutant flux transported back towards BeNeLux is reduced. Although the results could not be validated for ozone over BeNeLux, we show that the zooming approach provides a simple and immediate way to better represent scale interactions within a CTM, and constitutes a useful tool for apprehending the hot topic of megacities within their continental environment.
An Eulerian two-phase model for steady sheet flow using large-eddy simulation methodology
Cheng, Zhen; Hsu, Tian-Jian; Chauchat, Julien
2018-01-01
A three-dimensional Eulerian two-phase flow model for sediment transport in sheet flow conditions is presented. To resolve turbulence and turbulence-sediment interactions, the large-eddy simulation approach is adopted. Specifically, a dynamic Smagorinsky closure is used for the subgrid fluid and sediment stresses, while the subgrid contribution to the drag force is included using a drift velocity model with a similar dynamic procedure. The contribution of sediment stresses due to intergranular interactions is modeled by the kinetic theory of granular flow at low to intermediate sediment concentration, while at high sediment concentration of enduring contact, a phenomenological closure for particle pressure and frictional viscosity is used. The model is validated with a comprehensive high-resolution dataset of unidirectional steady sheet flow (Revil-Baudard et al., 2015, Journal of Fluid Mechanics, 767, 1-30). At a particle Stokes number of about 10, simulation results indicate a reduced von Kármán coefficient of κ ≈ 0.215 obtained from the fluid velocity profile. A fluid turbulence kinetic energy budget analysis further indicates that the drag-induced turbulence dissipation rate is significant in the sheet flow layer, while in the dilute transport layer, the pressure work plays a similar role as the buoyancy dissipation, which is typically used in the single-phase stratified flow formulation. The present model also reproduces the sheet layer thickness and mobile bed roughness similar to measured data. However, the resulting mobile bed roughness is more than two times larger than that predicted by the empirical formulae. Further analysis suggests that through intermittent turbulent motions near the bed, the resolved sediment Reynolds stress plays a major role in the enhancement of mobile bed roughness. Our analysis on near-bed intermittency also suggests that the turbulent ejection motions are highly correlated with the upward sediment suspension flux, while
The RIVM-MNP contribution to the evaluation of the EMEP Unified (Eulerian) model
Energy Technology Data Exchange (ETDEWEB)
Velders, G.J.M.; De Waal, E.S.; Van Jaarsveld, J.A.; De Ruiter, J.F.
2003-07-01
A few aspects of the EMEP Unified (Eulerian) model have been evaluated by analysing the deposition parametrisation for acidifying compounds and the concentration and deposition of SOx, NOx, and NHx in the Netherlands. Evaluation was also carried out by analysing the source-receptor matrices for the Netherlands and the geographical distribution of the emissions, comparing results with both the OPS model and measurements. The picture given of the Netherlands by the EMEP Unified model was found for most acidifying compounds to be a fair one. The source-receptor matrices calculated by the EMEP and OPS models were seen to be in good agreement for oxidised sulphur, and in reasonable agreement for reduced nitrogen. Large discrepancies between the models were found for oxidised nitrogen. The contribution of the Dutch emissions to local deposition in the Netherlands came to a factor of 4 higher in the OPS model, compared to the EMEP model. The contributions of Belgium and Germany to deposition are also much higher in the OPS model. These differences can be traced back to the lower concentration and dry deposition, along with higher wet deposition, of NOx in the EMEP model. For oxidised nitrogen, there was a large difference in the influence of the boundary and initial conditions on the source-receptor matrix. The EMEP model suggests that almost 30% of the deposition is due to sources outside Europe. The SO2 concentrations in the Netherlands calculated with the EMEP model are close to the measurements, while the NOx concentrations are about 40% lower and the NH3 concentrations 30% to 40% lower than the measurements.
A Eulerian nutrient to fish model of the Baltic Sea — A feasibility-study
Radtke, Hagen; Neumann, Thomas; Fennel, Wolfgang
2013-09-01
A nutrient-to-fish-model with an explicit two-way interaction between a biogeochemical model of the lower food web and a fish model component is presented for the example of the Baltic Sea, demonstrating the feasibility of a consistent coupling of the upper and lower parts of the food web in a Eulerian model system. In the Baltic Sea, the fish stock is dominated by two prey species (sprat and herring) and one predator (cod). The dynamics of the fish model is driven by size (mass-class) dependent predator-prey interactions while the interaction between the biogeochemical and Fish model component is established through feeding of prey fish on zooplankton and recycling of fish biomass to nutrients and detritus. The fish model component is coupled to an advanced three dimensional biogeochemical model (ERGOM, Neumann et al., 2002). A horizontally explicit representation of fish requires the implementation of fish behavior. As a first step, we propose an algorithm to stimulate fish migration by letting the fish follow the food. Moreover, fish species are guided to their respective spawning areas. Results of first three-dimensional simulations are presented with emphasis on the transport of matter by moving fish. The spawning areas of cod and sprat are in the deep basins, which are not well reached by advective transport. Hence the deposition of matter in these areas by spawning fish could play some role in the distribution of matter. The approach is not limited to applications for the Baltic and the model can be transferred also to other systems.
Analysis of LMFBR containment response to an HCDA using a multifield Eulerian code
International Nuclear Information System (INIS)
Chu, H.Y.; Chang, Y.W.
1977-01-01
During a hypothetical core disruptive accident (HCDA), a core meltdown may cause the fuel cladding to rupture and the fuel fragments to penetrate into the sodium coolant. The heat in the molten fuel may cause the liquid sodium to boil, changing its phase. The interactions between materials are so complicated that a single-material model with homogenized material properties is not adequate. In order to analyze the above phenomena more realistically, a Multifield Implicit Continuous-Fluid Eulerian containment code (MICE) is being developed at Argonne National Laboratory (ANL) to solve the multifield fluid-flow problems in which the interpenetrations of materials, heat transfer, and phase changes are considered in the analysis. The hydrodynamics of the MICE code is based upon the implicit multifield (IMF) method developed by Harlow and Amsden. A partial donor-cell formulation is used for the calculation of the convective fluxes to minimize the truncation errors, while the Newton-Raphson method is used for the numerical iterations. An implicit treatment of the mass convection together with the equation of state for each material enables the method to be applicable to both compressible and incompressible flows. A partial implicit treatment of the momentum-exchange functions allows the coupling drag forces between two material fields to range from very weak to those strong enough to tie the fields completely. The differential equations and exchange functions used in the MICE code, and the treatment of the fluid and structure interactions as well as the numerical procedure are described. Two sample calculations are given to illustrate the present capability of the MICE code
Pallas Sanz, E.; García-Carrillo, P.; Garcia Gomez, B. I.; Lilly, J. M.; Perez-Brunius, P.
2016-02-01
The time-average horizontal distribution of the near-inertial waves (NIWs) on the western Gulf of Mexico (GoM) is investigated using horizontal velocity data obtained from Lagrangian trajectories of 200 surface drifters drogued at 50m and deployed between September 2008 and September 2012. Preliminary results suggest maximum time-averaged near-inertial circle radius of 2.6km located in the southern Campeche bay near [22N,95W]; implying an inertial velocity of about 0.14m/s. Similar conclusions are delineated using horizontal velocity data obtained from 21 moorings deployed in the western GoM during the same time period. Maximum near-inertial kinetic energy and clockwise spectral energy is found in the mooring LNK3500 located at 21.850N and 94.028W. Maximum inertial circles measured with mooring data, however, are of about 1.6km leading to inertial currents of 0.087m/s, approximately a 40% smaller. This discrepancy seems to be due to the different depth level of the measurements and the bandwidth used to extract the near-inertial oscillations from the total flow. The time-average horizontal distributions of wind work computed from Lagrangian and Eulerian data are compared and they are not consistent with the time-averaged NIW field. The differences are not well understood but we speculate they may be due to the different time scales of wind fluctuations in the northwestern GoM compared to those observed in the Bay of Campeche, together with the change of sign of the background vorticity in the region; being negative (anticyclonic) in the northern GoM and positive (cyclonic) in the Bay of Campeche.
Eibern, Hendrik; Schmidt, Hauke
1999-08-01
The inverse problem of data assimilation of tropospheric trace gas observations into an Eulerian chemistry transport model has been solved by the four-dimensional variational technique including chemical reactions, transport, and diffusion. The University of Cologne European Air Pollution Dispersion Chemistry Transport Model 2 with the Regional Acid Deposition Model 2 gas phase mechanism is taken as the basis for developing a full four-dimensional variational data assimilation package, on the basis of the adjoint model version, which includes the adjoint operators of horizontal and vertical advection, implicit vertical diffusion, and the adjoint gas phase mechanism. To assess the potential and limitations of the technique without degrading the impact of nonperfect meteorological analyses and statistically not established error covariance estimates, artificial meteorological data and observations are used. The results are presented on the basis of a suite of experiments, where reduced records of artificial "observations" are provided to the assimilation procedure, while other "data" is retained for performance control of the analysis. The paper demonstrates that the four-dimensional variational technique is applicable for a comprehensive chemistry transport model in terms of computational and storage requirements on advanced parallel platforms. It is further shown that observed species can generally be analyzed, even if the "measurements" have unbiased random errors. More challenging experiments are presented, aiming to tax the skill of the method (1) by restricting available observations mostly to surface ozone observations for a limited assimilation interval of 6 hours and (2) by starting with poorly chosen first guess values. In this first such application to a three-dimensional chemistry transport model, success was also achieved in analyzing not only observed but also chemically closely related unobserved constituents.
PELE-IC, 2-D Eulerian Incompressible Hydrodynamic and Bubble Dynamic after LWR LOCA
International Nuclear Information System (INIS)
McMaster, W.H.; Gong, E.Y.
1981-01-01
1 - Description of problem or function: PELE-IC is a two-dimensional semi-implicit Eulerian hydrodynamics program for the solution of incompressible flow coupled to flexible structures. The code was developed to calculate fluid-structure interactions and bubble dynamics of a pressure-suppression system following a loss-of- coolant accident (LOCA). The fluid, structure, and coupling algorithms have been verified by calculation of benchmark problems and air and steam blowdown experiments. The code is written for both plane and cylindrical coordinates. The coupling algorithm is general enough to handle a wide variety of structural shapes. The concepts of void fractions and interface orientation are used to track the movement of free surfaces, allowing great versatility in following fluid-gas interfaces both for bubble definition and water surface motion without the use of marker particles. 2 - Method of solution: The solution strategy is to first solve the Navier-Stokes equations explicitly using values from the previous time-step. Since these values do not necessarily satisfy the continuity equation, the pressure field is iterated upon until the incompressibility condition for each computational cell is satisfied within prescribed limits. The structural motion is computed by a finite element code from the applied pressure at the fluid-structure interface. The shell structure algorithm uses conventional thin-shell theory with transverse shear. The finite-element spatial discretization employs piecewise-linear interpolation functions and one-point quadrature applied to conical frustra. The Newmark implicit time integration method is used as a one-step module. The fluid code then uses the structure's position and velocity as boundary conditions. The fluid pressure field and the structure's response are corrected iteratively until the normal velocities of fluid and structure are equal. The effects of steam condensation and oscillatory chugging on structures are
Development of a Cartesian grid based CFD solver (CARBS)
International Nuclear Information System (INIS)
Vaidya, A.M.; Maheshwari, N.K.; Vijayan, P.K.
2013-12-01
Formulation for 3D transient incompressible CFD solver is developed. The solution of variable property, laminar/turbulent, steady/unsteady, single/multi specie, incompressible with heat transfer in complex geometry will be obtained. The formulation can handle a flow system in which any number of arbitrarily shaped solid and fluid regions are present. The solver is based on the use of Cartesian grids. A method is proposed to handle complex shaped objects and boundaries on Cartesian grids. Implementation of multi-material, different types of boundary conditions, thermo physical properties is also considered. The proposed method is validated by solving two test cases. 1 st test case is that of lid driven flow in inclined cavity. 2 nd test case is the flow over cylinder. The 1 st test case involved steady internal flow subjected to WALL boundaries. The 2 nd test case involved unsteady external flow subjected to INLET, OUTLET and FREE-SLIP boundary types. In both the test cases, non-orthogonal geometry was involved. It was found that, under such a wide conditions, the Cartesian grid based code was found to give results which were matching well with benchmark data. Convergence characteristics are excellent. In all cases, the mass residue was converged to 1E-8. Based on this, development of 3D general purpose code based on the proposed approach can be taken up. (author)
Riemann solvers and undercompressive shocks of convex FPU chains
International Nuclear Information System (INIS)
Herrmann, Michael; Rademacher, Jens D M
2010-01-01
We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Anisotropic resonator analysis using the Fourier-Bessel mode solver
Gauthier, Robert C.
2018-03-01
A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.
Application of alternating decision trees in selecting sparse linear solvers
Bhowmick, Sanjukta; Eijkhout, Victor; Freund, Yoav; Fuentes, Erika; Keyes, David E.
2010-01-01
The solution of sparse linear systems, a fundamental and resource-intensive task in scientific computing, can be approached through multiple algorithms. Using an algorithm well adapted to characteristics of the task can significantly enhance the performance, such as reducing the time required for the operation, without compromising the quality of the result. However, the best solution method can vary even across linear systems generated in course of the same PDE-based simulation, thereby making solver selection a very challenging problem. In this paper, we use a machine learning technique, Alternating Decision Trees (ADT), to select efficient solvers based on the properties of sparse linear systems and runtime-dependent features, such as the stages of simulation. We demonstrate the effectiveness of this method through empirical results over linear systems drawn from computational fluid dynamics and magnetohydrodynamics applications. The results also demonstrate that using ADT can resolve the problem of over-fitting, which occurs when limited amount of data is available. © 2010 Springer Science+Business Media LLC.
High-Performance Small-Scale Solvers for Moving Horizon Estimation
DEFF Research Database (Denmark)
Frison, Gianluca; Vukov, Milan; Poulsen, Niels Kjølstad
2015-01-01
implementation techniques focusing on small-scale problems. The proposed MHE solver is implemented using custom linear algebra routines and is compared against implementations using BLAS libraries. Additionally, the MHE solver is interfaced to a code generation tool for nonlinear model predictive control (NMPC...
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
International Nuclear Information System (INIS)
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources
Identification of severe wind conditions using a Reynolds averaged Navier-Stokes solver
DEFF Research Database (Denmark)
Sørensen, Niels N.; Bechmann, Andreas; Johansen, Jeppe
2007-01-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting...
Scalable Newton-Krylov solver for very large power flow problems
Idema, R.; Lahaye, D.J.P.; Vuik, C.; Van der Sluis, L.
2010-01-01
The power flow problem is generally solved by the Newton-Raphson method with a sparse direct solver for the linear system of equations in each iteration. While this works fine for small power flow problems, we will show that for very large problems the direct solver is very slow and we present
The SX Solver: A New Computer Program for Analyzing Solvent-Extraction Equilibria
International Nuclear Information System (INIS)
McNamara, B.K.; Rapko, B.M.; Lumetta, G.J.
1999-01-01
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel and uses the built-in ''Solver'' function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributylphosphate has been modeled to illustrate the program's use
The SX Solver: A Computer Program for Analyzing Solvent-Extraction Equilibria: Version 3.0
International Nuclear Information System (INIS)
Lumetta, Gregg J.
2001-01-01
A new computer program, the SX Solver, has been developed to analyze solvent-extraction equilibria. The program operates out of Microsoft Excel and uses the built-in Solver function to minimize the sum of the square of the residuals between measured and calculated distribution coefficients. The extraction of nitric acid by tributyl phosphate has been modeled to illustrate the programs use
International Nuclear Information System (INIS)
Idomura, Yasuhiro; Jolliet, Sebastien
2010-01-01
A gyrokinetic toroidal five dimensional Eulerian code GT5D is ported on six advanced massively parallel platforms and comprehensive benchmark tests are performed. A parallelisation technique based on physical properties of the gyrokinetic equation is presented. By extending the parallelisation technique with a hybrid parallel model, the scalability of the code is improved on platforms with multi-core processors. In the benchmark tests, a good salability is confirmed up to several thousands cores on every platforms, and the maximum sustained performance of ∼18.6 Tflops is achieved using 16384 cores of BX900. (author)
Strategic Air Traffic Planning Using Eulerian Route Based Modeling and Optimization
Bombelli, Alessandro
Due to a soaring air travel growth in the last decades, air traffic management has become increasingly challenging. As a consequence, planning tools are being devised to help human decision-makers achieve a better management of air traffic. Planning tools are divided into two categories, strategic and tactical. Strategic planning generally addresses a larger planning domain and is performed days to hours in advance. Tactical planning is more localized and is performed hours to minutes in advance. An aggregate route model for strategic air traffic flow management is presented. It is an Eulerian model, describing the flow between cells of unidirectional point-to-point routes. Aggregate routes are created from flight trajectory data based on similarity measures. Spatial similarity is determined using the Frechet distance. The aggregate routes approximate actual well-traveled traffic patterns. By specifying the model resolution, an appropriate balance between model accuracy and model dimension can be achieved. For a particular planning horizon, during which weather is expected to restrict the flow, a procedure for designing airborne reroutes and augmenting the traffic flow model is developed. The dynamics of the traffic flow on the resulting network take the form of a discrete-time, linear time-invariant system. The traffic flow controls are ground holding, pre-departure rerouting and airborne rerouting. Strategic planning--determining how the controls should be used to modify the future traffic flow when local capacity violations are anticipated--is posed as an integer programming problem of minimizing a weighted sum of flight delays subject to control and capacity constraints. Several tests indicate the effectiveness of the modeling and strategic planning approach. In the final, most challenging, test, strategic planning is demonstrated for the six western-most Centers of the 22-Center national airspace. The planning time horizon is four hours long, and there is
Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows
Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan
2018-05-01
This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.
Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport solver
International Nuclear Information System (INIS)
Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.
2010-01-01
Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.
VCODE, Ordinary Differential Equation Solver for Stiff and Non-Stiff Problems
International Nuclear Information System (INIS)
Cohen, Scott D.; Hindmarsh, Alan C.
2001-01-01
1 - Description of program or function: CVODE is a package written in ANSI standard C for solving initial value problems for ordinary differential equations. It solves both stiff and non stiff systems. In the stiff case, it includes a variety of options for treating the Jacobian of the system, including dense and band matrix solvers, and a preconditioned Krylov (iterative) solver. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by functional iteration or Newton iteration. For the solution of linear systems within Newton iteration, users can select a dense solver, a band solver, a diagonal approximation, or a preconditioned Generalized Minimal Residual (GMRES) solver. In the dense and band cases, the user can supply a Jacobian approximation or let CVODE generate it internally. In the GMRES case, the pre-conditioner is user-supplied
Minos: a SPN solver for core calculation in the DESCARTES system
International Nuclear Information System (INIS)
Baudron, A.M.; Lautard, J.J.
2005-01-01
This paper describes a new development of a neutronic core solver done in the context of a new generation neutronic reactor computational system, named DESCARTES. For performance reasons, the numerical method of the existing MINOS solver in the SAPHYR system has been reused in the new system. It is based on the mixed dual finite element approximation of the simplified transport equation. The solver takes into account assembly discontinuity coefficients (ADF) in the simplified transport equation (SPN) context. The solver has been rewritten in C++ programming language using an object oriented design. Its general architecture was reconsidered in order to improve its capability of evolution and its maintainability. Moreover, the performances of the old version have been improved mainly regarding the matrix construction time; this result improves significantly the performance of the solver in the context of industrial application requiring thermal hydraulic feedback and depletion calculations. (authors)
Fast Multipole-Based Preconditioner for Sparse Iterative Solvers
Ibeid, Huda; Yokota, Rio; Keyes, David E.
2014-01-01
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.
Workload Characterization of CFD Applications Using Partial Differential Equation Solvers
Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)
1998-01-01
Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.
POSSOL, 2-D Poisson Equation Solver for Nonuniform Grid
International Nuclear Information System (INIS)
Orvis, W.J.
1988-01-01
1 - Description of program or function: POSSOL is a two-dimensional Poisson equation solver for problems with arbitrary non-uniform gridding in Cartesian coordinates. It is an adaptation of the uniform grid PWSCRT routine developed by Schwarztrauber and Sweet at the National Center for Atmospheric Research (NCAR). 2 - Method of solution: POSSOL will solve the Helmholtz equation on an arbitrary, non-uniform grid on a rectangular domain allowing only one type of boundary condition on any one side. It can also be used to handle more than one type of boundary condition on a side by means of a capacitance matrix technique. There are three types of boundary conditions that can be applied: fixed, derivative, or periodic
Extending the QUDA Library with the eigCG Solver
Energy Technology Data Exchange (ETDEWEB)
Strelchenko, Alexei [Fermilab; Stathopoulos, Andreas [William-Mary Coll.
2014-12-12
While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear solvers, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich
2010-01-01
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan
2010-10-05
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
Diffusion of Zonal Variables Using Node-Centered Diffusion Solver
Energy Technology Data Exchange (ETDEWEB)
Yang, T B
2007-08-06
Tom Kaiser [1] has done some preliminary work to use the node-centered diffusion solver (originally developed by T. Palmer [2]) in Kull for diffusion of zonal variables such as electron temperature. To avoid numerical diffusion, Tom used a scheme developed by Shestakov et al. [3] and found their scheme could, in the vicinity of steep gradients, decouple nearest-neighbor zonal sub-meshes leading to 'alternating-zone' (red-black mode) errors. Tom extended their scheme to couple the sub-meshes with appropriate chosen artificial diffusion and thereby solved the 'alternating-zone' problem. Because the choice of the artificial diffusion coefficient could be very delicate, it is desirable to use a scheme that does not require the artificial diffusion but still able to avoid both numerical diffusion and the 'alternating-zone' problem. In this document we present such a scheme.
A high order solver for the unbounded Poisson equation
DEFF Research Database (Denmark)
Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe
2013-01-01
. The method is extended to directly solve the derivatives of the solution to Poissonʼs equation. In this way differential operators such as the divergence or curl of the solution field can be solved to the same high order convergence without additional computational effort. The method, is applied......A high order converging Poisson solver is presented, based on the Greenʼs function solution to Poissonʼs equation subject to free-space boundary conditions. The high order convergence is achieved by formulating regularised integration kernels, analogous to a smoothing of the solution field...... and validated, however not restricted, to the equations of fluid mechanics, and can be used in many applications to solve Poissonʼs equation on a rectangular unbounded domain....
A General Symbolic PDE Solver Generator: Beyond Explicit Schemes
Directory of Open Access Journals (Sweden)
K. Sheshadri
2003-01-01
Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
GPU accelerated FDTD solver and its application in MRI.
Chi, J; Liu, F; Jin, J; Mason, D G; Crozier, S
2010-01-01
The finite difference time domain (FDTD) method is a popular technique for computational electromagnetics (CEM). The large computational power often required, however, has been a limiting factor for its applications. In this paper, we will present a graphics processing unit (GPU)-based parallel FDTD solver and its successful application to the investigation of a novel B1 shimming scheme for high-field magnetic resonance imaging (MRI). The optimized shimming scheme exhibits considerably improved transmit B(1) profiles. The GPU implementation dramatically shortened the runtime of FDTD simulation of electromagnetic field compared with its CPU counterpart. The acceleration in runtime has made such investigation possible, and will pave the way for other studies of large-scale computational electromagnetic problems in modern MRI which were previously impractical.
Visualising magnetic fields numerical equation solvers in action
Beeteson, John Stuart
2001-01-01
Visualizing Magnetic Fields: Numerical Equation Solvers in Action provides a complete description of the theory behind a new technique, a detailed discussion of the ways of solving the equations (including a software visualization of the solution algorithms), the application software itself, and the full source code. Most importantly, there is a succinct, easy-to-follow description of each procedure in the code.The physicist Michael Faraday said that the study of magnetic lines of force was greatly influential in leading him to formulate many of those concepts that are now so fundamental to our modern world, proving to him their "great utility as well as fertility." Michael Faraday could only visualize these lines in his mind's eye and, even with modern computers to help us, it has been very expensive and time consuming to plot lines of force in magnetic fields
Fast Multipole-Based Preconditioner for Sparse Iterative Solvers
Ibeid, Huda
2014-05-04
Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.
Incompressible SPH (ISPH) with fast Poisson solver on a GPU
Chow, Alex D.; Rogers, Benedict D.; Lind, Steven J.; Stansby, Peter K.
2018-05-01
This paper presents a fast incompressible SPH (ISPH) solver implemented to run entirely on a graphics processing unit (GPU) capable of simulating several millions of particles in three dimensions on a single GPU. The ISPH algorithm is implemented by converting the highly optimised open-source weakly-compressible SPH (WCSPH) code DualSPHysics to run ISPH on the GPU, combining it with the open-source linear algebra library ViennaCL for fast solutions of the pressure Poisson equation (PPE). Several challenges are addressed with this research: constructing a PPE matrix every timestep on the GPU for moving particles, optimising the limited GPU memory, and exploiting fast matrix solvers. The ISPH pressure projection algorithm is implemented as 4 separate stages, each with a particle sweep, including an algorithm for the population of the PPE matrix suitable for the GPU, and mixed precision storage methods. An accurate and robust ISPH boundary condition ideal for parallel processing is also established by adapting an existing WCSPH boundary condition for ISPH. A variety of validation cases are presented: an impulsively started plate, incompressible flow around a moving square in a box, and dambreaks (2-D and 3-D) which demonstrate the accuracy, flexibility, and speed of the methodology. Fragmentation of the free surface is shown to influence the performance of matrix preconditioners and therefore the PPE matrix solution time. The Jacobi preconditioner demonstrates robustness and reliability in the presence of fragmented flows. For a dambreak simulation, GPU speed ups demonstrate up to 10-18 times and 1.1-4.5 times compared to single-threaded and 16-threaded CPU run times respectively.
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Energy Technology Data Exchange (ETDEWEB)
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
Cucco, Andrea; Umgiesser, Georg
2015-09-15
In this work, we investigated if the Eulerian and the Lagrangian approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The Eulerian and Lagrangian TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an Eulerian only or from a Lagrangian only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Pang, Kar Mun; Jangi, Mehdi; Bai, Xue-Song
2017-01-01
The present numerical study aims to assess the performance of an Eulerian Stochastic Field (ESF) model in simulating spray flames produced by three fuel injectors with different nozzle diameters of 100 μm, 180 μm and 363 μm. A comparison to the measurements shows that although the simulated ignit...... serve as an important tool for the simulation of spray flames in marine diesel engines, where fuel injectors with different nozzle diameters are applied for pilot and main injections.......The present numerical study aims to assess the performance of an Eulerian Stochastic Field (ESF) model in simulating spray flames produced by three fuel injectors with different nozzle diameters of 100 μm, 180 μm and 363 μm. A comparison to the measurements shows that although the simulated...... ignition delay times are consistently overestimated, the relative differences remain below 28%. Furthermore, the change of the averaged pressure rise with respect to the variation of nozzle diameter is captured by the model. The simulated flame lift-off lengths also agree with the measurements...
Shih, Tsan-Hsing; Liu, Nan-Suey
2012-01-01
This paper presents the numerical simulations of the Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.
Implementation of density-based solver for all speeds in the framework of OpenFOAM
Shen, Chun; Sun, Fengxian; Xia, Xinlin
2014-10-01
In the framework of open source CFD code OpenFOAM, a density-based solver for all speeds flow field is developed. In this solver the preconditioned all speeds AUSM+(P) scheme is adopted and the dual time scheme is implemented to complete the unsteady process. Parallel computation could be implemented to accelerate the solving process. Different interface reconstruction algorithms are implemented, and their accuracy with respect to convection is compared. Three benchmark tests of lid-driven cavity flow, flow crossing over a bump, and flow over a forward-facing step are presented to show the accuracy of the AUSM+(P) solver for low-speed incompressible flow, transonic flow, and supersonic/hypersonic flow. Firstly, for the lid driven cavity flow, the computational results obtained by different interface reconstruction algorithms are compared. It is indicated that the one dimensional reconstruction scheme adopted in this solver possesses high accuracy and the solver developed in this paper can effectively catch the features of low incompressible flow. Then via the test cases regarding the flow crossing over bump and over forward step, the ability to capture characteristics of the transonic and supersonic/hypersonic flows are confirmed. The forward-facing step proves to be the most challenging for the preconditioned solvers with and without the dual time scheme. Nonetheless, the solvers described in this paper reproduce the main features of this flow, including the evolution of the initial transient.
Acceleration of FDTD mode solver by high-performance computing techniques.
Han, Lin; Xi, Yanping; Huang, Wei-Ping
2010-06-21
A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation.
The impact of improved sparse linear solvers on industrial engineering applications
Energy Technology Data Exchange (ETDEWEB)
Heroux, M. [Cray Research, Inc., Eagan, MN (United States); Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
International Nuclear Information System (INIS)
Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2015-01-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta–Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5–3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners. - Highlights: • We solve the multiple-right-hand-side problem in DOT with a block BiCGStab method. • We examine the CPU times of the block solver and the traditional sequential solver. • The block solver is faster than the sequential solver by a factor of 1.5–3.0. • Multi-threading block solvers give additional speedup under limited threads situation.
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.
2010-03-01
In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.
Robust large-scale parallel nonlinear solvers for simulations.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any
DEFF Research Database (Denmark)
Pang, Kar Mun; Ivarsson, Anders; Haider, Sajjad
2013-01-01
In the current work, a local time stepping (LTS) solver for the modeling of combustion, radiative heat transfer and soot formation is developed and validated. This is achieved using an open source computational fluid dynamics code, OpenFOAM. Akin to the solver provided in default assembly i...... library in the edcSimpleFoam solver which was introduced during the 6th OpenFOAM workshop is modified and coupled with the current solver. One of the main amendments made is the integration of soot radiation submodel since this is significant in rich flames where soot particles are formed. The new solver...
Verification of continuum drift kinetic equation solvers in NIMROD
Energy Technology Data Exchange (ETDEWEB)
Held, E. D.; Ji, J.-Y. [Utah State University, Logan, Utah 84322-4415 (United States); Kruger, S. E. [Tech-X Corporation, Boulder, Colorado 80303 (United States); Belli, E. A. [General Atomics, San Diego, California 92186-5608 (United States); Lyons, B. C. [Program in Plasma Physics, Princeton University, Princeton, New Jersey 08543-0451 (United States)
2015-03-15
Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
Shared memory parallelism for 3D cartesian discrete ordinates solver
International Nuclear Information System (INIS)
Moustafa, S.; Dutka-Malen, I.; Plagne, L.; Poncot, A.; Ramet, P.
2013-01-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multi-core + SIMD - Single Instruction on Multiple Data) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46*10 6 spatial cells and 1*10 12 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40.74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool. (authors)
Parallelization of elliptic solver for solving 1D Boussinesq model
Tarwidi, D.; Adytia, D.
2018-03-01
In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.
Development and acceleration of unstructured mesh-based cfd solver
Emelyanov, V.; Karpenko, A.; Volkov, K.
2017-06-01
The study was undertaken as part of a larger effort to establish a common computational fluid dynamics (CFD) code for simulation of internal and external flows and involves some basic validation studies. The governing equations are solved with ¦nite volume code on unstructured meshes. The computational procedure involves reconstruction of the solution in each control volume and extrapolation of the unknowns to find the flow variables on the faces of control volume, solution of Riemann problem for each face of the control volume, and evolution of the time step. The nonlinear CFD solver works in an explicit time-marching fashion, based on a three-step Runge-Kutta stepping procedure. Convergence to a steady state is accelerated by the use of geometric technique and by the application of Jacobi preconditioning for high-speed flows, with a separate low Mach number preconditioning method for use with low-speed flows. The CFD code is implemented on graphics processing units (GPUs). Speedup of solution on GPUs with respect to solution on central processing units (CPU) is compared with the use of different meshes and different methods of distribution of input data into blocks. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.
Advanced features of the fault tree solver FTREX
International Nuclear Information System (INIS)
Jung, Woo Sik; Han, Sang Hoon; Ha, Jae Joo
2005-01-01
This paper presents advanced features of a fault tree solver FTREX (Fault Tree Reliability Evaluation eXpert). Fault tree analysis is one of the most commonly used methods for the safety analysis of industrial systems especially for the probabilistic safety analysis (PSA) of nuclear power plants. Fault trees are solved by the classical Boolean algebra, conventional Binary Decision Diagram (BDD) algorithm, coherent BDD algorithm, and Bayesian networks. FTREX could optionally solve fault trees by the conventional BDD algorithm or the coherent BDD algorithm and could convert the fault trees into the form of the Bayesian networks. The algorithm based on the classical Boolean algebra solves a fault tree and generates MCSs. The conventional BDD algorithm generates a BDD structure of the top event and calculates the exact top event probability. The BDD structure is a factorized form of the prime implicants. The MCSs of the top event could be extracted by reducing the prime implicants in the BDD structure. The coherent BDD algorithm is developed to overcome the shortcomings of the conventional BDD algorithm such as the huge memory requirements and a long run time
Domain decomposition methods for core calculations using the MINOS solver
International Nuclear Information System (INIS)
Guerin, P.; Baudron, A. M.; Lautard, J. J.
2007-01-01
Cell by cell homogenized transport calculations of an entire nuclear reactor core are currently too expensive for industrial applications, even if a simplified transport (SPn) approximation is used. In order to take advantage of parallel computers, we propose here two domain decomposition methods using the mixed dual finite element solver MINOS. The first one is a modal synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second one is an iterative method based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the close sub-domains estimated at the previous iteration. For these two methods, we give numerical results which demonstrate their accuracy and their efficiency for the diffusion model on realistic 2D and 3D cores. (authors)
A generalized Poisson solver for first-principles device simulations
Energy Technology Data Exchange (ETDEWEB)
Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost, E-mail: joost.vandevondele@mat.ethz.ch [Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland); Brück, Sascha; Luisier, Mathieu [Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Parallelizable approximate solvers for recursions arising in preconditioning
Energy Technology Data Exchange (ETDEWEB)
Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Liu, Yang; Bagci, Hakan; Michielssen, Eric
2013-01-01
numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from
Hybrid direct and iterative solvers for h refined grids with singularities
Paszyński, Maciej R.
2015-04-27
This paper describes a hybrid direct and iterative solver for two and three dimensional h adaptive grids with point singularities. The point singularities are eliminated by using a sequential linear computational cost solver O(N) on CPU [1]. The remaining Schur complements are submitted to incomplete LU preconditioned conjugated gradient (ILUPCG) iterative solver. The approach is compared to the standard algorithm performing static condensation over the entire mesh and executing the ILUPCG algorithm on top of it. The hybrid solver is applied for two or three dimensional grids automatically h refined towards point or edge singularities. The automatic refinement is based on the relative error estimations between the coarse and fine mesh solutions [2], and the optimal refinements are selected using the projection based interpolation. The computational mesh is partitioned into sub-meshes with local point and edge singularities separated. This is done by using the following greedy algorithm.
Advanced field-solver techniques for RC extraction of integrated circuits
Yu, Wenjian
2014-01-01
Resistance and capacitance (RC) extraction is an essential step in modeling the interconnection wires and substrate coupling effect in nanometer-technology integrated circuits (IC). The field-solver techniques for RC extraction guarantee the accuracy of modeling, and are becoming increasingly important in meeting the demand for accurate modeling and simulation of VLSI designs. Advanced Field-Solver Techniques for RC Extraction of Integrated Circuits presents a systematic introduction to, and treatment of, the key field-solver methods for RC extraction of VLSI interconnects and substrate coupling in mixed-signal ICs. Various field-solver techniques are explained in detail, with real-world examples to illustrate the advantages and disadvantages of each algorithm. This book will benefit graduate students and researchers in the field of electrical and computer engineering, as well as engineers working in the IC design and design automation industries. Dr. Wenjian Yu is an Associate Professor at the Department of ...
FATCOP: A Fault Tolerant Condor-PVM Mixed Integer Program Solver
National Research Council Canada - National Science Library
Chen, Qun
1999-01-01
We describe FATCOP, a new parallel mixed integer program solver written in PVM. The implementation uses the Condor resource management system to provide a virtual machine composed of otherwise idle computers...
An Investigation of the Performance of the Colored Gauss-Seidel Solver on CPU and GPU
International Nuclear Information System (INIS)
Yoon, Jong Seon; Choi, Hyoung Gwon; Jeon, Byoung Jin
2017-01-01
The performance of the colored Gauss–Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss–Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss–Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.
2012-01-01
at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar
GPU-Accelerated Sparse Matrix Solvers for Large-Scale Simulations, Phase II
National Aeronautics and Space Administration — At the heart of scientific computing and numerical analysis are linear algebra solvers. In scientific computing, the focus is on the partial differential equations...
Tests of a 3D Self Magnetic Field Solver in the Finite Element Gun Code MICHELLE
Nelson, Eric M
2005-01-01
We have recently implemented a prototype 3d self magnetic field solver in the finite-element gun code MICHELLE. The new solver computes the magnetic vector potential on unstructured grids. The solver employs edge basis functions in the curl-curl formulation of the finite-element method. A novel current accumulation algorithm takes advantage of the unstructured grid particle tracker to produce a compatible source vector, for which the singular matrix equation is easily solved by the conjugate gradient method. We will present some test cases demonstrating the capabilities of the prototype 3d self magnetic field solver. One test case is self magnetic field in a square drift tube. Another is a relativistic axisymmetric beam freely expanding in a round pipe.
A distributed-memory hierarchical solver for general sparse linear systems
Energy Technology Data Exchange (ETDEWEB)
Chen, Chao [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering; Pouransari, Hadi [Stanford Univ., CA (United States). Dept. of Mechanical Engineering; Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Boman, Erik G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Darve, Eric [Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering and Dept. of Mechanical Engineering
2017-12-20
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.
Energy Technology Data Exchange (ETDEWEB)
Park, Sun Ho [Korea Maritime and Ocean University, Busan (Korea, Republic of); Rhee, Shin Hyung [Seoul National University, Seoul (Korea, Republic of)
2015-08-15
Incompressible flow solvers are generally used for numerical analysis of cavitating flows, but with limitations in handling compressibility effects on vapor phase. To study compressibility effects on vapor phase and cavity interface, pressure-based incompressible and isothermal compressible flow solvers based on a cell-centered finite volume method were developed using the OpenFOAM libraries. To validate the solvers, cavitating flow around a hemispherical head-form body was simulated and validated against the experimental data. The cavity shedding behavior, length of a re-entrant jet, drag history, and the Strouhal number were compared between the two solvers. The results confirmed that computations of the cavitating flow including compressibility effects improved the reproduction of cavitation dynamics.
Wang, XiaoLiang; Li, JiaChun
2017-12-01
A new solver based on the high-resolution scheme with novel treatments of source terms and interface capture for the Savage-Hutter model is developed to simulate granular avalanche flows. The capability to simulate flow spread and deposit processes is verified through indoor experiments of a two-dimensional granular avalanche. Parameter studies show that reduction in bed friction enhances runout efficiency, and that lower earth pressure restraints enlarge the deposit spread. The April 9, 2000, Yigong avalanche in Tibet, China, is simulated as a case study by this new solver. The predicted results, including evolution process, deposit spread, and hazard impacts, generally agree with site observations. It is concluded that the new solver for the Savage-Hutter equation provides a comprehensive software platform for granular avalanche simulation at both experimental and field scales. In particular, the solver can be a valuable tool for providing necessary information for hazard forecasts, disaster mitigation, and countermeasure decisions in mountainous areas.
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.
Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
Woźniak, Maciej; Paszyński, Maciej R.; Pardo, D.; Dalcin, Lisandro; Calo, Victor M.
2015-01-01
This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution
An Investigation of the Performance of the Colored Gauss-Seidel Solver on CPU and GPU
Energy Technology Data Exchange (ETDEWEB)
Yoon, Jong Seon; Choi, Hyoung Gwon [Seoul Nat’l Univ. of Science and Technology, Seoul (Korea, Republic of); Jeon, Byoung Jin [Yonsei Univ., Seoul (Korea, Republic of)
2017-02-15
The performance of the colored Gauss–Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss–Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss–Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-11-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Duddu, Ravindra
2011-10-05
We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.
Sharonov, M. A.; Sharonova, O. V.; Sharonova, V. P.
2018-03-01
The article is an attempt to create a model built using Eulerian circles (Venn diagrams) to illustrate the methodological impact of recent Federal Law 283-FZ “On the independent evaluation of qualifications” and new Federal State Educational Standards of higher education of generation 3++ on educational process in Russia. In modern economic conditions, the ability to correctly assess the role of professional standards, as a matter of fact, some set, the degree of intersection with the approximate basic educational program and the Federal State Educational Standards becomes an important factor on which in the future will depend not only the demand of graduates in the labor market, but also the possibility of passing the professional and public accreditation of the proposed program.
Haines, P. E.; Esler, J. G.; Carver, G. D.
2014-06-01
A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model, RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments) to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time symmetric, suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.
Energy Technology Data Exchange (ETDEWEB)
Pechstein, Astrid, E-mail: astrid.pechstein@jku.at [Johannes Kepler University Linz, Institute of Technical Mechanics (Austria); Gerstmayr, Johannes, E-mail: johannes.gerstmayr@accm.co.at [Austrian Center of Competence in Mechatronics (Austria)
2013-10-15
In the scope of this paper, a finite-element formulation for an axially moving beam is presented. The beam element is based on the absolute nodal coordinate formulation, where position and slope vectors are used as degrees of freedom instead of rotational parameters. The equations of motion for an axially moving beam are derived from generalized Lagrange equations in a Lagrange-Eulerian sense. This procedure yields equations which can be implemented as a straightforward augmentation to the standard equations of motion for a Bernoulli-Euler beam. Moreover, a contact model for frictional contact between an axially moving strip and rotating rolls is presented. To show the efficiency of the method, simulations of a belt drive are presented.
DEFF Research Database (Denmark)
Pang, Kar Mun; Jangi, Mehdi; Bai, Xue-Song
2018-01-01
This paper aims to simulate diesel spray flames across a wide range of engine-like conditions using the Eulerian Stochastic Field probability density function (ESF-PDF) model. The ESF model is coupled with the Chemistry Coordinate Mapping approach to expedite the calculation. A convergence study...... is carried out for a number of stochastic fields at five different conditions, covering both conventional diesel combustion and low-temperature combustion regimes. Ignition delay time, flame lift-off length as well as distributions of temperature and various combustion products are used to evaluate...... the performance of the model. The peak values of these properties generated using thirty-two stochastic fields are found to converge, with a maximum relative difference of 27% as compared to those from a greater number of stochastic fields. The ESF-PDF model with thirty-two stochastic fields performs reasonably...
Thermal Loss of High-Q Antennas in Time Domain vs. Frequency Domain Solver
DEFF Research Database (Denmark)
Bahramzy, Pevand; Pedersen, Gert Frølund
2014-01-01
High-Q structures pose great challenges to their loss simulations in Time Domain Solvers (TDS). Therefore, in this work the thermal loss of high-Q antennas is calculated both in TDS and Frequency Domain Solver (FDS), which are then compared with each other and with the actual measurements....... The thermal loss calculation in FDS is shown to be more accurate for high-Q antennas....
Motivation, Challenge, and Opportunity of Successful Solvers on an Innovation Platform
DEFF Research Database (Denmark)
Hossain, Mokter
2017-01-01
. The main motivational factors of successful solvers engaged in problem solving are money, learning, fun, sense of achievement, passion, and networking. Major challenges solvers face include unclear or insufficient problem description, lack of option for communication, language barrier, time zone...... other experts, the ability to work in a diverse environment, options of work after retirement and from distant locations, and a new source of income....
DEFF Research Database (Denmark)
Hossain, Mokter
2018-01-01
. The main motivational factors of successful solvers engaged in problem solving are money, learning, fun, sense of achievement, passion, and networking. Major challenges solvers face include unclear or insufficient problem description, lack of option for communication, language barrier, time zone...... other experts, the ability to work in a diverse environment, options of work after retirement and from distant locations, and a new source of income....
Development of RBDGG Solver and Its Application to System Reliability Analysis
International Nuclear Information System (INIS)
Kim, Man Cheol
2010-01-01
For the purpose of making system reliability analysis easier and more intuitive, RBDGG (Reliability Block diagram with General Gates) methodology was introduced as an extension of the conventional reliability block diagram. The advantage of the RBDGG methodology is that the structure of a RBDGG model is very similar to the actual structure of the analyzed system, and therefore the modeling of a system for system reliability and unavailability analysis becomes very intuitive and easy. The main idea of the development of the RBDGG methodology is similar with that of the development of the RGGG (Reliability Graph with General Gates) methodology, which is an extension of a conventional reliability graph. The newly proposed methodology is now implemented into a software tool, RBDGG Solver. RBDGG Solver was developed as a WIN32 console application. RBDGG Solver receives information on the failure modes and failure probabilities of each component in the system, along with the connection structure and connection logics among the components in the system. Based on the received information, RBDGG Solver automatically generates a system reliability analysis model for the system, and then provides the analysis results. In this paper, application of RBDGG Solver to the reliability analysis of an example system, and verification of the calculation results are provided for the purpose of demonstrating how RBDGG Solver is used for system reliability analysis
Influence of an SN solver in a fine-mesh neutronics/thermal-hydraulics framework
International Nuclear Information System (INIS)
Jareteg, Klas; Vinai, Paolo; Demaziere, Christophe; Sasic, Srdjan
2015-01-01
In this paper a study on the influence of a neutron discrete ordinates (S N ) solver within a fine-mesh neutronic/thermal-hydraulic methodology is presented. The methodology consists of coupling a neutronic solver with a single-phase fluid solver, and it is aimed at computing the two fields on a three-dimensional (3D) sub-pin level. The cross-sections needed for the neutron transport equations are pre-generated using a Monte Carlo approach. The coupling is resolved in an iterative manner with full convergence of both fields. A conservative transfer of the full 3D information is achieved, allowing for a proper coupling between the neutronic and the thermal-hydraulic meshes on the finest calculated scales. The discrete ordinates solver is benchmarked against a Monte Carlo reference solution for a two-dimensional (2D) system. The results confirm the need of a high number of ordinates, giving a satisfactory accuracy in k eff and scalar flux profile applying S 16 for 16 energy groups. The coupled framework is used to compare the S N implementation and a solver based on the neutron diffusion approximation for a full 3D system of a quarter of a symmetric, 7x7 array in an infinite lattice setup. In this case, the impact of the discrete ordinates solver shows to be significant for the coupled system, as demonstrated in the calculations of the temperature distributions. (author)
Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems
Chávez, Gustavo
2017-12-15
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.
Accelerated Cyclic Reduction: A Distributed-Memory Fast Solver for Structured Linear Systems
Chá vez, Gustavo; Turkiyyah, George; Zampini, Stefano; Ltaief, Hatem; Keyes, David E.
2017-01-01
We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions. Algorithmic synergies between Cyclic Reduction and hierarchical matrix arithmetic operations result in a solver that has O(kNlogN(logN+k2)) arithmetic complexity and O(k Nlog N) memory footprint, where N is the number of degrees of freedom and k is the rank of a block in the hierarchical approximation, and which exhibits substantial concurrency. We provide a baseline for performance and applicability by comparing with the multifrontal method with and without hierarchical semi-separable matrices, with algebraic multigrid and with the classic cyclic reduction method. Over a set of large-scale elliptic systems with features of nonsymmetry and indefiniteness, the robustness of the direct solvers extends beyond that of the multigrid solver, and relative to the multifrontal approach ACR has lower or comparable execution time and size of the factors, with substantially lower numerical ranks. ACR exhibits good strong and weak scaling in a distributed context and, as with any direct solver, is advantageous for problems that require the solution of multiple right-hand sides. Numerical experiments show that the rank k patterns are of O(1) for the Poisson equation and of O(n) for the indefinite Helmholtz equation. The solver is ideal in situations where low-accuracy solutions are sufficient, or otherwise as a preconditioner within an iterative method.
International Nuclear Information System (INIS)
Yeh, Gour-Tsyh
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N 2 as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids
Continuous-time quantum Monte Carlo impurity solvers
Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias
2011-04-01
Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as
Deploy production sliding mesh capability with linear solver benchmarking.
Energy Technology Data Exchange (ETDEWEB)
Domino, Stefan P. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Thomas, Stephen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Williams, Alan B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ananthan, Shreyas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knaus, Robert C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Overfelt, James [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sprague, Mike [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rood, Jon [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2018-02-01
overall simulation time when using the full Tpetra solver stack and nearly 35% when using a mixed Tpetra- Hypre-based solver stack. The report also highlights the project achievement of surpassing the 1 billion element mesh scale for a production V27 hybrid mesh. A detailed timing breakdown is presented that again suggests work to be done in the setup events associated with the linear system. In order to mitigate these initialization costs, several application paths have been explored, all of which are designed to reduce the frequency of matrix reinitialization. Methods such as removing Jacobian entries on the dynamic matrix columns (in concert with increased inner equation iterations), and lagging of Jacobian entries have reduced setup times at the cost of numerical stability. Artificially increasing, or bloating, the matrix stencil to ensure that full Jacobians are included is developed with results suggesting that this methodology is useful in decreasing reinitialization events without loss of matrix contributions. With the above foundational advances in computational capability, the project is well positioned to begin scientific inquiry on a variety of wind-farm physics such as turbine/turbine wake interactions.
A parallel solver for huge dense linear systems
Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.
2011-11-01
HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system
A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS
International Nuclear Information System (INIS)
Davis, Shane W.; Stone, James M.; Jiang Yanfei
2012-01-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
Using Python to Construct a Scalable Parallel Nonlinear Wave Solver
Mandli, Kyle
2011-01-01
Computational scientists seek to provide efficient, easy-to-use tools and frameworks that enable application scientists within a specific discipline to build and/or apply numerical models with up-to-date computing technologies that can be executed on all available computing systems. Although many tools could be useful for groups beyond a specific application, it is often difficult and time consuming to combine existing software, or to adapt it for a more general purpose. Python enables a high-level approach where a general framework can be supplemented with tools written for different fields and in different languages. This is particularly important when a large number of tools are necessary, as is the case for high performance scientific codes. This motivated our development of PetClaw, a scalable distributed-memory solver for time-dependent nonlinear wave propagation, as a case-study for how Python can be used as a highlevel framework leveraging a multitude of codes, efficient both in the reuse of code and programmer productivity. We present scaling results for computations on up to four racks of Shaheen, an IBM BlueGene/P supercomputer at King Abdullah University of Science and Technology. One particularly important issue that PetClaw has faced is the overhead associated with dynamic loading leading to catastrophic scaling. We use the walla library to solve the issue which does so by supplanting high-cost filesystem calls with MPI operations at a low enough level that developers may avoid any changes to their codes.
Control of error and convergence in ODE solvers
International Nuclear Information System (INIS)
Gustafsson, K.
1992-03-01
Feedback is a general principle that can be used in many different contexts. In this thesis it is applied to numerical integration of ordinary differential equations. An advanced integration method includes parameters and variables that should be adjusted during the execution. In addition, the integration method should be able to automatically handle situations such as: initialization, restart after failures, etc. In this thesis we regard the algorithms for parameter adjustment and supervision as a controller. The controlled measures different variable that tell the current status of the integration, and based on this information it decides how to continue. The design of the controller is vital in order to accurately and efficiently solve a large class of ordinary differential equations. The application of feedback control may appear farfetched, but numerical integration methods are in fact dynamical systems. This is often overlooked in traditional numerical analysis. We derive dynamic models that describe the behavior of the integration method as well as the standard control algorithms in use today. Using these models it is possible to analyze properties of current algorithms, and also explain some generally observed misbehaviors. Further, we use the acquired insight to derive new and improved control algorithms, both for explicit and implicit Runge-Kutta methods. In the explicit case, the new controller gives good overall performance. In particular it overcomes the problem with oscillating stepsize sequence that is often experienced when the stepsize is restricted by numerical stability. The controller for implicit methods is designed so that it tracks changes in the differential equation better than current algorithms. In addition, it includes a new strategy for the equation solver, which allows the stepsize to vary more freely. This leads to smoother error control without excessive operations on the iteration matrix. (87 refs.) (au)
A multi-solver quasi-Newton method for the partitioned simulation of fluid-structure interaction
International Nuclear Information System (INIS)
Degroote, J; Annerel, S; Vierendeels, J
2010-01-01
In partitioned fluid-structure interaction simulations, the flow equations and the structural equations are solved separately. Consequently, the stresses and displacements on both sides of the fluid-structure interface are not automatically in equilibrium. Coupling techniques like Aitken relaxation and the Interface Block Quasi-Newton method with approximate Jacobians from Least-Squares models (IBQN-LS) enforce this equilibrium, even with black-box solvers. However, all existing coupling techniques use only one flow solver and one structural solver. To benefit from the large number of multi-core processors in modern clusters, a new Multi-Solver Interface Block Quasi-Newton (MS-IBQN-LS) algorithm has been developed. This algorithm uses more than one flow solver and structural solver, each running in parallel on a number of cores. One-dimensional and three-dimensional numerical experiments demonstrate that the run time of a simulation decreases as the number of solvers increases, albeit at a slower pace. Hence, the presented multi-solver algorithm accelerates fluid-structure interaction calculations by increasing the number of solvers, especially when the run time does not decrease further if more cores are used per solver.
s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid
Energy Technology Data Exchange (ETDEWEB)
Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lijewski, Mike [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Almgren, Ann [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Carson, Erin [Univ. of California, Berkeley, CA (United States); Knight, Nicholas [Univ. of California, Berkeley, CA (United States); Demmel, James [Univ. of California, Berkeley, CA (United States)
2014-08-14
Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.
Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications
Sun, Xian-He
1997-01-01
Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm
Balancing Energy and Performance in Dense Linear System Solvers for Hybrid ARM+GPU platforms
Directory of Open Access Journals (Sweden)
Juan P. Silva
2016-04-01
Full Text Available The high performance computing community has traditionally focused uniquely on the reduction of execution time, though in the last years, the optimization of energy consumption has become a main issue. A reduction of energy usage without a degradation of performance requires the adoption of energy-efficient hardware platforms accompanied by the development of energy-aware algorithms and computational kernels. The solution of linear systems is a key operation for many scientific and engineering problems. Its relevance has motivated an important amount of work, and consequently, it is possible to find high performance solvers for a wide variety of hardware platforms. In this work, we aim to develop a high performance and energy-efficient linear system solver. In particular, we develop two solvers for a low-power CPU-GPU platform, the NVIDIA Jetson TK1. These solvers implement the Gauss-Huard algorithm yielding an efficient usage of the target hardware as well as an efficient memory access. The experimental evaluation shows that the novel proposal reports important savings in both time and energy-consumption when compared with the state-of-the-art solvers of the platform.
A CFD Heterogeneous Parallel Solver Based on Collaborating CPU and GPU
Lai, Jianqi; Tian, Zhengyu; Li, Hua; Pan, Sha
2018-03-01
Since Graphic Processing Unit (GPU) has a strong ability of floating-point computation and memory bandwidth for data parallelism, it has been widely used in the areas of common computing such as molecular dynamics (MD), computational fluid dynamics (CFD) and so on. The emergence of compute unified device architecture (CUDA), which reduces the complexity of compiling program, brings the great opportunities to CFD. There are three different modes for parallel solution of NS equations: parallel solver based on CPU, parallel solver based on GPU and heterogeneous parallel solver based on collaborating CPU and GPU. As we can see, GPUs are relatively rich in compute capacity but poor in memory capacity and the CPUs do the opposite. We need to make full use of the GPUs and CPUs, so a CFD heterogeneous parallel solver based on collaborating CPU and GPU has been established. Three cases are presented to analyse the solver’s computational accuracy and heterogeneous parallel efficiency. The numerical results agree well with experiment results, which demonstrate that the heterogeneous parallel solver has high computational precision. The speedup on a single GPU is more than 40 for laminar flow, it decreases for turbulent flow, but it still can reach more than 20. What’s more, the speedup increases as the grid size becomes larger.
A comparison of viscous-plastic sea ice solvers with and without replacement pressure
Kimmritz, Madlen; Losch, Martin; Danilov, Sergey
2017-07-01
Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian-free Newton-Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them.
International Nuclear Information System (INIS)
Marinelli, V.; Pellei, A.; Vallero, P.; Vitanza, C.
1975-01-01
The calculations performed in comparison of the ''Lagrangian point of view'', by means of the DOLCE computer code with the local space--time approach of the ''Eulerian point of view'' indicate that the two methods give substantially equivalent results and predict satisfactorily the onset of the transient CHF for the Centro Informazioni Studi Esperienze annuli experimental data and General Electric Company 16-rod bundles data under typical boiling water reactor transients, including loss-of-coolant accident simulations. 9 references
Parallelization of the preconditioned IDR solver for modern multicore computer systems
Bessonov, O. A.; Fedoseyev, A. I.
2012-10-01
This paper present the analysis, parallelization and optimization approach for the large sparse matrix solver CNSPACK for modern multicore microprocessors. CNSPACK is an advanced solver successfully used for coupled solution of stiff problems arising in multiphysics applications such as CFD, semiconductor transport, kinetic and quantum problems. It employs iterative IDR algorithm with ILU preconditioning (user chosen ILU preconditioning order). CNSPACK has been successfully used during last decade for solving problems in several application areas, including fluid dynamics and semiconductor device simulation. However, there was a dramatic change in processor architectures and computer system organization in recent years. Due to this, performance criteria and methods have been revisited, together with involving the parallelization of the solver and preconditioner using Open MP environment. Results of the successful implementation for efficient parallelization are presented for the most advances computer system (Intel Core i7-9xx or two-processor Xeon 55xx/56xx).
Status and Perspective of the Hydraulic Solver development for SPACE code
International Nuclear Information System (INIS)
Lee, S. Y.; Oh, M. T.; Park, J. C.; Ahn, S. J.; Park, C. E.; Lee, E. J.; Na, Y. W.
2008-01-01
KOPEC has been developing a hydraulic solver for SPACE code. The governing equations for the solver can be obtained through several steps of modeling and approximations from the basic material transport principles. Once the governing equations are fixed, a proper discretization procedure should be followed to get the difference equations that can be solved by well established matrix solvers. Of course, the mesh generation and handling procedures are necessary for the discretization process. At present, the preliminary test version has been constructed and being tested. The selection of the compiler language was debated openly. C++ was chosen as a basis compiler language. But other language such as FORTRAN can be used as it is necessary. The steps mentioned above are explained in the following sections. Test results are presented by other companion papers in this meeting. Future activities will be described in the conclusion section
A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.
A Kohn–Sham equation solver based on hexahedral finite elements
International Nuclear Information System (INIS)
Fang Jun; Gao Xingyu; Zhou Aihui
2012-01-01
We design a Kohn–Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C 60 , C 120 , and C 275 H 172 . It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.
Towards Green Multi-frontal Solver for Adaptive Finite Element Method
AbbouEisha, H.; Moshkov, Mikhail; Jopek, K.; Gepner, P.; Kitowski, J.; Paszyn'ski, M.
2015-01-01
In this paper we present the optimization of the energy consumption for the multi-frontal solver algorithm executed over two dimensional grids with point singularities. The multi-frontal solver algorithm is controlled by so-called elimination tree, defining the order of elimination of rows from particular frontal matrices, as well as order of memory transfers for Schur complement matrices. For a given mesh there are many possible elimination trees resulting in different number of floating point operations (FLOPs) of the solver or different amount of data trans- ferred via memory transfers. In this paper we utilize the dynamic programming optimization procedure and we compare elimination trees optimized with respect to FLOPs with elimination trees optimized with respect to energy consumption.
Efficiency optimization of a fast Poisson solver in beam dynamics simulation
Zheng, Dawei; Pöplau, Gisela; van Rienen, Ursula
2016-01-01
Calculating the solution of Poisson's equation relating to space charge force is still the major time consumption in beam dynamics simulations and calls for further improvement. In this paper, we summarize a classical fast Poisson solver in beam dynamics simulations: the integrated Green's function method. We introduce three optimization steps of the classical Poisson solver routine: using the reduced integrated Green's function instead of the integrated Green's function; using the discrete cosine transform instead of discrete Fourier transform for the Green's function; using a novel fast convolution routine instead of an explicitly zero-padded convolution. The new Poisson solver routine preserves the advantages of fast computation and high accuracy. This provides a fast routine for high performance calculation of the space charge effect in accelerators.
International Nuclear Information System (INIS)
Secher, Bernard; Belliard, Michel; Calvin, Christophe
2009-01-01
This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost
Towards Green Multi-frontal Solver for Adaptive Finite Element Method
AbbouEisha, H.
2015-06-01
In this paper we present the optimization of the energy consumption for the multi-frontal solver algorithm executed over two dimensional grids with point singularities. The multi-frontal solver algorithm is controlled by so-called elimination tree, defining the order of elimination of rows from particular frontal matrices, as well as order of memory transfers for Schur complement matrices. For a given mesh there are many possible elimination trees resulting in different number of floating point operations (FLOPs) of the solver or different amount of data trans- ferred via memory transfers. In this paper we utilize the dynamic programming optimization procedure and we compare elimination trees optimized with respect to FLOPs with elimination trees optimized with respect to energy consumption.
Energy Technology Data Exchange (ETDEWEB)
Secher, Bernard [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SFME/LGLS, Bat. 454, F-91191 Gif-sur-Yvette Cedex (France)], E-mail: bsecher@cea.fr; Belliard, Michel [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Cadarache DER/SSTH/LMDL, Bat. 238, F-13108 Saint-Paul-lez-Durance Cedex (France); Calvin, Christophe [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SERMA/LLPR, Bat. 470, F-91191 Gif-sur-Yvette Cedex (France)
2009-01-15
This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost.
A fast direct solver for boundary value problems on locally perturbed geometries
Zhang, Yabin; Gillman, Adrianna
2018-03-01
Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.
A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements
Chávez, Gustavo
2017-03-17
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\\\\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\\\\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.
Wavelet-Based Poisson Solver for Use in Particle-in-Cell Simulations
Terzic, Balsa; Mihalcea, Daniel; Pogorelov, Ilya V
2005-01-01
We report on a successful implementation of a wavelet-based Poisson solver for use in 3D particle-in-cell simulations. One new aspect of our algorithm is its ability to treat the general (inhomogeneous) Dirichlet boundary conditions. The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modelling of the Fermilab/NICADD and AES/JLab photoinjectors.
Wavelet-based Poisson Solver for use in Particle-In-Cell Simulations
International Nuclear Information System (INIS)
Terzic, B.; Mihalcea, D.; Bohn, C.L.; Pogorelov, I.V.
2005-01-01
We report on a successful implementation of a wavelet based Poisson solver for use in 3D particle-in-cell (PIC) simulations. One new aspect of our algorithm is its ability to treat the general(inhomogeneous) Dirichlet boundary conditions (BCs). The solver harnesses advantages afforded by the wavelet formulation, such as sparsity of operators and data sets, existence of effective preconditioners, and the ability simultaneously to remove numerical noise and further compress relevant data sets. Having tested our method as a stand-alone solver on two model problems, we merged it into IMPACT-T to obtain a fully functional serial PIC code. We present and discuss preliminary results of application of the new code to the modeling of the Fermilab/NICADD and AES/JLab photoinjectors
Rahaman, Md. Mashiur; Islam, Hafizul; Islam, Md. Tariqul; Khondoker, Md. Reaz Hasan
2017-12-01
Maneuverability and resistance prediction with suitable accuracy is essential for optimum ship design and propulsion power prediction. This paper aims at providing some of the maneuverability characteristics of a Japanese bulk carrier model, JBC in calm water using a computational fluid dynamics solver named SHIP Motion and OpenFOAM. The solvers are based on the Reynolds average Navier-Stokes method (RaNS) and solves structured grid using the Finite Volume Method (FVM). This paper comprises the numerical results of calm water test for the JBC model with available experimental results. The calm water test results include the total drag co-efficient, average sinkage, and trim data. Visualization data for pressure distribution on the hull surface and free water surface have also been included. The paper concludes that the presented solvers predict the resistance and maneuverability characteristics of the bulk carrier with reasonable accuracy utilizing minimum computational resources.
Pedone, Maria; Granieri, Domenico; Moretti, Roberto; Fedele, Alessandro; Troise, Claudia; Somma, Renato; De Natale, Giuseppe
2017-12-01
This study investigates fumarolic CO2 emissions at Campi Flegrei (Southern Italy) and their dispersion in the lowest atmospheric boundary layer. We innovatively utilize a Lagrangian Stochastic dispersion model (WindTrax) combined with an Eulerian model (DISGAS) to diagnose the dispersion of diluted gas plumes over large and complex topographic domains. New measurements of CO2 concentrations acquired in February and October 2014 in the area of Pisciarelli and Solfatara, the two major fumarolic fields of Campi Flegrei caldera, and simultaneous measurements of meteorological parameters are used to: 1) test the ability of WindTrax to calculate the fumarolic CO2 flux from the investigated sources, and 2) perform predictive numerical simulations to resolve the mutual interference between the CO2 emissions of the two adjacent areas. This novel approach allows us to a) better quantify the CO2 emission of the fumarolic source, b) discriminate ;true; CO2 contributions for each source, and c) understand the potential impact of the composite CO2 plume (Pisciarelli ;plus; Solfatara) on the highly populated areas inside the Campi Flegrei caldera.
Cetina-Heredia, Paulina; van Sebille, Erik; Matear, Richard J.; Roughan, Moninya
2018-02-01
The Great Australian Bight (GAB), a coastal sea bordered by the Pacific, Southern, and Indian Oceans, sustains one of the largest fisheries in Australia but the geographical origin of nutrients that maintain its productivity is not fully known. We use 12 years of modeled data from a coupled hydrodynamic and biogeochemical model and an Eulerian-Lagrangian approach to quantify nitrate supply to the GAB and the region between the GAB and the Subantarctic Australian Front (GAB-SAFn), identify phytoplankton growth within the GAB, and ascertain the source of nitrate that fuels it. We find that nitrate concentrations have a decorrelation timescale of ˜60 days; since most of the water from surrounding oceans takes longer than 60 days to reach the GAB, 23% and 75% of nitrate used by phytoplankton to grow are sourced within the GAB and from the GAB-SAFn, respectively. Thus, most of the nitrate is recycled locally. Although nitrate concentrations and fluxes into the GAB are greater below 100 m than above, 79% of the nitrate fueling phytoplankton growth is sourced from above 100 m. Our findings suggest that topographical uplift and stratification erosion are key mechanisms delivering nutrients from below the nutricline into the euphotic zone and triggering large phytoplankton growth. We find annual and semiannual periodicities in phytoplankton growth, peaking in the austral spring and autumn when the mixed layer deepens leading to a subsurface maximum of phytoplankton growth. This study highlights the importance of examining phytoplankton growth at depth and the utility of Lagrangian approaches.
Ndong, Mouhamed; Bird, David; Nguyen Quang, Tri; Kahawita, René; Hamilton, David; de Boutray, Marie Laure; Prévost, Michèle; Dorner, Sarah
2017-12-15
Toxic cyanobacteria (CB) blooms are being reported in an increasing number of water bodies worldwide. As drinking water (DW) treatment can be disrupted by CB, in addition to long term management plans, short term operational decision-making tools are needed that enable an understanding of the temporal variability of CB movement in relation to drinking water intakes. In this paper, we propose a novel conservative model based on a Eulerian framework and compare results with data from CB blooms in Missisquoi Bay (Québec, Canada). The hydrodynamic model considered the effects of wind and light intensity, demonstrated that current understanding of cell buoyancy in relation to light intensity in full-scale systems is incomplete and some factors are yet to be fully characterized. Factors affecting CB buoyancy play a major role in the formation of a thin surface layer that could be of ecological importance with regards to cell concentrations and toxin production. Depending on velocities, wind contributes either to the accumulation or to the dispersion of CB. Lake recirculation effects have a tendency to create zones of low CB concentrations in a water body. Monitoring efforts and future research should focus on short-term variations of CB throughout the water column and the characterization of factors other than light intensity that affect cell buoyancy. These factors are critical for understanding the risk of breakthrough into treatment plants as well as the formation of surface scums and subsequent toxin production. Copyright © 2017 Elsevier Ltd. All rights reserved.
A continuum treatment of sliding in Eulerian simulations of solid-solid and solid-fluid interfaces
Subramaniam, Akshay; Ghaisas, Niranjan; Lele, Sanjiva
2017-11-01
A novel treatment of sliding is developed for use in an Eulerian framework for simulating elastic-plastic deformations of solids coupled with fluids. In this method, embedded interfacial boundary conditions for perfect sliding are imposed by enforcing the interface normal to be a principal direction of the Cauchy stress and appropriate consistency conditions ensure correct transmission and reflection of waves at the interface. This sliding treatment may be used either to simulate a solid-solid sliding interface or to incorporate an internal slip boundary condition at a solid-fluid interface. Sliding laws like the Coulomb friction law can also be incorporated with relative ease into this framework. Simulations of sliding interfaces are conducted using a 10th order compact finite difference scheme and a Localized Artificial Diffusivity (LAD) scheme for shock and interface capturing. 1D and 2D simulations are used to assess the accuracy of the sliding treatment. The Richmyer-Meshkov instability between copper and aluminum is simulated with this sliding treatment as a demonstration test case. Support for this work was provided through Grant B612155 from the Lawrence Livermore National Laboratory, US Department of Energy.
K-FIX, Transient 2 Phase Flow Hydrodynamic in 2-D Planar or Cylindrical Geometry, Eulerian Method
International Nuclear Information System (INIS)
Rivard, W. C.; Torrey, M. D.
1980-01-01
1 - Description of problem or function: The transient dynamics of two- dimensional, two-phase flow with interfacial exchange are calculated at all flow speeds. Each phase is described in terms of its own density, velocity, and temperature. Separate sets of field equations govern the gas and liquid phase dynamics. The six field equations for the two phases couple through mass, momentum, and energy exchange. 2 - Method of solution: The equations are solved using an Eulerian finite difference technique that implicitly couples the rates of phase transitions, momentum, and energy exchange to determination of the pressure, density, and velocity fields. The implicit solution is accomplished iteratively using a point relaxation technique without linearizing the equations, thus eliminating the need for numerous derivative terms. Solutions can be obtained in one and two space dimensions in plane geometry and in cylindrical geometry with axial symmetry and zero azimuthal velocity. Solutions in spherical geometry can also be obtained in one space dimension. The geometric region of interest is divided into many finite-sized, space-fixed zones called cells which form the computing mesh. In plane geometry the cells are rectangular cylinders, in cylindrical geometry they are toroids with rectangular cross section, and in spherical geometry they are spherical shells
Janatka, Mirek; Ramdoo, Krishan S.; Tatla, Taran; Pachtrachai, Krittin; Elson, Daniel S.; Stoyanov, Danail
2017-03-01
The tympanic membrane (TM) is the bridging element between the pressure waves of sound in air and the ossicular chain. It allows for sound to be conducted into the inner ear, achieving the human sense of hearing. Otitis media with effusion (OME, commonly referred to as `glue ear') is a typical condition in infants that prevents the vibration of the TM and causes conductive hearing loss, this can lead to stunting early stage development if undiagnosed. Furthermore, OME is hard to identify in this age group; as they cannot respond to typical audiometry tests. Tympanometry allows for the mobility of the TM to be examined without patient response, but requires expensive apparatus and specialist training. By combining a smartphone equipped with a 240 frames per second video recording capability with an otoscopic clip-on accessory, this paper presents a novel application of Eulerian Video Magnification (EVM) to video-otology, that could provide assistance in diagnosing OME. We present preliminary results showing a spatio-temporal slice taken from an exaggerated video visualization of the TM being excited in vivo on a healthy ear. Our preliminary results demonstrate the potential for using such an approach for diagnosing OME under visual inspection as alternative to tympanometry, which could be used remotely and hence help diagnosis in a wider population pool.
International Nuclear Information System (INIS)
Briere, E.; Larrauri, D.; Olive, J.
1995-01-01
For about four years, Electricite de France has been developing a 3-D computer code for the Eulerian simulation of two-phase flows. This code, named ASTRID, is based on the six-equation two-fluid model. Boiling water flows, such as those encountered in nuclear reactors, are among the main applications of ASTRID. In order to provide ASTRID with closure laws and boundary conditions suitable for boiling flows, a boiling model has been developed by EDF and the Institut de Mecanique des Fluides de Toulouse. In the fluid, the heat and mass transfer between a bubble and the liquid is being modelled. At the heating wall, the incipient boiling point is determined according to Hsu's criterion and the boiling heat flux is split into three additive terms: a convective term, a quenching term and a vaporisation term. This model uses several correlations. EDF's program in boiling two-phase flows also includes experimental studies, some of which are performed in collaboration with other laboratories. Refrigerant subcooled boiling both in tubular (DEBORA experiment, CEN Grenoble) and in annular geometry (Arizona State University Experiment) have been computed with ASTRID. The simulations show the satisfactory results already obtained on void fraction and liquid temperature. Ways of improvement of the model are drawn especially on the dynamical part
Energy Technology Data Exchange (ETDEWEB)
Wang, C.Y.
1993-06-01
This paper describes fluid-structure-interaction and structure response analyses of a reactor vessel subjected to loadings associated with postulated accidents, using the hybrid Lagrangian-Eulerian code ALICE-II. This code has been improved recently to accommodate many features associated with innovative designs of reactor vessels. Calculational capabilities have been developed to treat water in the reactor cavity outside the vessel, internal shield structures and internal thin shells. The objective of the present analyses is to study the cover response and potential for missile generation in response to a fuel-coolant interaction in the core region. Three calculations were performed using the cover weight as a parameter. To study the effect of the cavity water, vessel response calculations for both wet- and dry-cavity designs are compared. Results indicate that for all cases studied and for the design parameters assumed, the calculated cover displacements are all smaller than the bolts` ultimate displacement and no missile generation of the closure head is predicted. Also, solutions reveal that the cavity water of the wet-cavity design plays an important role of restraining the downward displacement of the bottom head. Based on these studies, the analyses predict that the structure integrity is maintained throughout the postulated accident for the wet-cavity design.
Energy Technology Data Exchange (ETDEWEB)
Wang, C.Y.
1993-01-01
This paper describes fluid-structure-interaction and structure response analyses of a reactor vessel subjected to loadings associated with postulated accidents, using the hybrid Lagrangian-Eulerian code ALICE-II. This code has been improved recently to accommodate many features associated with innovative designs of reactor vessels. Calculational capabilities have been developed to treat water in the reactor cavity outside the vessel, internal shield structures and internal thin shells. The objective of the present analyses is to study the cover response and potential for missile generation in response to a fuel-coolant interaction in the core region. Three calculations were performed using the cover weight as a parameter. To study the effect of the cavity water, vessel response calculations for both wet- and dry-cavity designs are compared. Results indicate that for all cases studied and for the design parameters assumed, the calculated cover displacements are all smaller than the bolts' ultimate displacement and no missile generation of the closure head is predicted. Also, solutions reveal that the cavity water of the wet-cavity design plays an important role of restraining the downward displacement of the bottom head. Based on these studies, the analyses predict that the structure integrity is maintained throughout the postulated accident for the wet-cavity design.
Energy Technology Data Exchange (ETDEWEB)
Briere, E.; Larrauri, D.; Olive, J. [Electricite de France, Chatou (France)
1995-09-01
For about four years, Electricite de France has been developing a 3-D computer code for the Eulerian simulation of two-phase flows. This code, named ASTRID, is based on the six-equation two-fluid model. Boiling water flows, such as those encountered in nuclear reactors, are among the main applications of ASTRID. In order to provide ASTRID with closure laws and boundary conditions suitable for boiling flows, a boiling model has been developed by EDF and the Institut de Mecanique des Fluides de Toulouse. In the fluid, the heat and mass transfer between a bubble and the liquid is being modelled. At the heating wall, the incipient boiling point is determined according to Hsu`s criterion and the boiling heat flux is split into three additive terms: a convective term, a quenching term and a vaporisation term. This model uses several correlations. EDF`s program in boiling two-phase flows also includes experimental studies, some of which are performed in collaboration with other laboratories. Refrigerant subcooled boiling both in tubular (DEBORA experiment, CEN Grenoble) and in annular geometry (Arizona State University Experiment) have been computed with ASTRID. The simulations show the satisfactory results already obtained on void fraction and liquid temperature. Ways of improvement of the model are drawn especially on the dynamical part.
Yamaguchi, Satoshi; Tsutsui, Kihei; Satake, Koji; Morikawa, Shigehiro; Shirai, Yoshiaki; Tanaka, Hiromi T
2014-10-01
Our goal was to develop a three-dimensional finite element model that enables dynamic analysis of needle insertion for soft materials. To demonstrate large deformation and fracture, we used the arbitrary Lagrangian-Eulerian (ALE) method for fluid analysis. We performed ALE-based finite element analysis for 3% agar gel and three types of copper needle with bevel tips. To evaluate simulation results, we compared the needle deflection and insertion force with corresponding experimental results acquired with a uniaxial manipulator. We studied the shear stress distribution of agar gel on various time scales. For 30°, 45°, and 60°, differences in deflections of each needle between both sets of results were 2.424, 2.981, and 3.737mm, respectively. For the insertion force, there was no significant difference for mismatching area error (p<0.05) between simulation and experimental results. Our results have the potential to be a stepping stone to develop pre-operative surgical planning to estimate an optimal needle insertion path for MR image-guided microwave coagulation therapy and for analyzing large deformation and fracture in biological tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Rafael Del Valle Vega
2015-10-01
Full Text Available The Brualdi-Shen Conjecture on Eulerian Bipartite Tournaments states that any such graph can be decomposed into oriented 4-cycles. In this article we prove the balanced case of the mentioned conjecture. We show that for any $2n\\times 2n$ bipartite graph $G=(U\\cup V, E$ in which each vertex has $n$-neighbors with biadjacency matrix $M$ (or its transpose there is a proper edge coloring of a column permutation of $M$ denoted $M^{\\sigma}$ in which the nonzero entries of each of the $first$ $n$ columns are colored with elements from the set $\\{n+1, n+2, \\ldots, 2n\\}$ and the nonzero entries of each of the $last$ $n$ columns are colored with elements from the set $\\{1, 2, \\ldots, n\\}$ and if the nonzero entry $M^{\\sigma}_{r,j}$ is colored with color $i$ then $M^{\\sigma}_{r,i}$ must be a zero entry. Such a coloring will induce an oriented 4-cycle decomposition of the bipartite tournament corresponding to $M$. We achieve this by constructing an euler tour on the bipartite tournament which avoids traversing both pair of edges of any two internally disjoint $s$-$t$ 2-paths consecutively, where $s$ and $t$ belong to $V$.
International Nuclear Information System (INIS)
Nelson, E.M.
1993-12-01
Some two-dimensional finite element electromagnetic field solvers are described and tested. For TE and TM modes in homogeneous cylindrical waveguides and monopole modes in homogeneous axisymmetric structures, the solvers find approximate solutions to a weak formulation of the wave equation. Second-order isoparametric lagrangian triangular elements represent the field. For multipole modes in axisymmetric structures, the solver finds approximate solutions to a weak form of the curl-curl formulation of Maxwell's equations. Second-order triangular edge elements represent the radial (ρ) and axial (z) components of the field, while a second-order lagrangian basis represents the azimuthal (φ) component of the field weighted by the radius ρ. A reduced set of basis functions is employed for elements touching the axis. With this basis the spurious modes of the curl-curl formulation have zero frequency, so spurious modes are easily distinguished from non-static physical modes. Tests on an annular ring, a pillbox and a sphere indicate the solutions converge rapidly as the mesh is refined. Computed eigenvalues with relative errors of less than a few parts per million are obtained. Boundary conditions for symmetric, periodic and symmetric-periodic structures are discussed and included in the field solver. Boundary conditions for structures with inversion symmetry are also discussed. Special corner elements are described and employed to improve the accuracy of cylindrical waveguide and monopole modes with singular fields at sharp corners. The field solver is applied to three problems: (1) cross-field amplifier slow-wave circuits, (2) a detuned disk-loaded waveguide linear accelerator structure and (3) a 90 degrees overmoded waveguide bend. The detuned accelerator structure is a critical application of this high accuracy field solver. To maintain low long-range wakefields, tight design and manufacturing tolerances are required
A high-performance Riccati based solver for tree-structured quadratic programs
DEFF Research Database (Denmark)
Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz
2017-01-01
the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...
High-Order Calderón Preconditioned Time Domain Integral Equation Solvers
Valdes, Felipe
2013-05-01
Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.
A Comparison Between Mıcrosoft Excel Solver and Ncss, Spss Routines for Nonlinear Regression Models
Directory of Open Access Journals (Sweden)
Didem Tetik Küçükelçi
2018-02-01
Full Text Available In this study we have tried to compare the results obtained by Microsoft Excel Solver program with those of NCSS and SPSS in some nonlinear regression models. We fit some nonlinear models to data present in http//itl.nist.gov/div898/strd/nls/nls_main.shtml by the three packages. Although EXCEL did not succeed as well as the other packages, we conclude that Microsoft Excel Solver provides us a cheaper and a more interactive way of studying nonlinear models.
High-Order Calderón Preconditioned Time Domain Integral Equation Solvers
Valdes, Felipe; Ghaffari-Miab, Mohsen; Andriulli, Francesco P.; Cools, Kristof; Michielssen,
2013-01-01
Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.
Collier, Nathan; Pardo, David; Dalcí n, Lisandro D.; Paszyński, Maciej R.; Calo, Victor M.
2012-01-01
We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.
Collier, Nathan
2012-03-01
We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause. © 2011 Elsevier B.V.
Development of a global toroidal gyrokinetic Vlasov code with new real space field solver
International Nuclear Information System (INIS)
Obrejan, Kevin; Imadera, Kenji; Li, Ji-Quan; Kishimoto, Yasuaki
2015-01-01
This work introduces a new full-f toroidal gyrokinetic (GK) Vlasov simulation code that uses a real space field solver. This solver enables us to compute the gyro-averaging operators in real space to allow proper treatment of finite Larmor radius (FLR) effects without requiring any particular hypothesis and in any magnetic field configuration (X-point, D-shaped etc). The code was well verified through benchmark tests such as toroidal Ion Temperature Gradient (ITG) instability and collisionless damping of zonal flow. (author)
Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles
Moffitt, Nicholas J.
This work extends existing Galerkin CFD solvers for use in a multi-disciplinary suite. The suite is proposed as a means of modeling advanced flight vehicles, which exhibit strong coupling between aerodynamics, structural dynamics, controls, rigid body motion, propulsion, and heat transfer. Such applications include aeroelastics, aeroacoustics, stability and control, and other highly coupled applications. The suite uses NASA STARS for modeling structural dynamics and heat transfer. Aerodynamics, propulsion, and rigid body dynamics are modeled in one of the five CFD solvers below. Euler2D and Euler3D are Galerkin CFD solvers created at OSU by Cowan (2003). These solvers are capable of modeling compressible inviscid aerodynamics with modal elastics and rigid body motion. This work reorganized these solvers to improve efficiency during editing and at run time. Simple and efficient propulsion models were added, including rocket, turbojet, and scramjet engines. Viscous terms were added to the previous solvers to create NS2D and NS3D. The viscous contributions were demonstrated in the inertial and non-inertial frames. Variable viscosity (Sutherland's equation) and heat transfer boundary conditions were added to both solvers but not verified in this work. Two turbulence models were implemented in NS2D and NS3D: Spalart-Allmarus (SA) model of Deck, et al. (2002) and Menter's SST model (1994). A rotation correction term (Shur, et al., 2000) was added to the production of turbulence. Local time stepping and artificial dissipation were adapted to each model. CFDsol is a Taylor-Galerkin solver with an SA turbulence model. This work improved the time accuracy, far field stability, viscous terms, Sutherland?s equation, and SA model with NS3D as a guideline and added the propulsion models from Euler3D to CFDsol. Simple geometries were demonstrated to utilize current meshing and processing capabilities. Air-breathing hypersonic flight vehicles (AHFVs) represent the ultimate
Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows
Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.
2009-01-01
A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.
A multilevel in space and energy solver for multigroup diffusion eigenvalue problems
Directory of Open Access Journals (Sweden)
Ben C. Yee
2017-09-01
Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.
High-performance small-scale solvers for linear Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca; Sørensen, Hans Henrik Brandenborg; Dammann, Bernd
2014-01-01
, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach...
Efficient Implementation of Solvers for Linear Model Predictive Control on Embedded Devices
DEFF Research Database (Denmark)
Frison, Gianluca; Kwame Minde Kufoalor, D.; Imsland, Lars
2014-01-01
This paper proposes a novel approach for the efficient implementation of solvers for linear MPC on embedded devices. The main focus is to explain in detail the approach used to optimize the linear algebra for selected low-power embedded devices, and to show how the high-performance implementation...
A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver
Liu, Yang
2015-10-26
© 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
Woźniak, Maciej
2014-06-01
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.
A fast mass spring model solver for high-resolution elastic objects
Zheng, Mianlun; Yuan, Zhiyong; Zhu, Weixu; Zhang, Guian
2017-03-01
Real-time simulation of elastic objects is of great importance for computer graphics and virtual reality applications. The fast mass spring model solver can achieve visually realistic simulation in an efficient way. Unfortunately, this method suffers from resolution limitations and lack of mechanical realism for a surface geometry model, which greatly restricts its application. To tackle these problems, in this paper we propose a fast mass spring model solver for high-resolution elastic objects. First, we project the complex surface geometry model into a set of uniform grid cells as cages through *cages mean value coordinate method to reflect its internal structure and mechanics properties. Then, we replace the original Cholesky decomposition method in the fast mass spring model solver with a conjugate gradient method, which can make the fast mass spring model solver more efficient for detailed surface geometry models. Finally, we propose a graphics processing unit accelerated parallel algorithm for the conjugate gradient method. Experimental results show that our method can realize efficient deformation simulation of 3D elastic objects with visual reality and physical fidelity, which has a great potential for applications in computer animation.
Integrated tokamak modelling with the fast-ion Fokker–Planck solver adapted for transient analyses
International Nuclear Information System (INIS)
Toma, M; Hamamatsu, K; Hayashi, N; Honda, M; Ide, S
2015-01-01
Integrated tokamak modelling that enables the simulation of an entire discharge period is indispensable for designing advanced tokamak plasmas. For this purpose, we extend the integrated code TOPICS to make it more suitable for transient analyses in the fast-ion part. The fast-ion Fokker–Planck solver is integrated into TOPICS at the same level as the bulk transport solver so that the time evolutions of the fast ion and the bulk plasma are consistent with each other as well as with the equilibrium magnetic field. The fast-ion solver simultaneously handles neutral beam-injected ions and alpha particles. Parallelisation of the fast-ion solver in addition to its computational lightness owing to a dimensional reduction in the phase space enables transient analyses for long periods in the order of tens of seconds. The fast-ion Fokker–Planck calculation is compared and confirmed to be in good agreement with an orbit following a Monte Carlo calculation. The integrated code is applied to ramp-up simulations for JT-60SA and ITER to confirm its capability and effectiveness in transient analyses. In the integrated simulations, the coupled evolution of the fast ions, plasma profiles, and equilibrium magnetic fields are presented. In addition, the electric acceleration effect on fast ions is shown and discussed. (paper)
Experimental validation of a boundary element solver for exterior acoustic radiation problems
Visser, Rene; Nilsson, A.; Boden, H.
2003-01-01
The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for
Status for the two-dimensional Navier-Stokes solver EllipSys2D
DEFF Research Database (Denmark)
Bertagnolio, F.; Sørensen, Niels N.; Johansen, J.
2001-01-01
This report sets up an evaluation of the two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risø. Two airfoils are investigated by computing theflow at several angles of attack ranging from...
Hybrid direct and iterative solvers for h refined grids with singularities
Paszyński, Maciej R.; Paszyńska, Anna; Dalcin, Lisandro; Calo, Victor M.
2015-01-01
on top of it. The hybrid solver is applied for two or three dimensional grids automatically h refined towards point or edge singularities. The automatic refinement is based on the relative error estimations between the coarse and fine mesh solutions [2
A Comparison of Monte Carlo and Deterministic Solvers for keff and Sensitivity Calculations
Energy Technology Data Exchange (ETDEWEB)
Haeck, Wim [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Parsons, Donald Kent [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); White, Morgan Curtis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Saller, Thomas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-12
Verification and validation of our solutions for calculating the neutron reactivity for nuclear materials is a key issue to address for many applications, including criticality safety, research reactors, power reactors, and nuclear security. Neutronics codes solve variations of the Boltzmann transport equation. The two main variants are Monte Carlo versus deterministic solutions, e.g. the MCNP [1] versus PARTISN [2] codes, respectively. There have been many studies over the decades that examined the accuracy of such solvers and the general conclusion is that when the problems are well-posed, either solver can produce accurate results. However, the devil is always in the details. The current study examines the issue of self-shielding and the stress it puts on deterministic solvers. Most Monte Carlo neutronics codes use continuous-energy descriptions of the neutron interaction data that are not subject to this effect. The issue of self-shielding occurs because of the discretisation of data used by the deterministic solutions. Multigroup data used in these solvers are the average cross section and scattering parameters over an energy range. Resonances in cross sections can occur that change the likelihood of interaction by one to three orders of magnitude over a small energy range. Self-shielding is the numerical effect that the average cross section in groups with strong resonances can be strongly affected as neutrons within that material are preferentially absorbed or scattered out of the resonance energies. This affects both the average cross section and the scattering matrix.
Development of a CANDU Moderator Analysis Model; Based on Coupled Solver
International Nuclear Information System (INIS)
Yoon, Churl; Park, Joo Hwan
2006-01-01
A CFD model for predicting the CANDU-6 moderator temperature has been developed for several years in KAERI, which is based on CFX-4. This analytic model(CFX4-CAMO) has some strength in the modeling of hydraulic resistance in the core region and in the treatment of heat source term in the energy equations. But the convergence difficulties and slow computing speed reveal to be the limitations of this model, because the CFX-4 code adapts a segregated solver to solve the governing equations with strong coupled-effect. Compared to CFX-4 using segregated solver, CFX-10 adapts high efficient and robust coupled-solver. Before December 2005 when CFX-10 was distributed, the previous version of CFX-10(CFX-5. series) also adapted coupled solver but didn't have any capability to apply porous media approaches correctly. In this study, the developed moderator analysis model based on CFX- 4 (CFX4-CAMO) is transformed into a new moderator analysis model based on CFX-10. The new model is examined and the results are compared to the former
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
International Nuclear Information System (INIS)
Fisicaro, G.; Goedecker, S.; Genovese, L.; Andreussi, O.; Marzari, N.
2016-01-01
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.
Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
Modelling dynamic liquid-gas systems: Extensions to the volume-of-fluid solver
CSIR Research Space (South Africa)
Heyns, Johan A
2013-06-01
Full Text Available This study presents the extension of the volume-of-fluid solver, interFoam, for improved accuracy and efficiency when modelling dynamic liquid-gas systems. Examples of these include the transportation of liquids, such as in the case of fuel carried...
VDJSeq-Solver: in silico V(DJ recombination detection tool.
Directory of Open Access Journals (Sweden)
Giulia Paciello
Full Text Available In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(DJ rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/.
Effects of high-frequency damping on iterative convergence of implicit viscous solver
Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko
2017-11-01
This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.
A heterogeneous CPU+GPU Poisson solver for space charge calculations in beam dynamics studies
Energy Technology Data Exchange (ETDEWEB)
Zheng, Dawei; Rienen, Ursula van [University of Rostock, Institute of General Electrical Engineering (Germany)
2016-07-01
In beam dynamics studies in accelerator physics, space charge plays a central role in the low energy regime of an accelerator. Numerical space charge calculations are required, both, in the design phase and in the operation of the machines as well. Due to its efficiency, mostly the Particle-In-Cell (PIC) method is chosen for the space charge calculation. Then, the solution of Poisson's equation for the charge distribution in the rest frame is the most prominent part within the solution process. The Poisson solver directly affects the accuracy of the self-field applied on the charged particles when the equation of motion is solved in the laboratory frame. As the Poisson solver consumes the major part of the computing time in most simulations it has to be as fast as possible since it has to be carried out once per time step. In this work, we demonstrate a novel heterogeneous CPU+GPU routine for the Poisson solver. The novel solver also benefits from our new research results on the utilization of a discrete cosine transform within the classical Hockney and Eastwood's convolution routine.
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.; Pardo, David; Torres-Verdí n, Carlos; Demkowicz, Leszek F.; Calo, Victor M.
2010-01-01
measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements
2017-11-13
finite element flow solver JENRE developed at the Naval Research Laboratory. The Crocco- Busemann relation is used to account for the compressibility. In...3 1. Comparison with the measurement data...Naval Research Laboratory. The Crocco-Busemann relation is used to account for the compressibility. In this wall-model implementation, the first
Seo, Jongmin; Schiavazzi, Daniele; Marsden, Alison
2017-11-01
Cardiovascular simulations are increasingly used in clinical decision making, surgical planning, and disease diagnostics. Patient-specific modeling and simulation typically proceeds through a pipeline from anatomic model construction using medical image data to blood flow simulation and analysis. To provide confidence intervals on simulation predictions, we use an uncertainty quantification (UQ) framework to analyze the effects of numerous uncertainties that stem from clinical data acquisition, modeling, material properties, and boundary condition selection. However, UQ poses a computational challenge requiring multiple evaluations of the Navier-Stokes equations in complex 3-D models. To achieve efficiency in UQ problems with many function evaluations, we implement and compare a range of iterative linear solver and preconditioning techniques in our flow solver. We then discuss applications to patient-specific cardiovascular simulation and how the problem/boundary condition formulation in the solver affects the selection of the most efficient linear solver. Finally, we discuss performance improvements in the context of uncertainty propagation. Support from National Institute of Health (R01 EB018302) is greatly appreciated.
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
Woźniak, Maciej; Kuźnik, Krzysztof M.; Paszyński, Maciej R.; Calo, Victor M.; Pardo, D.
2014-01-01
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.
An Analysis of Elliptic Grid Generation Techniques Using an Implicit Euler Solver.
1986-06-09
at M. =0.90 and a=00 is when interpolating for the radius of curvature obtained. One expects the computed shock strength (r), a second examination is...solver to yield accurate second-order, ... v.s zd solutions. References Snn, .:-P.. Flr.e ’rference Methods In Z, .tational Fluid DinamIcs , to he published
Determining the Optimal Values of Exponential Smoothing Constants--Does Solver Really Work?
Ravinder, Handanhal V.
2013-01-01
A key issue in exponential smoothing is the choice of the values of the smoothing constants used. One approach that is becoming increasingly popular in introductory management science and operations management textbooks is the use of Solver, an Excel-based non-linear optimizer, to identify values of the smoothing constants that minimize a measure…
Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
Scalable domain decomposition solvers for stochastic PDEs in high performance computing
International Nuclear Information System (INIS)
Desai, Ajit; Pettit, Chris; Poirel, Dominique; Sarkar, Abhijit
2017-01-01
Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Kuźnik, Krzysztof
2012-06-02
This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
Energy Technology Data Exchange (ETDEWEB)
Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Genovese, L. [University of Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Andreussi, O. [Institute of Computational Science, Università della Svizzera Italiana, Via Giuseppe Buffi 13, CH-6904 Lugano (Switzerland); Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland); Marzari, N. [Theory and Simulations of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne (Switzerland)
2016-01-07
The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS
Directory of Open Access Journals (Sweden)
Mr. Vladimir A. Smagin
2016-12-01
Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
A coupled systems code-CFD MHD solver for fusion blanket design
Energy Technology Data Exchange (ETDEWEB)
Wolfendale, Michael J., E-mail: m.wolfendale11@imperial.ac.uk; Bluck, Michael J.
2015-10-15
Highlights: • A coupled systems code-CFD MHD solver for fusion blanket applications is proposed. • Development of a thermal hydraulic systems code with MHD capabilities is detailed. • A code coupling methodology based on the use of TCP socket communications is detailed. • Validation cases are briefly discussed for the systems code and coupled solver. - Abstract: The network of flow channels in a fusion blanket can be modelled using a 1D thermal hydraulic systems code. For more complex components such as junctions and manifolds, the simplifications employed in such codes can become invalid, requiring more detailed analyses. For magnetic confinement reactor blanket designs using a conducting fluid as coolant/breeder, the difficulties in flow modelling are particularly severe due to MHD effects. Blanket analysis is an ideal candidate for the application of a code coupling methodology, with a thermal hydraulic systems code modelling portions of the blanket amenable to 1D analysis, and CFD providing detail where necessary. A systems code, MHD-SYS, has been developed and validated against existing analyses. The code shows good agreement in the prediction of MHD pressure loss and the temperature profile in the fluid and wall regions of the blanket breeding zone. MHD-SYS has been coupled to an MHD solver developed in OpenFOAM and the coupled solver validated for test geometries in preparation for modelling blanket systems.
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
Koehl, Patrice; Delarue, Marc
2010-02-14
The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE
International Nuclear Information System (INIS)
Na, Y. W.; Park, C. E.; Lee, S. Y.
2009-01-01
As a part of the Ministry of Knowledge Economy (MKE) project, 'Development of safety analysis codes for nuclear power plants', KOPEC has been developing the hydraulic solver code package applicable to the safety analyses of nuclear power plants (NPP's). The matrices of the hydraulic solver are usually sparse and may be asymmetric. In the earlier stage of this project, typical direct matrix solver packages MA48 and MA28 had been tested as matrix solver for the hydraulic solver code, SPACE. The selection was based on the reasonably reliable performance experience from their former version MA18 in RELAP computer code. In the later stage of this project, the iterative methodologies have been being tested in the SPACE code. Among a few candidate iterative solution methodologies tested so far, the biconjugate gradient stabilization methodology (BICGSTAB) has shown the best performance in the applicability test and in the application to the SPACE code. Regardless of all the merits of using the direct solver packages, there are some other aspects of tackling the iterative solution methodologies. The algorithm is much simpler and easier to handle. The potential problems related to the robustness of the iterative solution methodologies have been resolved by applying pre-conditioning methods adjusted and modified as appropriate to the application in the SPACE code. The application strategy of conjugate gradient method was introduced in detail by Schewchuk, Golub and Saad in the middle of 1990's. The application of his methodology to nuclear engineering in Korea started about the same time and is still going on and there are quite a few examples of application to neutronics. Besides, Yang introduced a conjugate gradient method programmed in C++ language. The purpose of this study is to assess the performance and behavior of the iterative solution methodology compared to those of the direct solution methodology still being preferred due to its robustness and reliability. The
Uysal, Ismail Enes
2016-10-01
Plasmonic structures are utilized in many applications ranging from bio-medicine to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods. One of these quantum effects is the tunneling, which is observed when two structures are located within a sub-nanometer distance of each other. At these small distances electrons “jump" from one structure to another and introduce a path for electric current to flow. Classical equations of electrodynamics and the schemes used for solving them do not account for this additional current path. This limitation can be lifted by introducing an auxiliary tunnel with material properties obtained using quantum models and applying a classical solver to the structures connected by this auxiliary tunnel. Early work on this topic focused on quantum models that are generated using a simple one-dimensional wave function to find the tunneling probability and assume a simple Drude model for the permittivity of the tunnel. These tunnel models are then used together with a classical frequency domain solver. In this thesis, a time domain surface integral equation solver for quantum corrected analysis of transient plasmonic interactions is proposed. This solver has several advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces the radiation condition implicitly (increasing the accuracy), and allows for time step selection independent of spatial discretization (increasing efficiency). The quantum model
Energy Technology Data Exchange (ETDEWEB)
Birkholzer, J.; Karasaki, K. [Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.
1996-07-01
Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.
Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.
Suk, Heejun
2016-07-01
MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.
Directory of Open Access Journals (Sweden)
Jürgen eSchmidhuber
2013-06-01
Full Text Available Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. The novel algorithmic framework POWERPLAY (2011 continually searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Wow-effects are achieved by continually making previously learned skills more efficient such that they require less time and space. New skills may (partially re-use previously learned skills. POWERPLAY's search orders candidate pairs of tasks and solver modifications by their conditional computational (time & space complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. The computational costs of validating new tasks need not grow with task repertoire size. POWERPLAY's ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Goedel's sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. POWERPLAY may be viewed as a greedy but practical implementation of basic principles of creativity. A first experimental analysis can be found in separate papers [58, 56, 57].
International Nuclear Information System (INIS)
Devals, C; Zhang, Y; Dompierre, J; Guibault, F; Vu, T C; Mangani, L
2014-01-01
Nowadays, computational fluid dynamics is commonly used by design engineers to evaluate and compare losses in hydraulic components as it is less expensive and less time consuming than model tests. For that purpose, an automatic tool for casing and distributor analysis will be presented in this paper. An in-house mesh generator and a Reynolds Averaged Navier-Stokes equation solver using the standard k-ω SST turbulence model will be used to perform all computations. Two solvers based on the C++ OpenFOAM library will be used and compared to a commercial solver. The performance of the new fully coupled block solver developed by the University of Lucerne and Andritz will be compared to the standard 1.6ext segregated simpleFoam solver and to a commercial solver. In this study, relative comparisons of different geometries of casing and distributor will be performed. The present study is thus aimed at validating the block solver and the tool chain and providing design engineers with a faster and more reliable analysis tool that can be integrated into their design process
Energy Technology Data Exchange (ETDEWEB)
King, G P [Instituto de Oceanografia, Faculdade de Ciencias, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa (Portugal); Rudman, Murray [CSIRO Manufacturing and Infrastructure Technology, P.O. Box 56, Highett, Vic. 3190 (Australia); Rowlands, G [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)], E-mail: gkinglisboa@gmail.com, E-mail: Murray.Rudman@csiro.au, E-mail: G.Rowlands@warwick.ac.uk
2008-01-31
The dimensionless effective axial diffusion coefficient, D{sub z}, calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor-Couette system, has been determined as a function of Reynolds number (R = Re/Re{sub c}), axial wavelength ({lambda}{sub z}), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when R < 3.5, D{sub z} has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when R > 3.5, D{sub z} decreases monotonically. Eulerian quantities measuring the departure from rotational symmetry, {psi}{sub {theta}}, and flexion-free flow, {psi}{sub {nu}}, were calculated. The space-averaged quantities {phi}-bar{sub {theta}} and {phi}-bar{sub {nu}} were found to have, unlike D{sub z}, a simple unimodal dependence on R. In the low R regime the correlation between D{sub z} and {psi}{sub {theta}}{psi}{sub {nu}} was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of R. In the large R regime, however, the correlation simplified to D{sub z}{approx}{phi}-bar{sub {theta}}{phi}-bar{sub {nu}} for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets. A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the 'escape basins' (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin ({gamma}{sub O}) is larger than the inflow basin ({gamma}{sub I}), and both {gamma}{sub O} and {gamma}{sub I} are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase
Cardall, Christian Y.; Budiardja, Reuben D.
2018-01-01
The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.
Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver
Kestener, Pierre
2017-10-01
RamsesGPU is a reimplementation of RAMSES (ascl:1011.007) which drops the adaptive mesh refinement (AMR) features to optimize 3D uniform grid algorithms for modern graphics processor units (GPU) to provide an efficient software package for astrophysics applications that do not need AMR features but do require a very large number of integration time steps. RamsesGPU provides an very efficient C++/CUDA/MPI software implementation of a second order MUSCL-Handcock finite volume fluid solver for compressible hydrodynamics as a magnetohydrodynamics solver based on the constraint transport technique. Other useful modules includes static gravity, dissipative terms (viscosity, resistivity), and forcing source term for turbulence studies, and special care was taken to enhance parallel input/output performance by using state-of-the-art libraries such as HDF5 and parallel-netcdf.
A Massively Parallel Solver for the Mechanical Harmonic Analysis of Accelerator Cavities
International Nuclear Information System (INIS)
2015-01-01
ACE3P is a 3D massively parallel simulation suite that developed at SLAC National Accelerator Laboratory that can perform coupled electromagnetic, thermal and mechanical study. Effectively utilizing supercomputer resources, ACE3P has become a key simulation tool for particle accelerator R and D. A new frequency domain solver to perform mechanical harmonic response analysis of accelerator components is developed within the existing parallel framework. This solver is designed to determine the frequency response of the mechanical system to external harmonic excitations for time-efficient accurate analysis of the large-scale problems. Coupled with the ACE3P electromagnetic modules, this capability complements a set of multi-physics tools for a comprehensive study of microphonics in superconducting accelerating cavities in order to understand the RF response and feedback requirements for the operational reliability of a particle accelerator. (auth)
A Generic High-performance GPU-based Library for PDE solvers
DEFF Research Database (Denmark)
Glimberg, Stefan Lemvig; Engsig-Karup, Allan Peter
, the privilege of high-performance parallel computing is now in principle accessible for many scientific users, no matter their economic resources. Though being highly effective units, GPUs and parallel architectures in general, pose challenges for software developers to utilize their efficiency. Sequential...... legacy codes are not always easily parallelized and the time spent on conversion might not pay o in the end. We present a highly generic C++ library for fast assembling of partial differential equation (PDE) solvers, aiming at utilizing the computational resources of GPUs. The library requires a minimum...... of GPU computing knowledge, while still oering the possibility to customize user-specic solvers at kernel level if desired. Spatial dierential operators are based on matrix free exible order nite dierence approximations. These matrix free operators minimize both memory consumption and main memory access...
Constraint Solver Techniques for Implementing Precise and Scalable Static Program Analysis
DEFF Research Database (Denmark)
Zhang, Ye
solver using unification we could make a program analysis easier to design and implement, much more scalable, and still as precise as expected. We present an inclusion constraint language with the explicit equality constructs for specifying program analysis problems, and a parameterized framework...... developers to build reliable software systems more quickly and with fewer bugs or security defects. While designing and implementing a program analysis remains a hard work, making it both scalable and precise is even more challenging. In this dissertation, we show that with a general inclusion constraint...... data flow analyses for C language, we demonstrate a large amount of equivalences could be detected by off-line analyses, and they could then be used by a constraint solver to significantly improve the scalability of an analysis without sacrificing any precision....
A fast, high-order solver for the Grad–Shafranov equation
International Nuclear Information System (INIS)
Pataki, Andras; Cerfon, Antoine J.; Freidberg, Jeffrey P.; Greengard, Leslie; O’Neil, Michael
2013-01-01
We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented
Solving non-linear Horn clauses using a linear Horn clause solver
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre
2016-01-01
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....
Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai
2014-10-20
We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.
SuperLU{_}DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Li, Xiaoye S.; Demmel, James W.
2002-03-27
In this paper, we present the main algorithmic features in the software package SuperLU{_}DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate the parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication pattern for sparse Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we designed highly parallel and scalable algorithms for both LU decomposition and triangular solve and we show that they are suitable for large-scale distributed memory machines.
Analysis of transient plasmonic interactions using an MOT-PMCHWT integral equation solver
Uysal, Ismail Enes
2014-07-01
Device design involving metals and dielectrics at nano-scales and optical frequencies calls for simulation tools capable of analyzing plasmonic interactions. To this end finite difference time domain (FDTD) and finite element methods have been used extensively. Since these methods require volumetric meshes, the discretization size should be very small to accurately resolve fast-decaying fields in the vicinity of metal/dielectric interfaces. This can be avoided using integral equation (IE) techniques that discretize only on the interfaces. Additionally, IE solvers implicitly enforce the radiation condition and consequently do not need (approximate) absorbing boundary conditions. Despite these advantages, IE solvers, especially in time domain, have not been used for analyzing plasmonic interactions.
Linear optical response of finite systems using multishift linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
GPU TECHNOLOGIES EMBODIED IN PARALLEL SOLVERS OF LINEAR ALGEBRAIC EQUATION SYSTEMS
Directory of Open Access Journals (Sweden)
Sidorov Alexander Vladimirovich
2012-10-01
Full Text Available The author reviews existing shareware solvers that are operated by graphical computer devices. The purpose of this review is to explore the opportunities and limitations of the above parallel solvers applicable for resolution of linear algebraic problems that arise at Research and Educational Centre of Computer Modeling at MSUCE, and Research and Engineering Centre STADYO. The author has explored new applications of the GPU in the PETSc suite and compared them with the results generated absent of the GPU. The research is performed within the CUSP library developed to resolve the problems of linear algebra through the application of GPU. The author has also reviewed the new MAGMA project which is analogous to LAPACK for the GPU.
Multitasking domain decomposition fast Poisson solvers on the Cray Y-MP
Chan, Tony F.; Fatoohi, Rod A.
1990-01-01
The results of multitasking implementation of a domain decomposition fast Poisson solver on eight processors of the Cray Y-MP are presented. The object of this research is to study the performance of domain decomposition methods on a Cray supercomputer and to analyze the performance of different multitasking techniques using highly parallel algorithms. Two implementations of multitasking are considered: macrotasking (parallelism at the subroutine level) and microtasking (parallelism at the do-loop level). A conventional FFT-based fast Poisson solver is also multitasked. The results of different implementations are compared and analyzed. A speedup of over 7.4 on the Cray Y-MP running in a dedicated environment is achieved for all cases.
Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers
Atanasov, Atanas
2016-10-17
We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.
Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB
Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.
2017-01-01
Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.
Pyrolysis and gasification of single biomass particle – new openFoam solver
International Nuclear Information System (INIS)
Kwiatkowski, K; Zuk, P J; Bajer, K; Dudyński, M
2014-01-01
We present a new solver biomassGasificationFoam that extended the functionalities of the well-supported open-source CFD code OpenFOAM. The main goal of this development is to provide a comprehensive computational environment for a wide range of applications involving reacting gases and solids. The biomassGasificationFoam is an integrated solver capable of modelling thermal conversion, including evaporation, pyrolysis, gasification, and combustion, of various solid materials. In the paper we show that the gas is hotter than the solid except at the centre of the sample, where the temperature of the solid is higher. This effect is expected because the thermal conductivity of the porous matrix of the solid phase is higher than the thermal conductivity of the gases. This effect, which cannot be considered if thermal equilibrium between the gas and solid is assumed, leads to precise description of heat transfer into wood particles.
Sayed, Sadeed Bin; Uysal, Ismail Enes; Bagci, Hakan; Ulku, H. Arda
2018-01-01
Quantum tunneling is observed between two nanostructures that are separated by a sub-nanometer gap. Electrons “jumping” from one structure to another create an additional current path. An auxiliary tunnel is introduced between the two structures as a support for this so that a classical electromagnetic solver can account for the effects of quantum tunneling. The dispersive permittivity of the tunnel is represented by a Drude model, whose parameters are obtained from the electron tunneling probability. The transient scattering from the connected nanostructures (i.e., nanostructures plus auxiliary tunnel) is analyzed using a time domain volume integral equation solver. Numerical results demonstrating the effect of quantum tunneling on the scattered fields are provided.
Essential imposition of Neumann condition in Galerkin-Legendre elliptic solvers
Auteri, F; Quartapelle, L
2003-01-01
A new Galerkin-Legendre direct spectral solver for the Neumann problem associated with Laplace and Helmholtz operators in rectangular domains is presented. The algorithm differs from other Neumann spectral solvers by the high sparsity of the matrices, exploited in conjunction with the direct product structure of the problem. The homogeneous boundary condition is satisfied exactly by expanding the unknown variable into a polynomial basis of functions which are built upon the Legendre polynomials and have a zero slope at the interval extremes. A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results are given to illustrate the performance of the proposed spectral elliptic solv...
Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver
International Nuclear Information System (INIS)
Soerensen, N N; Bechmann, A; Johansen, J; Myllerup, L; Botha, P; Vinther, S; Nielsen, B S
2007-01-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow conditions, in the form of high wind shear and directional shear which may seriously lower the lifetime of a wind turbine
The Quantum Mechanics Solver How to Apply Quantum Theory to Modern Physics
Basdevant, Jean-Louis
2006-01-01
The Quantum Mechanics Solver grew from topics which are part of the final examination in quantum theory at the Ecole Polytechnique at Palaiseau near Paris, France. The aim of the text is to guide the student towards applying quantum mechanics to research problems in fields such as atomic and molecular physics, condensed matter physics, and laser physics. Advanced undergraduates and graduate students will find a rich and challenging source for improving their skills in this field.
The value of continuity: Refined isogeometric analysis and fast direct solvers
Garcia, Daniel
2016-08-26
We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce . C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method
libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2015-04-01
This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations
Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.
2014-11-01
This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.
The value of continuity: Refined isogeometric analysis and fast direct solvers
Garcia, Daniel; Pardo, David; Dalcin, Lisandro; Paszyński, Maciej; Collier, Nathan; Calo, Victor M.
2016-01-01
We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce . C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method
ROMI 3.1 Least-cost lumber grade mix solver using open source statistical software
Rebecca A. Buck; Urs Buehlmann; R. Edward. Thomas
2010-01-01
The least-cost lumber grade mix solution has been a topic of interest to both industry and academia for many years due to its potential to help wood processing operations reduce costs. A least-cost lumber grade mix solver is a rough mill decision support system that describes the lumber grade or grade mix needed to minimize raw material or total production cost (raw...
Mang, Andreas; Ruthotto, Lars
2017-01-01
We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
Directory of Open Access Journals (Sweden)
Yuma Fukushima
2015-01-01
Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.
A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures
Directory of Open Access Journals (Sweden)
Piero Colli Franzone
2018-04-01
Full Text Available We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1 the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2 the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3 the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4 the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.
Use of direct and iterative solvers for estimation of SNP effects in genome-wide selection
Directory of Open Access Journals (Sweden)
Eduardo da Cruz Gouveia Pimentel
2010-01-01
Full Text Available The aim of this study was to compare iterative and direct solvers for estimation of marker effects in genomic selection. One iterative and two direct methods were used: Gauss-Seidel with Residual Update, Cholesky Decomposition and Gentleman-Givens rotations. For resembling different scenarios with respect to number of markers and of genotyped animals, a simulated data set divided into 25 subsets was used. Number of markers ranged from 1,200 to 5,925 and number of animals ranged from 1,200 to 5,865. Methods were also applied to real data comprising 3081 individuals genotyped for 45181 SNPs. Results from simulated data showed that the iterative solver was substantially faster than direct methods for larger numbers of markers. Use of a direct solver may allow for computing (covariances of SNP effects. When applied to real data, performance of the iterative method varied substantially, depending on the level of ill-conditioning of the coefficient matrix. From results with real data, Gentleman-Givens rotations would be the method of choice in this particular application as it provided an exact solution within a fairly reasonable time frame (less than two hours. It would indeed be the preferred method whenever computer resources allow its use.
A comparison of SuperLU solvers on the intel MIC architecture
Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.
2016-10-01
In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.
Uysal, Ismail Enes
2016-08-09
Transient electromagnetic interactions on plasmonic nanostructures are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation (SIE). Equivalent (unknown) electric and magnetic current densities, which are introduced on the surfaces of the nanostructures, are expanded using Rao-Wilton-Glisson and polynomial basis functions in space and time, respectively. Inserting this expansion into the PMCHWT-SIE and Galerkin testing the resulting equation at discrete times yield a system of equations that is solved for the current expansion coefficients by a marching on-in-time (MOT) scheme. The resulting MOT-PMCHWT-SIE solver calls for computation of additional convolutions between the temporal basis function and the plasmonic medium\\'s permittivity and Green function. This computation is carried out with almost no additional cost and without changing the computational complexity of the solver. Time-domain samples of the permittivity and the Green function required by these convolutions are obtained from their frequency-domain samples using a fast relaxed vector fitting algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver. © 2016 Optical Society of America.
Directory of Open Access Journals (Sweden)
Jianfei Zhang
2013-01-01
Full Text Available Graphics processing unit (GPU has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture (CUDA. Sliced block ELLPACK (SBELL format is introduced to store sparse matrix arising from finite element discretization of elasticity with fewer padding zeros than traditional ELLPACK-based formats. Polynomial preconditioning methods have been investigated both in convergence and running time. From the overall performance, the least-squares (L-S polynomial method is chosen as a preconditioner in PCG solver to finite element equations derived from elasticity for its best results on different example meshes. In the PCG solver, mixed precision algorithm is used not only to reduce the overall computational, storage requirements and bandwidth but to make full use of the capacity of the GPU devices. With SBELL format and mixed precision algorithm, the GPU-based L-S preconditioned CG can get a speedup of about 7–9 to CPU-implementation.
Liu, Yang
2013-07-01
The computational complexity and memory requirements of multilevel plane wave time domain (PWTD)-accelerated marching-on-in-time (MOT)-based surface integral equation (SIE) solvers scale as O(NtNs(log 2)Ns) and O(Ns 1.5); here N t and Ns denote numbers of temporal and spatial basis functions discretizing the current [Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003]. In the past, serial versions of these solvers have been successfully applied to the analysis of scattering from perfect electrically conducting as well as homogeneous penetrable targets involving up to Ns ≈ 0.5 × 106 and Nt ≈ 10 3. To solve larger problems, parallel PWTD-enhanced MOT solvers are called for. Even though a simple parallelization strategy was demonstrated in the context of electromagnetic compatibility analysis [M. Lu et al., in Proc. IEEE Int. Symp. AP-S, 4, 4212-4215, 2004], by and large, progress in this area has been slow. The lack of progress can be attributed wholesale to difficulties associated with the construction of a scalable PWTD kernel. © 2013 IEEE.
Applications of an implicit HLLC-based Godunov solver for steady state hypersonic problems
International Nuclear Information System (INIS)
Link, R.A.; Sharman, B.
2005-01-01
Over the past few years, there has been considerable activity developing research vehicles for studying hypersonic propulsion. Successful launches of the Australian Hyshot and the US Hyper-X vehicles have added a significant amount of flight test data to a field that had previously been limited to numerical simulation. A number of approaches have been proposed for hypersonics propulsion, including attached detonation wave, supersonics combustion, and shock induced combustion. Due to the high cost of developing flight hardware, CFD simulations will continue to be a key tool for investigating the feasibility of these concepts. Capturing the interactions of the vehicle body with the boundary layer and chemical reactions pushes the limits of available modelling tools and computer hardware. Explicit formulations are extremely slow in converging to a steady state; therefore, the use of implicit methods are warranted. An implicit LLC-based Godunov solver has been developed at Martec in collaboration with DRDC Valcartier to solve hypersonic problems with a minimum of CPU time and RAM storage. The solver, Chinook Implicit, is based upon the implicit formulation adopted by Batten et. al. The solver is based on a point implicit Gauss-Seidel method for unstructured grids, and includes fully implicit boundary conditions. Preliminary results for small and large scale inviscid hypersonics problems will be presented. (author)
Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique
Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi
2013-09-01
According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.
Development and validation of a magneto-hydrodynamic solver for blood flow analysis
Energy Technology Data Exchange (ETDEWEB)
Kainz, W; Guag, J; Krauthamer, V; Myklebust, J; Bassen, H; Chang, I [Center for Devices and Radiological Health, FDA, Silver Spring, MD (United States); Benkler, S; Chavannes, N [Schmid and Partner Engineering AG, Zurich (Switzerland); Szczerba, D; Neufeld, E; Kuster, N [Foundation for Research on Information Technology in Society (IT' IS), Zurich (Switzerland); Kim, J H; Sarntinoranont, M, E-mail: wolfgang.kainz@fda.hhs.go [Soft Tissue Mechanics and Drug Delivery Laboratory, Mechanical and Aerospace Engineering, University of Florida, FL (United States)
2010-12-07
The objective of this study was to develop a numerical solver to calculate the magneto-hydrodynamic (MHD) signal produced by a moving conductive liquid, i.e. blood flow in the great vessels of the heart, in a static magnetic field. We believe that this MHD signal is able to non-invasively characterize cardiac blood flow in order to supplement the present non-invasive techniques for the assessment of heart failure conditions. The MHD signal can be recorded on the electrocardiogram (ECG) while the subject is exposed to a strong static magnetic field. The MHD signal can only be measured indirectly as a combination of the heart's electrical signal and the MHD signal. The MHD signal itself is caused by induced electrical currents in the blood due to the moving of the blood in the magnetic field. To characterize and eventually optimize MHD measurements, we developed a MHD solver based on a finite element code. This code was validated against literature, experimental and analytical data. The validation of the MHD solver shows good agreement with all three reference values. Future studies will include the calculation of the MHD signals for anatomical models. We will vary the orientation of the static magnetic field to determine an optimized location for the measurement of the MHD blood flow signal.
A GPU-based incompressible Navier-Stokes solver on moving overset grids
Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.
2013-07-01
In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.
Placati, Silvio; Guermandi, Marco; Samore, Andrea; Scarselli, Eleonora Franchi; Guerrieri, Roberto
2016-09-01
Diffuse optical tomography is an imaging technique, based on evaluation of how light propagates within the human head to obtain the functional information about the brain. Precision in reconstructing such an optical properties map is highly affected by the accuracy of the light propagation model implemented, which needs to take into account the presence of clear and scattering tissues. We present a numerical solver based on the radiosity-diffusion model, integrating the anatomical information provided by a structural MRI. The solver is designed to run on parallel heterogeneous platforms based on multiple GPUs and CPUs. We demonstrate how the solver provides a 7 times speed-up over an isotropic-scattered parallel Monte Carlo engine based on a radiative transport equation for a domain composed of 2 million voxels, along with a significant improvement in accuracy. The speed-up greatly increases for larger domains, allowing us to compute the light distribution of a full human head ( ≈ 3 million voxels) in 116 s for the platform used.
Zubair, Mohammad; Nielsen, Eric; Luitjens, Justin; Hammond, Dana
2016-01-01
In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.
Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media
Efendiev, Y.
2012-08-01
In this paper, we study robust iterative solvers for finite element systems resulting in approximation of steady-state Richards\\' equation in porous media with highly heterogeneous conductivity fields. It is known that in such cases the contrast, ratio between the highest and lowest values of the conductivity, can adversely affect the performance of the preconditioners and, consequently, a design of robust preconditioners is important for many practical applications. The proposed iterative solvers consist of two kinds of iterations, outer and inner iterations. Outer iterations are designed to handle nonlinearities by linearizing the equation around the previous solution state. As a result of the linearization, a large-scale linear system needs to be solved. This linear system is solved iteratively (called inner iterations), and since it can have large variations in the coefficients, a robust preconditioner is needed. First, we show that under some assumptions the number of outer iterations is independent of the contrast. Second, based on the recently developed iterative methods, we construct a class of preconditioners that yields convergence rate that is independent of the contrast. Thus, the proposed iterative solvers are optimal with respect to the large variation in the physical parameters. Since the same preconditioner can be reused in every outer iteration, this provides an additional computational savings in the overall solution process. Numerical tests are presented to confirm the theoretical results. © 2012 Global-Science Press.
Energy Technology Data Exchange (ETDEWEB)
Clark, M. A. [NVIDIA Corp., Santa Clara; Strelchenko, Alexei [Fermilab; Vaquero, Alejandro [Utah U.; Wagner, Mathias [NVIDIA Corp., Santa Clara; Weinberg, Evan [Boston U.
2017-10-26
Lattice quantum chromodynamics simulations in nuclear physics have benefited from a tremendous number of algorithmic advances such as multigrid and eigenvector deflation. These improve the time to solution but do not alleviate the intrinsic memory-bandwidth constraints of the matrix-vector operation dominating iterative solvers. Batching this operation for multiple vectors and exploiting cache and register blocking can yield a super-linear speed up. Block-Krylov solvers can naturally take advantage of such batched matrix-vector operations, further reducing the iterations to solution by sharing the Krylov space between solves. However, practical implementations typically suffer from the quadratic scaling in the number of vector-vector operations. Using the QUDA library, we present an implementation of a block-CG solver on NVIDIA GPUs which reduces the memory-bandwidth complexity of vector-vector operations from quadratic to linear. We present results for the HISQ discretization, showing a 5x speedup compared to highly-optimized independent Krylov solves on NVIDIA's SaturnV cluster.
PUFoam : A novel open-source CFD solver for the simulation of polyurethane foams
Karimi, M.; Droghetti, H.; Marchisio, D. L.
2017-08-01
In this work a transient three-dimensional mathematical model is formulated and validated for the simulation of polyurethane (PU) foams. The model is based on computational fluid dynamics (CFD) and is coupled with a population balance equation (PBE) to describe the evolution of the gas bubbles/cells within the PU foam. The front face of the expanding foam is monitored on the basis of the volume-of-fluid (VOF) method using a compressible solver available in OpenFOAM version 3.0.1. The solver is additionally supplemented to include the PBE, solved with the quadrature method of moments (QMOM), the polymerization kinetics, an adequate rheological model and a simple model for the foam thermal conductivity. The new solver is labelled as PUFoam and is, for the first time in this work, validated for 12 different mixing-cup experiments. Comparison of the time evolution of the predicted and experimentally measured density and temperature of the PU foam shows the potentials and limitations of the approach.
ELSI: A unified software interface for Kohn-Sham electronic structure solvers
Yu, Victor Wen-zhe; Corsetti, Fabiano; García, Alberto; Huhn, William P.; Jacquelin, Mathias; Jia, Weile; Lange, Björn; Lin, Lin; Lu, Jianfeng; Mi, Wenhui; Seifitokaldani, Ali; Vázquez-Mayagoitia, Álvaro; Yang, Chao; Yang, Haizhao; Blum, Volker
2018-01-01
Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.
International Nuclear Information System (INIS)
Boucker, M.; Laviaville, J.; Martin, A.; Bechaud, C.; Bestion, D.; Coste, P.
2004-01-01
The objective of this communication is to present some preliminary applications to pressurized thermal shock (PTS) investigations of the CFD (Computational Fluid Dynamics) two-phase flow solver of the new NEPTUNE thermal-hydraulics platform. In the framework of plant life extension, the Reactor Pressure Vessel (RPV) integrity is a major concern, and an important part of RPV integrity assessment is related to PTS analysis. In the case where the cold legs are partially filled with steam, it becomes a two-phase problem and new important effects occur, such as condensation due to the Emergency Core Cooling (ECC) injections of sub-cooled water. Thus, an advanced prediction of RPV thermal loading during these transients requires sophisticated two-phase, local scale, 3-dimensional codes. In that purpose, a program has been set up to extend the capabilities of the NEPTUNE two-phase CFD solver. A simple set of turbulence and condensation model for free surface steam-water flow has been tested in simulation of an ECC high pressure injection representing facility, using a full 3-dimensional mesh and the new NEPTUNE solver. Encouraging results have been obtained but it should be noticed that several sources of error can compensate for one another. Nevertheless, the computation presented here allows to be reasonable confident in the use of two-phase CFD in order to carry out refined analysis of two-phase PTS scenarios within the next years
AbouEisha, Hassan M.
2014-06-06
In this paper we present a dynamic programming algorithm for finding optimal elimination trees for computational grids refined towards point or edge singularities. The elimination tree is utilized to guide the multi-frontal direct solver algorithm. Thus, the criterion for the optimization of the elimination tree is the computational cost associated with the multi-frontal solver algorithm executed over such tree. We illustrate the paper with several examples of optimal trees found for grids with point, isotropic edge and anisotropic edge mixed with point singularity. We show the comparison of the execution time of the multi-frontal solver algorithm with results of MUMPS solver with METIS library, implementing the nested dissection algorithm.
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.
2013-01-01
on NVIDIA CUDA GPU, delivering logarithmic execution time for linear, quadratic, cubic and higher order B-splines. Thus, the CUDA implementation delivers the optimal performance predicted by our graph grammar analysis. We utilize the solver for multiple
AbouEisha, Hassan M.; Moshkov, Mikhail; Calo, Victor M.; Paszynski, Maciej; Goik, Damian; Jopek, Konrad
2014-01-01
In this paper we present a dynamic programming algorithm for finding optimal elimination trees for computational grids refined towards point or edge singularities. The elimination tree is utilized to guide the multi-frontal direct solver algorithm
Directory of Open Access Journals (Sweden)
Jeng Hei Chow
2016-07-01
Full Text Available An implicit method of solving the six degree-of-freedom rigid body motion equations based on the second order Adams-Bashforth-Moulten method was utilised as an improvement over the leapfrog scheme by making modifications to the rigid body motion solver libraries directly. The implementation will depend on predictor-corrector steps still residing within the hybrid Pressure Implicit with Splitting of Operators - Semi-Implicit Method for Pressure Linked Equations (PIMPLE outer corrector loops to ensure strong coupling between fluid and motion. Aitken's under-relaxation is also introduced in this study to optimise the convergence rate and stability of the coupled solver. The resulting coupled solver ran on a free floating object tutorial test case when converged matches the original solver. It further allows a varying 70%–80% reduction in simulation times compared using a fixed under-relaxation to achieve the required stability.
Energy Technology Data Exchange (ETDEWEB)
Bordner, J.; Saied, F. [Univ. of Illinois, Urbana, IL (United States)
1996-12-31
GLab3D is an enhancement of an interactive environment (MGLab) for experimenting with iterative solvers and multigrid algorithms. It is implemented in MATLAB. The new version has built-in 3D elliptic pde`s and several iterative methods and preconditioners that were not available in the original version. A sparse direct solver option has also been included. The multigrid solvers have also been extended to 3D. The discretization and pde domains are restricted to standard finite differences on the unit square/cube. The power of this software studies in the fact that no programming is needed to solve, for example, the convection-diffusion equation in 3D with TFQMR and a customized V-cycle preconditioner, for a variety of problem sizes and mesh Reynolds, numbers. In addition to the graphical user interface, some sample drivers are included to show how experiments can be composed using the underlying suite of problems and solvers.
DEFF Research Database (Denmark)
N., Kroll; P., Renzoni; M., Amato
1998-01-01
The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage.......The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage....
Calo, Victor M.; Collier, Nathan; Pardo, David; Paszyński, Maciej R.
2011-01-01
The multi-frontal direct solver is the state of the art for the direct solution of linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct solver algorithm on linear systems resulting from p finite elements. Specifically we provide the estimates for systems resulting from C0 polynomial spaces spanned by B-splines. The structured grid and uniform polynomial order used in isogeometric meshes simplifies the analysis.
A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid
Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.
1995-01-01
In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.
Calo, Victor M.
2011-05-14
The multi-frontal direct solver is the state of the art for the direct solution of linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct solver algorithm on linear systems resulting from p finite elements. Specifically we provide the estimates for systems resulting from C0 polynomial spaces spanned by B-splines. The structured grid and uniform polynomial order used in isogeometric meshes simplifies the analysis.
International Nuclear Information System (INIS)
Fiorina, Carlo; Hursin, Mathieu; Pautz, Andreas
2017-01-01
Highlights: • Development and verification of an SP 3 solver based on OpenFOAM. • Integration into the GeN-Foam multi-physics platform. • Application of the new GeN-Foam SP 3 solver to the CROCUS reactor. - Abstract: The Laboratory for Reactor Physics and Systems Behaviour at the PSI and at the EPFL has been developing since 2013 a multi-physics platform for coupled reactor analysis named GeN-Foam. The developed tool includes a solver for the eigenvalue and transient solution of multi-group neutron diffusion equations. Although frequently used in reactor analysis, the diffusion theory shows some limitations for core configurations involving strong anisotropies, which is the case for the CROCUS research reactor at the EPFL. The use of an SP 3 approximation to neutron transport can often lead to visible improvements in a code predictive capabilities, especially for one-directional anisotropies, with acceptable added computational cost vs diffusion. Following some modelling issues for the CROCUS reactor, and in order to improve the GeN-Foam modelling capabilities, the GeN-Foam diffusion solver has been extended to allow for SP 3 analyses. The present paper describes such extension and a preliminary verification using a mini-core PWR benchmark. The newly developed solver is then applied to the analysis of the CROCUS experimental reactor and results are compared to Monte Carlo calculations, as well as to the results of the diffusion solver.
Energy Technology Data Exchange (ETDEWEB)
Munoz-Cobo, J.L. [Univ. Politecnica de Valencia, Inst. de Ingenieria Energetica, Valencia (Spain); Chiva, S. [Univ. Jaume I, Dept. of Mechnical Engineering and Construction, Castellon (Spain); Abd El Aziz Essa, M. [Univ. Politecnica de Valencia, Inst. de Ingenieria Energetica, Valencia (Spain); Mendes, S. [Univ. Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica (Mexico)
2011-07-01
A set of air-water experiments have been performed under isothermal upward concurrent flow in a vertical column. The interfacial velocity, interfacial area of the bubbles and the void fraction distributions was obtained. Numerical validation of these results for bubbly flow conditions were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. Both Lagrangian and Eulerian calculations were performed in parallel and iterative self-consistent method was developed. The bubbles-induced turbulence is an important issue considered, to obtain good predictions of experimental results. (author)
Evaluating the performance of the two-phase flow solver interFoam
International Nuclear Information System (INIS)
Deshpande, Suraj S; Anumolu, Lakshman; Trujillo, Mario F
2012-01-01
The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios ∼O(10 3 ) yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure–surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys. 213 141–73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious currents, we
Evaluating the performance of the two-phase flow solver interFoam
Deshpande, Suraj S.; Anumolu, Lakshman; Trujillo, Mario F.
2012-01-01
The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios {\\sim }\\mathscr {O}(10^3) yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure-surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys. 213 141-73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious