Sample records for reacting flow solver

  1. Navier-Stokes Solvers and Generalizations for Reacting Flow Problems

    Elman, Howard C


    This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).

  2. An improved high-order scheme for DNS of low Mach number turbulent reacting flows based on stiff chemistry solver

    Yu, Rixin; Yu, Jiangfei; Bai, Xue-Song


    We present an improved numerical scheme for numerical simulations of low Mach number turbulent reacting flows with detailed chemistry and transport. The method is based on a semi-implicit operator-splitting scheme with a stiff solver for integration of the chemical kinetic rates, developed by Knio et al. [O.M. Knio, H.N. Najm, P.S. Wyckoff, A semi-implicit numerical scheme for reacting flow II. Stiff, operator-split formulation, Journal of Computational Physics 154 (2) (1999) 428-467]. Using the material derivative form of continuity equation, we enhance the scheme to allow for large density ratio in the flow field. The scheme is developed for direct numerical simulation of turbulent reacting flow by employing high-order discretization for the spatial terms. The accuracy of the scheme in space and time is verified by examining the grid/time-step dependency on one-dimensional benchmark cases: a freely propagating premixed flame in an open environment and in an enclosure related to spark-ignition engines. The scheme is then examined in simulations of a two-dimensional laminar flame/vortex-pair interaction. Furthermore, we apply the scheme to direct numerical simulation of a homogeneous charge compression ignition (HCCI) process in an enclosure studied previously in the literature. Satisfactory agreement is found in terms of the overall ignition behavior, local reaction zone structures and statistical quantities. Finally, the scheme is used to study the development of intrinsic flame instabilities in a lean H2/air premixed flame, where it is shown that the spatial and temporary accuracies of numerical schemes can have great impact on the prediction of the sensitive nonlinear evolution process of flame instability.

  3. PDF approach for compressible turbulent reacting flows

    Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.


    The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

  4. A hybrid Eulerian-Lagrangian flow solver

    Palha, Artur; Ferreira, Carlos Simao; van Bussel, Gerard


    Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...

  5. Stochastic models for turbulent reacting flows

    Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)


    The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.

  6. Chemically reacting supersonic flow calculation using an assumed PDF model

    Farshchi, M.


    This work is motivated by the need to develop accurate models for chemically reacting compressible turbulent flow fields that are present in a typical supersonic combustion ramjet (SCRAMJET) engine. In this paper the development of a new assumed probability density function (PDF) reaction model for supersonic turbulent diffusion flames and its implementation into an efficient Navier-Stokes solver are discussed. The application of this model to a supersonic hydrogen-air flame will be considered.

  7. Laser Diagnostics for Reacting Flows


    absorption diagnostic for vapor-phase measurements in an evaporating n-decane aerosol,” Appied Physics B. 97, 215-225, (2009). 30. J.M. Porter, J.B...fluorescence of toluene for time- resolved imaging of gaseous flows,” Appied Physics B, 2010, in press. 35. J.M. Porter, J.B. Jeffries and R.K. Hanson

  8. Algorithm For Computation Of Chemically Reacting Flow

    Chen, Yen-Sen; Chen, Chein-Pin; Shang, Huan-Min


    Efficient algorithm developed for use in solving differential equations of transient, chemically reacting flows at all speeds from zero to high mach numbers. Mathematical models represent coupling of thermal, chemical, and dynamical effects. Original intended application is numerical simulation of flows in rocket engines; also applicable to other complex flows affected by finite-rate chemistry - for example, flows in turbines and in internal-combustion engines.

  9. Numerical Solver for Multiphase Flows

    Sousa, Victor C B; Scalo, Carlo


    The technological development of micro-scale electronic devices is bounded by the challenge of dissipating their heat output. Latent heat absorbed by a fluid during phase transition offers exceptional cooling capabilities while allowing for the design of compact heat exchangers. The understanding of heat transport dynamics in the context of multiphase flow physics is hampered by the limited access to detailed flow features offered by experimental measurements. Computational Fluid Dynamics (CF...

  10. Nonlinear Krylov acceleration of reacting flow codes

    Kumar, S.; Rawat, R.; Smith, P.; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)


    We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.

  11. Implicit compressible flow solvers on unstructured meshes

    Nagaoka, Makoto; Horinouchi, Nariaki


    An implicit solver for compressible flows using Bi-CGSTAB method is proposed. The Euler equations are discretized with the delta-form by the finite volume method on the cell-centered triangular unstructured meshes. The numerical flux is calculated by Roe's upwind scheme. The linearized simultaneous equations with the irregular nonsymmetric sparse matrix are solved by the Bi-CGSTAB method with the preconditioner of incomplete LU factorization. This method is also vectorized by the multi-colored ordering. Although the solver requires more computational memory, it shows faster and more robust convergence than the other conventional methods: three-stage Runge-Kutta method, point Gauss-Seidel method, and Jacobi method for two-dimensional inviscid steady flows.

  12. Numerical Methods For Chemically Reacting Flows

    Leveque, R. J.; Yee, H. C.


    Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.

  13. Multiphase reacting flows modelling and simulation

    Marchisio, Daniele L


    The papers in this book describe the most widely applicable modeling approaches and are organized in six groups covering from fundamentals to relevant applications. In the first part, some fundamentals of multiphase turbulent reacting flows are covered. In particular the introduction focuses on basic notions of turbulence theory in single-phase and multi-phase systems as well as on the interaction between turbulence and chemistry. In the second part, models for the physical and chemical processes involved are discussed. Among other things, particular emphasis is given to turbulence modeling strategies for multiphase flows based on the kinetic theory for granular flows. Next, the different numerical methods based on Lagrangian and/or Eulerian schemes are presented. In particular the most popular numerical approaches of computational fluid dynamics codes are described (i.e., Direct Numerical Simulation, Large Eddy Simulation, and Reynolds-Averaged Navier-Stokes approach). The book will cover particle-based meth...

  14. Pdf - Transport equations for chemically reacting flows

    Kollmann, W.


    The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

  15. Quantitative imaging of turbulent and reacting flows

    Paul, P.H. [Sandia National Laboratories, Livermore, CA (United States)


    Quantitative digital imaging, using planar laser light scattering techniques is being developed for the analysis of turbulent and reacting flows. Quantitative image data, implying both a direct relation to flowfield variables as well as sufficient signal and spatial dynamic range, can be readily processed to yield two-dimensional distributions of flowfield scalars and in turn two-dimensional images of gradients and turbulence scales. Much of the development of imaging techniques to date has concentrated on understanding the requisite molecular spectroscopy and collision dynamics to be able to determine how flowfield variable information is encoded into the measured signal. From this standpoint the image is seen as a collection of single point measurements. The present effort aims at realizing necessary improvements in signal and spatial dynamic range, signal-to-noise ratio and spatial resolution in the imaging system as well as developing excitation/detection strategies which provide for a quantitative measure of particular flowfield scalars. The standard camera used for the study is an intensified CCD array operated in a conventional video format. The design of the system was based on detailed modeling of signal and image transfer properties of fast UV imaging lenses, image intensifiers and CCD detector arrays. While this system is suitable for direct scalar imaging, derived quantities (e.g. temperature or velocity images) require an exceptionally wide dynamic range imaging detector. To apply these diagnostics to reacting flows also requires a very fast shuttered camera. The authors have developed and successfully tested a new type of gated low-light level detector. This system relies on fast switching of proximity focused image-diode which is direct fiber-optic coupled to a cooled CCD array. Tests on this new detector show significant improvements in detection limit, dynamic range and spatial resolution as compared to microchannel plate intensified arrays.

  16. Direct numerical simulation of turbulent reacting flows

    Chen, J.H. [Sandia National Laboratories, Livermore, CA (United States)


    The development of turbulent combustion models that reflect some of the most important characteristics of turbulent reacting flows requires knowledge about the behavior of key quantities in well defined combustion regimes. In turbulent flames, the coupling between the turbulence and the chemistry is so strong in certain regimes that is is very difficult to isolate the role played by one individual phenomenon. Direct numerical simulation (DNS) is an extremely useful tool to study in detail the turbulence-chemistry interactions in certain well defined regimes. Globally, non-premixed flames are controlled by two limiting cases: the fast chemistry limit, where the turbulent fluctuations. In between these two limits, finite-rate chemical effects are important and the turbulence interacts strongly with the chemical processes. This regime is important because industrial burners operate in regimes in which, locally the flame undergoes extinction, or is at least in some nonequilibrium condition. Furthermore, these nonequilibrium conditions strongly influence the production of pollutants. To quantify the finite-rate chemistry effect, direct numerical simulations are performed to study the interaction between an initially laminar non-premixed flame and a three-dimensional field of homogeneous isotropic decaying turbulence. Emphasis is placed on the dynamics of extinction and on transient effects on the fine scale mixing process. Differential molecular diffusion among species is also examined with this approach, both for nonreacting and reacting situations. To address the problem of large-scale mixing and to examine the effects of mean shear, efforts are underway to perform large eddy simulations of round three-dimensional jets.

  17. An HLLC Solver for Relativistic Flows

    Mignone, A


    We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.

  18. Dynamic Load Balancing Strategies for Parallel Reacting Flow Simulations

    Pisciuneri, Patrick; Meneses, Esteban; Givi, Peyman


    Load balancing in parallel computing aims at distributing the work as evenly as possible among the processors. This is a critical issue in the performance of parallel, time accurate, flow simulators. The constraint of time accuracy requires that all processes must be finished with their calculation for a given time step before any process can begin calculation of the next time step. Thus, an irregularly balanced compute load will result in idle time for many processes for each iteration and thus increased walltimes for calculations. Two existing, dynamic load balancing approaches are applied to the simplified case of a partially stirred reactor for methane combustion. The first is Zoltan, a parallel partitioning, load balancing, and data management library developed at the Sandia National Laboratories. The second is Charm++, which is its own machine independent parallel programming system developed at the University of Illinois at Urbana-Champaign. The performance of these two approaches is compared, and the prospects for their application to full 3D, reacting flow solvers is assessed.

  19. Numerical simulation of high speed chemically reacting flows

    Schuricht, Scott Richard

    A single step second-order accurate flux-difference-splitting method has been developed for solving unsteady quasi-one-dimensional and two-dimensional flows of multispecies fluids with finite rate chemistry. A systematic method for incorporating the source term effects into the wave strength parameters of Roe's linearized approximate Riemann solver is presented that is consistent with characteristic theory. The point implicit technique is utilized to achieve second-order time accuracy of the local area source term The stiffness associated with the chemical reactions is removed by implicitly integrating the kinetics system using the LSODE package. From the implicit integration, values of the species production rates are developed and incorporated into the flux-difference-splitting framework using a source term projection and splitting technique that preserves the upwind nature of source terms. Numerous validation studies are presented to illustrate the capability of the numerical method. Shock tube and converging-diverging nozzle cases show the method is second order accurate in space and time for one-dimensional flows. A supersonic source flow case and a subsonic sink flow case show the method is second order spatially accurate for two-dimensional flows. Static combustion and steady supersonic combustion cases illustrate the ability of the method to accurately capture the ignition delay for hydrogen-air mixtures. Demonstration studies are presented to illustrate the capabilities of the method. One-dimensional flow in a shock tube predicts species dissociation behind the main shock wave. One-dimension flow in supersonic nozzles predicts the well-known chemical freezing effect in an expanding flow. Two-dimensional cases consisted of a model of a scramjet combustor and a rocket motor nozzle. A parametric study was performed on a model of a scramjet combustor. The parameters studied were; wall angle, inlet Mach number, inlet temperature, and inlet equivalence ratio

  20. Measurements of Non-reacting and Reacting Flow Fields of a Liquid Swirl Flame Burner

    CHONG Cheng Tung; HOCHGREB Simone


    The understanding of the liquid fuel spray and flow field characteristics inside a combustor is crucial for designing a fuel efficient and low emission device. Characterisation of the flow field of a model gas turbine liquid swirl burner is performed by using a 2-D particle imaging velocimetry(PIV) system. The flow field pattern of an axial flow burner with a fixed swirl intensity is compared under confined and unconfined conditions, i.e., with and without the combustor wall. The effect of temperature on the main swirling air flow is investigated under open and non-reacting conditions. The result shows that axial and radial velocities increase as a result of decreased flow density and increased flow volume. The flow field of the main swirling flow with liquid fuel spray injection is compared to non-spray swirling flow. Introduction of liquid fuel spray changes the swirl air flow field at the burner outlet, where the radial velocity components increase for both open and confined environment. Under reacting condition, the enclosure generates a corner recirculation zone that intensifies the strength of radial velocity. The reverse flow and corner recirculation zone assists in stabilizing the flame by preheating the reactants. The flow field data can be used as validation target for swirl combustion modelling.

  1. Species Source Term Mapping for Reacting Flow CFD Project

    National Aeronautics and Space Administration — Simulations of reacting flow in applications such as scramjet engines are currently limited in their utility or accuracy by the chemistry sub-models employed....

  2. Simultaneous Temperature and Velocity Diagnostic for Reacting Flows Project

    National Aeronautics and Space Administration — A diagnostic technique is proposed for measuring temperature and velocity simultaneously in a high temperature reacting flow for aiding research in propulsion. The...

  3. A PDF closure model for compressible turbulent chemically reacting flows

    Kollmann, W.


    The objective of the proposed research project was the analysis of single point closures based on probability density function (pdf) and characteristic functions and the development of a prediction method for the joint velocity-scalar pdf in turbulent reacting flows. Turbulent flows of boundary layer type and stagnation point flows with and without chemical reactions were be calculated as principal applications. Pdf methods for compressible reacting flows were developed and tested in comparison with available experimental data. The research work carried in this project was concentrated on the closure of pdf equations for incompressible and compressible turbulent flows with and without chemical reactions.

  4. General purpose flow solver applied to flow over hills

    Soerensen, N.N.


    The present report describes the development a 2D and 3D finite-volume code in general curvilinear coordinates using the Basis 2D/3D platform by Michelsen. The codes are based on the Reynolds averaged incompressible isothermal Navier-Stokes equations and use primitive variables (U, V, W and P). The turbulence is modelled by the high Reynolds number {kappa} - {epsilon} model. Cartesian velocity components are used in a non-staggered arrangement following the methodology of Rhie. The equation system is solved using the SIMPLE method of Patankar and Spalding. Solution of the transport equations is obtained by a successive application of a TDMA solver in alternating direction. The solution of the pressure correction equation is accelerated using the multigrid tools from the Basis 2D/3D platform. Additionally a three-level grid sequence is implemented in order to minimize the overall solution time. Higher-order schemes (SUDS and QUICK) are implemented as explicit corrections to a first-order upwind difference scheme. In both the 2D and the 3D code it is possible to handle multiblock configurations. This feature is added in order to obtain a greater geometric flexibility. To mesh natural terrain in connection with atmospheric flow over complex terrain, a two- and a three-dimensional hyperbolic mesh generator are constructed. Additionally, a two- and a three-dimensional mesh generator based on a simple version of the transfinite interpolation technique are implemented. Several two-dimensional test cases are calculated e.g. laminar flow over a circular cylinder, turbulent channel flow, and turbulent flow over a backward facing step, all with satisfying results. In order to illustrate the application of the codes to atmospheric flow two cases are calculated, flow over a cube in a thick turbulent boundary-layer, and the atmospheric flow over the Askervein hill. (au) 13 tabs., 75 ills., 66 refs.

  5. Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation

    Chen, Meng-Huo


    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.

  6. MP Salsa: a finite element computer program for reacting flow problems. Part 1--theoretical development

    Shadid, J.N.; Moffat, H.K.; Hutchinson, S.A.; Hennigan, G.L.; Devine, K.D.; Salinger, A.G.


    The theoretical background for the finite element computer program, MPSalsa, is presented in detail. MPSalsa is designed to solve laminar, low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow, heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solver coupled multiple Poisson or advection-diffusion- reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurring in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMKIN, respectively. The code employs unstructured meshes, using the EXODUS II finite element data base suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec solver library.

  7. Gpu Implementation of a Viscous Flow Solver on Unstructured Grids

    Xu, Tianhao; Chen, Long


    Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.

  8. Combined LAURA-UPS solution procedure for chemically-reacting flows. M.S. Thesis

    Wood, William A.


    A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flowfields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a noncatalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the noncatalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated and the nonequilibrium results are compared with a perfect gas solution, showing that while the surface pressure is relatively unchanged by the inclusion of reacting chemistry the nonequilibrium heating is 25 percent higher. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three dimensional case over an all thin-layer Navier-Stokes solution.

  9. Gerris Flow Solver: Implementation and Application


    processes include the interaction of clay particles with turbulent flows driven by tides and waves. This study thus reinforces the lesson that...boundaries. Journal of Fluid Mechanics, 418:189-212. Lindgren, E.R. 1956. Properties of Certain Bentonite Suspensions and water—a note on the...of sediment will be parameterized for several classes of materiel, including sand, clay , and organic detritus. Processing input Once an autoCAD

  10. Flow Field Effects on Nucleation in a Reacting Mixture Layer.


    chemically reacting flows has been analysed by Fendell (1965) who considered the effect of the straining motion in a stagnation point flow on ignition...stagnation point diffusion flame ( Fendell , 1965, Linan, 1974). In the present study the effect of the strain rate or velocity gradient on nucleation kinetics...Symposium (International) on Corn- bustion, 799-810, Academic Press. Fendell , F. E. (1965). Ignition and extinction in combustion of initially unmixed

  11. Turbulent Flow Validation in the Helios Strand Solver


    aerodynamics solution procedure consists of unstructured meshes in the near-body to capture viscous flow around complex geometry , and block structured...on the approximate Riemann solver of Roe,20 F̂ = 1 2 (F (QR)+F (QL))− 1 2 |A(QR,QL)|(QR−QL) , (45) where F = Fjn j is the directed flux at a face with...uniform cartesian mesh that is 16×16×24. The off-body mesh is then adapted to the geometry and flow physics with up to nine levels of isotropic mesh

  12. Computation of Non-Equilibrium Chemically Reacting Hypersonic Flow from a Cartesian Mesh with Near Wall Viscous Resolution

    V. Ashok


    Full Text Available A hybrid solution methodology has been developed to solve chemically reacting laminar hypersonic flow in chemical Non-equilibrium and thermal equilibrium, by a Cartesian mesh based hybrid solution methodology, which uses an unstructured prism layer solution near the wall and a Cartesian mesh solution away from the wall. The unstructured prism layer for near wall solution is obtained from the normal projection of wall panels of the Cartesian mesh and are stitched with the outer Cartesian mesh. The solver, developed based on this approach when compared with other chemically reacting CFD codes and limited experimental results show good comparison. This procedure has a good potential to handle near-wall resolution for chemically reacting flows with a Cartesian mesh for complex geometries as well.

  13. A new numerical solver for flows at various Mach numbers

    Miczek, F; Edelmann, P V F


    Many problems in stellar astrophysics feature low Mach number flows. However, conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Ma...

  14. High speed turbulent reacting flows: DNS and LES

    Givi, Peyman


    Work on understanding the mechanisms of mixing and reaction in high speed turbulent reacting flows was continued. Efforts, in particular, were concentrated on taking advantage of modern computational methods to simulate high speed turbulent flows. In doing so, two methodologies were used: large eddy simulations (LES) and direct numerical simulations (DNS). In the work related with LES the objective is to study the behavior of the probability density functions (pdfs) of scalar properties within the subgrid in reacting turbulent flows. The data base obtained by DNS for a detailed study of the pdf characteristics within the subgrid was used. Simulations are performed for flows under various initializations to include the effects of compressibility on mixing and chemical reactions. In the work related with DNS, a two-dimensional temporally developing high speed mixing layer under the influence of a second-order non-equilibrium chemical reaction of the type A + B yields products + heat was considered. Simulations were performed with different magnitudes of the convective Mach numbers and with different chemical kinetic parameters for the purpose of examining the isolated effects of the compressibility and the heat released by the chemical reactions on the structure of the layer. A full compressible code was developed and utilized, so that the coupling between mixing and chemical reactions is captured in a realistic manner.

  15. Toward parallel, adaptive mesh refinement for chemically reacting flow simulations

    Devine, K.D.; Shadid, J.N.; Salinger, A.G. Hutchinson, S.A. [Sandia National Labs., Albuquerque, NM (United States); Hennigan, G.L. [New Mexico State Univ., Las Cruces, NM (United States)


    Adaptive numerical methods offer greater efficiency than traditional numerical methods by concentrating computational effort in regions of the problem domain where the solution is difficult to obtain. In this paper, the authors describe progress toward adding mesh refinement to MPSalsa, a computer program developed at Sandia National laboratories to solve coupled three-dimensional fluid flow and detailed reaction chemistry systems for modeling chemically reacting flow on large-scale parallel computers. Data structures that support refinement and dynamic load-balancing are discussed. Results using uniform refinement with mesh sequencing to improve convergence to steady-state solutions are also presented. Three examples are presented: a lid driven cavity, a thermal convection flow, and a tilted chemical vapor deposition reactor.

  16. Spectral kinetic energy transfer in turbulent premixed reacting flows.

    Towery, C A Z; Poludnenko, A Y; Urzay, J; O'Brien, J; Ihme, M; Hamlington, P E


    Spectral kinetic energy transfer by advective processes in turbulent premixed reacting flows is examined using data from a direct numerical simulation of a statistically planar turbulent premixed flame. Two-dimensional turbulence kinetic-energy spectra conditioned on the planar-averaged reactant mass fraction are computed through the flame brush and variations in the spectra are connected to terms in the spectral kinetic energy transport equation. Conditional kinetic energy spectra show that turbulent small-scale motions are suppressed in the burnt combustion products, while the energy content of the mean flow increases. An analysis of spectral kinetic energy transfer further indicates that, contrary to the net down-scale transfer of energy found in the unburnt reactants, advective processes transfer energy from small to large scales in the flame brush close to the products. Triadic interactions calculated through the flame brush show that this net up-scale transfer of energy occurs primarily at spatial scales near the laminar flame thermal width. The present results thus indicate that advective processes in premixed reacting flows contribute to energy backscatter near the scale of the flame.

  17. Simulation of Compressible Multi-Phase Turbulent Reacting Flows


    positivity and entropy preservation. The known instability of this solver to odd-even decoupling and carbuncle phenomenon is cured by employing the HLLE...Two-Shock Riemann Solver and the Roe Riemann solver with Harten-Hyman entropy corrections showed very strong sensitiveness to the instability. The...Paper 2005–0314, 2005. [23] B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb , P. Mac- Neice, R. Rosner, J. W. Truran, and H. Tufo

  18. 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.

  19. On the implicit density based OpenFOAM solver for turbulent compressible flows

    Fürst Jiří


    Full Text Available 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.

  20. 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.

  1. A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part One: Zero-Dimensional Analysis

    Vincent Casseau


    Full Text Available A two-temperature CFD (computational fluid dynamics solver is a prerequisite to any spacecraft re-entry numerical study that aims at producing results with a satisfactory level of accuracy within realistic timescales. In this respect, a new two-temperature CFD solver, hy2Foam, has been developed within the framework of the open-source CFD platform OpenFOAM for the prediction of hypersonic reacting flows. This solver makes the distinct juncture between the trans-rotational and multiple vibrational-electronic temperatures. hy2Foam has the capability to model vibrational-translational and vibrational-vibrational energy exchanges in an eleven-species air mixture. It makes use of either the Park TTv model or the coupled vibration-dissociation-vibration (CVDV model to handle chemistry-vibration coupling and it can simulate flows with or without electronic energy. Verification of the code for various zero-dimensional adiabatic heat baths of progressive complexity has been carried out. hy2Foam has been shown to produce results in good agreement with those given by the CFD code LeMANS (The Michigan Aerothermodynamic Navier-Stokes solver and previously published data. A comparison is also performed with the open-source DSMC (direct simulation Monte Carlo code dsmcFoam. It has been demonstrated that the use of the CVDV model and rates derived from Quantum-Kinetic theory promote a satisfactory consistency between the CFD and DSMC chemistry modules.

  2. Non-reacting Flow Analysis from Combustor Inlet to Outlet using Computational Fluid Dynamics Code

    G. Ananda Reddy


    Full Text Available This paper describes non-reacting flow analysis of a gas turbine combustion system. The method is based on the solution of Navier-Strokes equations using generalised non-orthogonal coordinate system. The turbulence effects are modelled through the renormalisation group k-E model. The method has been applied to a practical gas turbine combustor. The combustionsystem includes swirler vane passages, fuel nozzles, rotor bleed, customer bleed, air-blast atomiser, swirl cone, and all holes in primary , dilution , dome, flare, and cooling ring. Thetotal geometry has been created using the pre-processors GAMBIT and CATIA, and the meshing has been done using GAMBIT, and the analysis carried out in a FLUENT solver. The interaction between the diffuser and the combustor external flows plays a key role in controlling the pressure loss, air flow distribution around the combustor liner, durability, and stability. The aero gas turbine combustor designs are generally guided by experimental methods and past experience; however, experimental methods are inherently slow, costly, especially at hightemperature engine-operating conditions. These drawbacks and the growing need to understand the complex flow-field phenomenon involved, have led to the development of a numericalmodel for predicting flow in the gas turbine combustor. These models are used to optimise the design of the combustor and its subcomponents, and reduce cost, time, and the number ofexperiments.

  3. Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver

    Turnquist, Brian; Owkes, Mark


    Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.

  4. 3D Reacting Flow Analysis of LANTR Nozzles

    Stewart, Mark E. M.; Krivanek, Thomas M.; Hemminger, Joseph A.; Bulman, M. J.


    This paper presents performance predictions for LANTR nozzles and the system implications for their use in a manned Mars mission. The LANTR concept is rocket thrust augmentation by injecting Oxygen into the nozzle to combust the Hydrogen exhaust of a Nuclear Thermal Rocket. The performance predictions are based on three-dimensional reacting flow simulations using VULCAN. These simulations explore a range of O2/H2 mixture ratios, injector configurations, and concepts. These performance predictions are used for a trade analysis within a system study for a manned Mars mission. Results indicate that the greatest benefit of LANTR will occur with In-Situ Resource Utilization (ISRU). However, Hydrogen propellant volume reductions may allow greater margins for fitting tanks within the launch vehicle where packaging issues occur.

  5. Numerical Investigation of a Statistically Stationary Turbulent Reacting Flow

    Overholt, Matthew R.; Pope, Stephen B.


    Direct numerical simulation (DNS) has been very useful in the study of inert scalar mixing in turbulent flows, and has recently become feasible for studies of reacting scalars. We have formulated an accessible inhomogeneous nonpremixed turbulent reactive flow for investigating the effects of mixing on reaction and testing mixing models. The mixture fraction-progress variable approach is used with a model single-step reversible finite-rate thermochemistry, yielding non-trivial stationary solutions corresponding to stable reaction and allowing local extinction to occur. A mean gradient in the mixture fraction gives rise to stationarity without forcing, as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behavior, ranging from thick to thin flames, and from local extinction to near equilibrium. Based on this study results from full probability density function (PDF) simulations using the IEM and EMST mixing models are evaluated. Conditional moment closure (CMC) results are evaluated as well.

  6. A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis †

    Vincent Casseau


    Full Text Available hy2Foam is a newly-coded open-source two-temperature computational fluid dynamics (CFD solver that has previously been validated for zero-dimensional test cases. It aims at (1 giving open-source access to a state-of-the-art hypersonic CFD solver to students and researchers; and (2 providing a foundation for a future hybrid CFD-DSMC (direct simulation Monte Carlo code within the OpenFOAM framework. This paper focuses on the multi-dimensional verification of hy2Foam and firstly describes the different models implemented. In conjunction with employing the coupled vibration-dissociation-vibration (CVDV chemistry–vibration model, novel use is made of the quantum-kinetic (QK rates in a CFD solver. hy2Foam has been shown to produce results in good agreement with previously published data for a Mach 11 nitrogen flow over a blunted cone and with the dsmcFoam code for a Mach 20 cylinder flow for a binary reacting mixture. This latter case scenario provides a useful basis for other codes to compare against.

  7. The development of an intelligent interface to a computational fluid dynamics flow-solver code

    Williams, Anthony D.


    Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.

  8. Flow-distributed oscillations: Stationary chemical waves in a reacting flow

    Kærn, Mads; Menzinger, Michael


    A recent prediction of stationary waves in open, reacting flows is experimentally verified. We show that stationary waves are generated by a mechanism whereby the flow carries a time-oscillating subelement, behaving like a batch reactor, through space while a fixed boundary condition at the inflow locks the phase of the oscillation. This mechanism can generate stationary patterns when all diffusion coefficients are equal. The experimental system is the ferroin-catalyzed Belousov-Zhabotinsky reaction in a tubular reactor, fed by the outflow of a continuous flow stirred tank reactor (CSTR). Parameter conditions are such that the concentrations are constant in the CSTR while they oscillate in the flow tube.




    The recent developments and advances of studies on multiphase and reacting flows, including gas-solid, gas-liquid, liquid-solid and reacting flows, in China are reviewed. Special emphasis is laid on the fundamental studies and numerical models. Some important experimental results are also reported. But measurement techniques are not covered.


    Sankaran Sundaresan


    The principal goal of this project, funded under the ''DOE Vision 21 Virtual Demonstration Initiative'' is virtual demonstration of circulating fluidized bed performance. We had proposed a ''virtual demonstration tool'', which is based on the open-domain CFD code MFIX. The principal challenge funded through this grant is to devise and implement in this CFD code sound physical models for the rheological characteristics of the gas-particle mixtures. Within the past year, which was the third year of the project, we have made the following specific advances. (a) We have completed a study of the impact of sub-grid models of different levels of detail on the results obtained in coarse-grid simulations of gas-particle flow. (b) We have also completed a study of a model problem to understand the effect of wall friction, which was proved in our earlier work to be very important for stable operation of standpipes in a circulating fluidized bed circuit. These are described in a greater detail in this report.

  11. Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

    Blanchard, M., E-mail: [LadHyX, CNRS and Ecole Polytechnique, 91128 Palaiseau (France); Schuller, T. [CNRS, UPR 288, Laboratoire d’Energétique Moléculaire et Macroscopique Combustion (EM2C), Grande Voie des Vignes, 92290 Châtenay-Malabry (France); Centrale-Supélec, Grande Voie des Vignes, 92290 Châtenay-Malabry (France); Sipp, D. [ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon (France); Schmid, P. J. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom)


    The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated.

  12. On Riemann Solvers and Kinetic Relations for Isothermal Two-Phase Flows with Surface Tension

    Rohde, Christian


    We consider a sharp-interface approach for the inviscid isothermal dynamics of compressible two-phase flow, that accounts for phase transition and surface tension effects. To fix the mass exchange and entropy dissipation rate across the interface kinetic relations are frequently used. The complete uni-directional dynamics can then be understood by solving generalized two-phase Riemann problems. We present new well-posedness theorems for the Riemann problem and corresponding computable Riemann solvers, that cover quite general equations of state, metastable input data and curvature effects. The new Riemann solver is used to validate different kinetic relations on physically relevant problems including a comparison with experimental data. Riemann solvers are building blocks for many numerical schemes that are used to track interfaces in two-phase flow. It is shown that the new Riemann solver enables reliable and efficient computations for physical situations that could not be treated before.

  13. Adaptive methods in computational fluid dynamics of chemically reacting flows

    Rogg, B.


    Possible approaches to fully implicit adaptive algorithms suitable for the numerical simulation of unsteady two-dimensional reactive flows are examined. Emphasis is placed on self-adaptive gridding procedures applicable to time-dependent two-dimensional reactive flows. Pulsating flame propagation, autoignition in a nonpremixed flow, flame propagation in a strained mixing layer, and hot-spot-like self-ignition are considered as examples.

  14. A Solver for Massively Parallel Direct Numerical Simulation of Three-Dimensional Multiphase Flows

    Shin, S; Juric, D


    We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 65536 threads or more (limited only by the availability to us of more threads). The code is wholly written by the authors in Fortran 2003 and uses a domain decomposition strategy for parallelization with MPI. The fluid interface solver is based on a parallel implementation of the LCRM hybrid Front Tracking/Level Set method designed to handle highly deforming interfaces with complex topology changes. We discuss the implementation of this interface method and its particular suitability to distributed processing where all operations are carried out locally on distributed subdomains. We have developed parallel GMRES and Multigrid iterative solvers suited to the linear systems arising from the implicit solution of the fluid velocities and pressure in the presence of strong density and viscosity discontinuities across flu...

  15. Simulation of Unsteady Flows Using an Unstructured Navier-Stokes Solver on Moving and Stationary Grids

    Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.


    We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.

  16. A meshless method for compressible flows with the HLLC Riemann solver

    Ma, Z H; Qian, L


    The HLLC Riemann solver, which resolves both the shock waves and contact discontinuities, is popular to the computational fluid dynamics community studying compressible flow problems with mesh methods. Although it was reported to be used in meshless methods, the crucial information and procedure to realise this scheme within the framework of meshless methods were not clarified fully. Moreover, the capability of the meshless HLLC solver to deal with compressible liquid flows is not completely clear yet as very few related studies have been reported. Therefore, a comprehensive investigation of a dimensional non-split HLLC Riemann solver for the least-square meshless method is carried out in this study. The stiffened gas equation of state is adopted to capacitate the proposed method to deal with single-phase gases and/or liquids effectively, whilst direct applying the perfect gas equation of state for compressible liquid flows might encounter great difficulties in correlating the state variables. The spatial der...

  17. Rule-Based Multidisciplinary Tool for Unsteady Reacting Real-Fluid Flows Project

    National Aeronautics and Space Administration — A design and analysis computational tool is proposed for simulating unsteady reacting flows in combustor devices used in reusable launch vehicles. Key aspects...

  18. GPU accelerated flow solver for direct numerical simulation of turbulent flows

    Salvadore, Francesco; Bernardini, Matteo; Botti, Michela


    Graphical processing units (GPUs), characterized by significant computing performance, are nowadays very appealing for the solution of computationally demanding tasks in a wide variety of scientific applications. However, to run on GPUs, existing codes need to be ported and optimized, a procedure which is not yet standardized and may require non trivial efforts, even to high-performance computing specialists. In the present paper we accurately describe the porting to CUDA (Compute Unified Device Architecture) of a finite-difference compressible Navier-Stokes solver, suitable for direct numerical simulation (DNS) of turbulent flows. Porting and validation processes are illustrated in detail, with emphasis on computational strategies and techniques that can be applied to overcome typical bottlenecks arising from the porting of common computational fluid dynamics solvers. We demonstrate that a careful optimization work is crucial to get the highest performance from GPU accelerators. The results show that the overall speedup of one NVIDIA Tesla S2070 GPU is approximately 22 compared with one AMD Opteron 2352 Barcelona chip and 11 compared with one Intel Xeon X5650 Westmere core. The potential of GPU devices in the simulation of unsteady three-dimensional turbulent flows is proved by performing a DNS of a spatially evolving compressible mixing layer.

  19. GPU accelerated flow solver for direct numerical simulation of turbulent flows

    Salvadore, Francesco [CASPUR – via dei Tizii 6/b, 00185 Rome (Italy); Bernardini, Matteo, E-mail: [Department of Mechanical and Aerospace Engineering, University of Rome ‘La Sapienza’ – via Eudossiana 18, 00184 Rome (Italy); Botti, Michela [CASPUR – via dei Tizii 6/b, 00185 Rome (Italy)


    Graphical processing units (GPUs), characterized by significant computing performance, are nowadays very appealing for the solution of computationally demanding tasks in a wide variety of scientific applications. However, to run on GPUs, existing codes need to be ported and optimized, a procedure which is not yet standardized and may require non trivial efforts, even to high-performance computing specialists. In the present paper we accurately describe the porting to CUDA (Compute Unified Device Architecture) of a finite-difference compressible Navier–Stokes solver, suitable for direct numerical simulation (DNS) of turbulent flows. Porting and validation processes are illustrated in detail, with emphasis on computational strategies and techniques that can be applied to overcome typical bottlenecks arising from the porting of common computational fluid dynamics solvers. We demonstrate that a careful optimization work is crucial to get the highest performance from GPU accelerators. The results show that the overall speedup of one NVIDIA Tesla S2070 GPU is approximately 22 compared with one AMD Opteron 2352 Barcelona chip and 11 compared with one Intel Xeon X5650 Westmere core. The potential of GPU devices in the simulation of unsteady three-dimensional turbulent flows is proved by performing a DNS of a spatially evolving compressible mixing layer.

  20. DNS, LES and Stochastic Modeling of Turbulent Reacting Flows


    the analytical results derived by Fendell (1965) via the method of matched asymptotic expansions. A typical DNS scatter plot of the product mass...fields. In Buckmaster, J. D., Jackson, T. L., and Kumar, A., editors, Combustion in High-Speed Flows. in press. Fendell , F. E. (1965). Ignition and

  1. Development of a Chemically Reacting Flow Solver on the Graphic Processing Units


    been implemented on the GPU by Schive et al. (2010). The outcome of their work is the GAMER code for astrophysical simulation. Thibault and...model all the elementary reactions and their reverse processes. 4.2 Chemistry Model An elementary reaction takes the form       N s sr K...are read from separated data files which contain all the species information used for the computation along with the elementary reactions. 4.3

  2. Unsteady Non-Newtonian Solver on Unstructured Grid for the Simulation of Blood Flow

    Guojie Li


    Full Text Available Blood is in fact a suspension of different cells with yield stress, shear thinning, and viscoelastic properties, which can be represented by different non-Newtonian models. Taking Casson fluid as an example, an unsteady solver on unstructured grid for non-Newtonian fluid is developed to simulate transient blood flow in complex flow region. In this paper, a steady solver for Newtonian fluid is firstly developed with the discretization of convective flux, diffusion flux, and source term on unstructured grid. For the non-Newtonian characteristics of blood, the Casson fluid is approximated by the Papanastasiou's model and treated as Newtonian fluid with variable viscosity. Then considering the transient property of blood flow, an unsteady non-Newtonian solver based on unstructured grid is developed by introducing the temporal term by first-order upwind difference scheme. Using the proposed solver, the blood flows in carotid bifurcation of hypertensive patients and healthy people are simulated. The result shows that the possibility of the genesis and development of atherosclerosis is increased, because of the increase in incoming flow shock and backflow areas of the hypertensive patients, whose WSS was 20~87.1% lower in outer vascular wall near the bifurcation than that of the normal persons and 3.7~5.5% lower in inner vascular wall downstream the bifurcation.

  3. A semi-direct solver for compressible three-dimensional rotational flow

    Chang, S.-C.; Adamczyk, J. J.


    An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.

  4. A semi-direct solver for compressible 3-dimensional rotational flow

    Chang, S. C.; Adamczyk, J. J.


    An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel.

  5. An Immersed Boundary Finite-Element Solver for Flow-Induced Deformation of Soft Structures with Application in Cardiac Flows

    Bhardwaj, Rajneesh; Mittal, Rajat


    The modeling of complex biological phenomena such as cardiac mechanics is challenging. It involves complex three dimensional geometries, moving structure boundaries inside the fluid domain and large flow-induced deformations of the structure. We present a fluid-structure interaction solver (FSI) which couples a sharp-interface immersed boundary method for flow simulation with a powerful finite-element based structure dynamics solver. An implicit partitioned (or segregated) approach is implemented to ensure the stability of the solver. We validate the FSI solver with published benchmark for a configuration which involves a thin elastic plate attached to a rigid cylinder. The frequency and amplitude of the oscillations of the plate are in good agreement with published results and non-linear dynamics of the plate and its coupling with the flow field are discussed. The FSI solver is used to understand left-ventricular hemodynamics and flow-induced dynamics of mitral leaflets during early diastolic filling and results from this study are presented.

  6. A New Equation Solver for Modeling Turbulent Flow in Coupled Matrix-Conduit Flow Models.

    Hubinger, Bernhard; Birk, Steffen; Hergarten, Stefan


    Karst aquifers represent dual flow systems consisting of a highly conductive conduit system embedded in a less permeable rock matrix. Hybrid models iteratively coupling both flow systems generally consume much time, especially because of the nonlinearity of turbulent conduit flow. To reduce calculation times compared to those of existing approaches, a new iterative equation solver for the conduit system is developed based on an approximated Newton-Raphson expression and a Gauß-Seidel or successive over-relaxation scheme with a single iteration step at the innermost level. It is implemented and tested in the research code CAVE but should be easily adaptable to similar models such as the Conduit Flow Process for MODFLOW-2005. It substantially reduces the computational effort as demonstrated by steady-state benchmark scenarios as well as by transient karst genesis simulations. Water balance errors are found to be acceptable in most of the test cases. However, the performance and accuracy may deteriorate under unfavorable conditions such as sudden, strong changes of the flow field at some stages of the karst genesis simulations.

  7. A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

    Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)


    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.

  8. Non-equilibrium reacting gas flows kinetic theory of transport and relaxation processes

    Nagnibeda, Ekaterina; Nagnibeda, Ekaterina


    This volume develops the kinetic theory of transport phenomena and relaxation processes in the flows of reacting gas mixtures. The theory is applied to the modeling of non-equilibrium flows behind strong shock waves, in the boundary layer, and in nozzles.

  9. Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

    Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban


    Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

  10. An efficient parallel flow solver for two-way coupled turbulent flows with deformable bodies

    Verzicco, Roberto; Spandan, Vamsi; Meschini, Valentina; Lohse, Detlef; de Tullio, Marco D.


    There are countless examples in Nature and technology in which a flow and a deformable structure interact dynamically and determine each other's behaviour. Among many, two contexts in which this is particularly relevant is in two-phase flows with finite size deformable bubbles or immiscible drops and in cardiovascular flows of heart valves and deformable vessels. Since the standard methods become terminally expensive when the number of deformable bodies become large or the set-up has a complex geometric configuration, in this work, we discuss a simple yet effective approach to cope with the above problems. The main ingredients are: i) an efficient Navier-Stokes solver, ii) an interaction potential approach for the dynamics of a deformable structure, iii) an immersed boundary procedure to deal with the geometrical complexity iv) a set of fluid/structure interaction approaches (strong or loose) and v) a simple and efficient parallelisation strategy to handle large-scale simulations. Several complex examples will be shown and discussed with the results validated either by ad-hoc experiments or by comparisons with results from the literature.

  11. A steady-state solver and stability calculator for nonlinear internal wave flows

    Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.


    A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.

  12. Gauss-Seidel Accelerated: Implementing Flow Solvers on Field Programmable Gate Arrays

    Chassin, David P.; Armstrong, Peter R.; Chavarría-Miranda, Daniel; Guttromson, Ross T.


    Non-linear steady-state power flow solvers have typically relied on the Newton-Raphson method to efficiently compute solutions on today's computer systems. Field Programmable Gate Array (FPGA) devices, which have recently been integrated into high-performance computers by major computer system vendors, offer an opportunity to significantly increase the performance of power flow solvers. However, only some algorithms are suitable for an FPGA implementation. The Gauss-Seidel method of solving the AC power flow problem is an excellent example of such an opportunity. In this paper we discuss algorithmic design considerations, optimization, implementation, and performance results of the implementation of the Gauss-Seidel method running on a Silicon Graphics Inc. Altix-350 computer equipped with a Xilinx Virtex II 6000 FPGA.

  13. An Eulerian-Lagrangian open source solver for bubbly flow in vertical pipes

    Pena-Monferrer, C.; Munoz-Cobo, J. L.; Monros-Andreu, G.; Martinez-Cuenca, R.; Chiva, S.


    Air-water two-phase flow is present in natural and industrial processes of different nature as nuclear reactors. An accurate local prediction of the boiling flow could support safety and operation analyses of nuclear reactors. An Eulerian-Lagrangian approach is investigated in this contribution as it can be used as a virtual facility to investigate the two-phase flow phenomena. A solver based on the PISO algorithm coupled with the Lagrangian equation of motion have been implemented for computing incompressible bubbly flows. (Author)

  14. Refining a relativistic, hydrodynamic solver: Admitting ultra-relativistic flows

    Bernstein, J. P.; Hughes, P. A.


    We have undertaken the simulation of hydrodynamic flows with bulk Lorentz factors in the range 102-106. We discuss the application of an existing relativistic, hydrodynamic primitive variable recovery algorithm to a study of pulsar winds, and, in particular, the refinement made to admit such ultra-relativistic flows. We show that an iterative quartic root finder breaks down for Lorentz factors above 102 and employ an analytic root finder as a solution. We find that the former, which is known to be robust for Lorentz factors up to at least 50, offers a 24% speed advantage. We demonstrate the existence of a simple diagnostic allowing for a hybrid primitives recovery algorithm that includes an automatic, real-time toggle between the iterative and analytical methods. We further determine the accuracy of the iterative and hybrid algorithms for a comprehensive selection of input parameters and demonstrate the latter’s capability to elucidate the internal structure of ultra-relativistic plasmas. In particular, we discuss simulations showing that the interaction of a light, ultra-relativistic pulsar wind with a slow, dense ambient medium can give rise to asymmetry reminiscent of the Guitar nebula leading to the formation of a relativistic backflow harboring a series of internal shockwaves. The shockwaves provide thermalized energy that is available for the continued inflation of the PWN bubble. In turn, the bubble enhances the asymmetry, thereby providing positive feedback to the backflow.

  15. Verification of a binary fluid solidification model in the finite-volume flow solver

    Waclawczyk, Tomasz


    The aim of this paper is to verify the new numerical implementation of a binary fluid, heat conduction dominated solidification model. First, we extend a semi-analytical solution to the heat diffusion equation, next, the range of its applicability is investigated. It was found that the linearization introduced to the heat diffusion equation negatively affects the ability to predict solidus and liquidus lines positions whenever the magnitude of latent heat of fusion exceeds a certain value. Next, a binary fluid solidification model is coupled with a flow solver, and is used in a numerical study of Al-4.1%Cu alloy solidification in a two-dimensional rectangular cavity. An accurate coupling between the solidification model and the flow solver is crucial for the correct forecast of solidification front positions and macrosegregation patterns.

  16. Fluid structure interaction solver coupled with volume of fluid method for two-phase flow simulations

    Cerroni, D.; Fancellu, L.; Manservisi, S.; Menghini, F.


    In this work we propose to study the behavior of a solid elastic object that interacts with a multiphase flow. Fluid structure interaction and multiphase problems are of great interest in engineering and science because of many potential applications. The study of this interaction by coupling a fluid structure interaction (FSI) solver with a multiphase problem could open a large range of possibilities in the investigation of realistic problems. We use a FSI solver based on a monolithic approach, while the two-phase interface advection and reconstruction is computed in the framework of a Volume of Fluid method which is one of the more popular algorithms for two-phase flow problems. The coupling between the FSI and VOF algorithm is efficiently handled with the use of MEDMEM libraries implemented in the computational platform Salome. The numerical results of a dam break problem over a deformable solid are reported in order to show the robustness and stability of this numerical approach.

  17. MPDATA: A positive definite solver for geophysical flows

    Smolarkiewicz, P.K.; Margolin, L.G. [Los Alamos National Lab., NM (United States)


    This paper is a review of MPDATA, a class of methods for the numerical simulation of advection based on the sign-preserving properties of upstream differencing. MPDATA was designed originally as an inexpensive alternative to flux-limited schemes for evaluating the transport of nonnegative thermodynamic variables (such as liquid water or water vapor) in atmospheric models. During the last decade, MPDATA has evolved from a simple advection scheme to a general approach for integrating the conservation laws of geophysical fluids on micro-to-planetary scales. The purpose of this paper is to summarize the basic concepts leading to a family of MPDATA schemes, review the existing MPDATA options, as well as to demonstrate the efficacy of the approach using diverse examples of complex geophysical flows.

  18. Heat and mass transfer for turbulent flow of chemically reacting gas in eccentric annular channels

    Besedina, T. V.; Tverkovkin, B. E.; Udot, A. V.; Yakushev, A. P.


    An algorithm is proposed for calculating the velocity, temperature, and concentration fields under conditions of cooling of a cylindrical heat-releasing rod, placed off-center in a circular casing pipe, by a longitudinal flow of chemically reacting gas [N2O4].

  19. Development and validation of a magneto-hydrodynamic solver for blood flow analysis

    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)


    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.

  20. Notes on Newton-Krylov based Incompressible Flow Projection Solver

    Robert Nourgaliev; Mark Christon; J. Bakosi


    The purpose of the present document is to formulate Jacobian-free Newton-Krylov algorithm for approximate projection method used in Hydra-TH code. Hydra-TH is developed by Los Alamos National Laboratory (LANL) under the auspices of the Consortium for Advanced Simulation of Light-Water Reactors (CASL) for thermal-hydraulics applications ranging from grid-to-rod fretting (GTRF) to multiphase flow subcooled boiling. Currently, Hydra-TH is based on the semi-implicit projection method, which provides an excellent platform for simulation of transient single-phase thermalhydraulics problems. This algorithm however is not efficient when applied for very slow or steady-state problems, as well as for highly nonlinear multiphase problems relevant to nuclear reactor thermalhydraulics with boiling and condensation. These applications require fully-implicit tightly-coupling algorithms. The major technical contribution of the present report is the formulation of fully-implicit projection algorithm which will fulfill this purpose. This includes the definition of non-linear residuals used for GMRES-based linear iterations, as well as physics-based preconditioning techniques.

  1. Evaluating the performance of the two-phase flow solver interFoam

    Deshpande, Suraj S.; Anumolu, Lakshman; Trujillo, Mario F.


    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

  2. Gas-Kinetic Navier-Stokes Solver for Hypersonic Flows in Thermal and Chemical Non-Equilibrium Project

    National Aeronautics and Space Administration — This SBIR project proposes to develop a gas-kinetic Navier-Stokes solver for simulation of hypersonic flows in thermal and chemical non-equilibrium. The...

  3. A Fourier-based elliptic solver for vortical flows with periodic and unbounded directions

    Chatelain, Philippe; Koumoutsakos, Petros


    We present a computationally efficient, adaptive solver for the solution of the Poisson and Helmholtz equation used in flow simulations in domains with combinations of unbounded and periodic directions. The method relies on using FFTs on an extended domain and it is based on the method proposed by Hockney and Eastwood for plasma simulations. The method is well-suited to problems with dynamically growing domains and in particular flow simulations using vortex particle methods. The efficiency of the method is demonstrated in simulations of trailing vortices.

  4. Recent progress of laser metrology in chemically reacting flows at onera

    Mohamed, A.; Dorval, N.; Vilmart, G.; Orain, M.; George, R.; Scherman, M.; Nafa, M.; Bresson, A.; Attal-Tretout, B.; Lefebvre, M.


    This paper presents some of the development actions performed these last years at ONERA using laser spectroscopic techniques to probe chemically reacting flows. Techniques like laser absorption, laser induced fluorescence (LIF), and Raman scattering will be described with focus on present drawbacks as well as expectations from new laser technologies (Interband Cascade Lasers (ICL) diodes, Optical Parametrical Oscillators (OPO), frequency comb, and femto/picosecond lasers) before showing some results of recent applications in ground facilities.

  5. Numerical simulation of reacting and non-reacting flow in a combustion chamber; Numerisk simulering av reagerande och icke-reagerande stroemning i en braennkammare

    Borg, A.; Revstedt, J.


    The purpose of this work has been to do a preliminary study of how well numerical calculations with different turbulence models can predict the flow and temperature fields of a strongly swirling and combusting flow in an experimental combustion chamber and to see which parameters in the mathematical model are the most important. The combustion chamber on which we have done the calculations is called Validation Rig II and was designed by Volvo Aero Corporation. The main part of the study has been carried out on a non-reacting flow but some work has also been done on reacting flow. In most cases it has not been meaningful to compare the calculations with the measurements because they differ quite a lot from each other. For the non-reacting case the following investigations have been made: * How the solution differs for different turbulence models, * The solutions sensitivity to inlet boundary conditions, * How different types of leakage disturb the flow, and * The difference in results between two different CFD-codes, the commercial code CFDS-Flow3D and a code developed at the department of fluid mechanics. For the reacting cases we have studied the influence of: * one or two reaction steps, * the effects of a change in reaction rate, * the influence of thermal radiation, and * the effects of changing the boundary conditions for temperature on the walls. The results from these calculations show that the inlet turbulence intensity has very little effect on the values of the turbulent quantities as well as the velocity profiles at the outlet. Changing the turbulence model or the outlet boundary conditions gives some change in velocity profiles at the outlet but only marginal effects on the swirl number. 21 refs, 54 figs, 19 tabs

  6. Numerical simulation of perfect fluid flows around complex 3D configurations by a multidomain solver using the MUSCL approach

    Guillen, Ph.; Borrel, M.; Dormieux, M.


    A numerical scheme of the MUSCL type used for the numerical simulation of gas flow of different types around complex configurations is described. Approximate Riemann solvers of the Van Leer, Roc, and Osher types, developed for perfect gas flows are used. These solvers have been extended to non-reactive mixtures of two species and real gas flows by Abgrall, Montagne and Vinokur. The architecture of the code, dictated by constraints in geometrical considerations, computational aspects, the specific nature of the flow, and ergonomy, is described.

  7. Numerical Computation of the Chemically Reacting Flow around the National Aero-Space Plane

    Tannehill, J. C.


    This final report summarizes the research accomplished. The research performed during the grant period can be divided into the following major areas: (1) Computation of chemically reacting Supersonic combustion ramjet (scramjet) flowfields. (2) Application of a two-equation turbulence model to supersonic combustion flowfields. (3) Computation of the integrated aerodynamic and propulsive flowfields of a generic hypersonic space plane. (4) Computation of hypersonic flows with finite-catalytic walls. (5) Development of an upwind Parabolized Navier-Stokes (PNS) code for thermo-chemical nonequilibrium flows.

  8. A mathematical basis for automated structured grid generation with close coupling to the flow solver

    Barnette, D.W.


    The first two truncation error terms resulting from finite differencing the convection terms in the two-dimensional Navier-Stokes equations are examined for the purpose of constructing two-dimensional grid generation schemes. These schemes are constructed such that the resulting grid distributions drive the error terms to zero. Two sets of equations result, one for each error term, that show promise in generating grids that provide more accurate flow solutions and possibly faster convergence. One set results in an algebraic scheme that drives the first truncation term to zero, and the other a hyperbolic scheme that drives the second term to zero. Also discussed is the possibility of using the schemes in sequentially constructing a grid in an iterative algorithm involving the flow solver. In essence, the process is envisioned to generate not only a flow field solution but the grid as well, rendering the approach a hands-off method for grid generation

  9. Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows

    Shih, Tsan-Hsing; Liu, Nan-Suey


    In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.

  10. The non-linear microscale flow solver 3DWind Developments and validation

    Undheim, Ove


    This PhD thesis describes the implementation of a Reynolds Stress Model in the RANS microscale solver 3DWind, which is developed to model wind flow in complex terrain. The solver is also calibrated and validated with the two-dimensional channel flow test case C18 from the ERCOFTAC Classic database and the full-scale atmospheric flow case of the Askervein hill. The implemented equations calculate both flow cases in good accordance with available experimental and numerical results. Still, the simulation experience and obtained results show that modelling of recirculation is a difficult task. The calculated flow field is very sensitive to the separation point, which is sensitive to several other factors. One important factor is the wall functions, which cause the separation zone to depend on the thickness of the first grid cell. Compared to the k-{epsilon} model, results from simulations with the Reynolds Stress Model gave improvements in the calculated turbulence upstream the C18 hill. There were also differences in the solutions in the wake of both the C18 and the Askervein hills; still, the differences are too small to make any conclusions about the quality of the models. The disadvantages of decreased stability, more wiggles in the solution and increased computational effort are considered larger than the advantages of accounting for anisotropy and historical effects in the Reynolds stresses. The solver is further used to quantify the effects of roughness and topography by generalized two-dimensional investigations of atmospheric flow. Hills and ridges are in this analysis found to increase wind velocities at 80m by up to 38%, and wind velocities above the ocean at 80m are 14% higher than corresponding open land velocities. Finally, a full wind resource assessment has been carried out at Eldsfjellet at the Norwegian island Hitra. Results were compared with measured data and simulation results from the linearized model WAsP. WAsP was found to estimate higher

  11. Extension of Finite Volume Compressible Flow Solvers to Multi-dimensional, Variable Density Zero Mach Number Flows

    Schneider, T.; Botta, N.; Geratz, K. J.; Klein, R.


    When attempting to compute unsteady, variable density flows at very small or zero Mach number using a standard finite volume compressible flow solver one faces at least the following difficulties: (i) Spatial pressure variations vanish as the Mach number M→0, but they do affect the velocity field at leading order; (ii) the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux; (iii) violations of this constraint crucially affect the transport of mass, preventing a code to properly advect even a constant density distribution. We overcome these difficulties through a new algorithm for constructing numerical fluxes in the context of multi-dimensional finite volume methods in conservation form. The construction of numerical fluxes involves: (1) An explicit upwind step yielding predictions for the nonlinear convective flux components. (2) A first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint. This step requires the solution of a first Poisson-type equation. (3) A second projection step which provides the yet unknown (non-convective) pressure contribution to the total flux of momentum. This second projection requires the solution of another Poisson-type equation and yields the cell centered velocity field at the new time. This velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit. Step (1) can be done by any standard finite volume compressible flow solver. The input to steps (2) and (3) involves solely the fluxes from step (1) and is independent of how these were obtained. Thus, our approach allows any such solver to be extended to compute variable density incompressible flows.

  12. A weakly compressible free-surface flow solver for liquid–gas systems using the volume-of-fluid approach

    Heyns, Johan A


    Full Text Available of the gas has a noteworthy effect on predicted pressure loads in liquid–gas flow in certain instances. With the aim of providing a more accurate numerical representation of dynamic two-fluid flow, the solver is subsequently extended to account for variations...

  13. Droplet in micro-channels: A numerical approach using an adaptive two phase flow solver

    Fullana, Jose-Maria; Popinet, Stéphane; Josserand, Christophe


    We propose a numerical approach to study the mechanics of a flowing bubble in a constraint micro channel. Using an open source two phase flow solver (Gerris, we compute solutions of the bubble dynamics (i.e. shape and terminal velocity) induced by the interaction between the bubble movement, the Laplace pressure variation, and the lubrication film near the channel wall. Quantitative and qualitative results are presented and compared against both theory and experimental data for small Capillary numbers. We discuss the technical issues of explicit integration methods on small Capillary numbers computations, and the possibility of adding Van der Walls forces to give a more precise picture of the Droplet-based microfluidic problem.

  14. A second-order coupled immersed boundary-SAMR construction for chemically reacting flow over a heat-conducting Cartesian grid-conforming solid

    Kedia, Kushal S.


    In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A "buffer zone" methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed. © 2014 Elsevier Inc.

  15. Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

    Anciaux-Sedrakian Ani


    Full Text Available In the past few years, High Performance Computing (HPC technologies led to General Purpose Processing on Graphics Processing Units (GPGPU and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO2 geological sequestration or Enhanced Oil Recovery (EOR simulation. However the crucial point is “are current algorithms and software able to use these new technologies efficiently?” The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPU-consuming part of such simulators. This paper proposes a survey on various solver and preconditioner algorithms, analyzes their efficiency and performance regarding these distinct architectures. Furthermore it proposes a novel approach based on a hybrid programming model for both GPU and many-core clusters. The proposed optimization techniques are validated through a Krylov subspace solver; BiCGStab and some preconditioners like ILU0 on GPU, multi-core and many-core architectures, on various large real study cases in EOR simulation.

  16. Methods for Prediction of High-Speed Reacting Flows in Aerospace Propulsion

    Drummond, J. Philip


    Research to develop high-speed airbreathing aerospace propulsion systems was underway in the late 1950s. A major part of the effort involved the supersonic combustion ramjet, or scramjet, engine. Work had also begun to develop computational techniques for solving the equations governing the flow through a scramjet engine. However, scramjet technology and the computational methods to assist in its evolution would remain apart for another decade. The principal barrier was that the computational methods needed for engine evolution lacked the computer technology required for solving the discrete equations resulting from the numerical methods. Even today, computer resources remain a major pacing item in overcoming this barrier. Significant advances have been made over the past 35 years, however, in modeling the supersonic chemically reacting flow in a scramjet combustor. To see how scramjet development and the required computational tools finally merged, we briefly trace the evolution of the technology in both areas.

  17. Hybrid Multiphase CFD Solver for Coupled Dispersed/Segregated Flows in Liquid-Liquid Extraction

    Kent E. Wardle


    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.

  18. Multiphysics Simulations of Entrained Flow Gasification. Part I: Validating the Nonreacting Flow Solver and the Particle Turbulent Dispersion Model

    Kumar, Mayank


    In this two-part paper, we describe the construction, validation, and application of a multiscale model of entrained flow gasification. The accuracy of the model is demonstrated by (1) rigorously constructing and validating the key constituent submodels against relevant canonical test cases from the literature and (2) validating the integrated model against experimental data from laboratory scale and commercial scale gasifiers. In part I, the flow solver and particle turbulent dispersion models are validated against experimental data from nonswirling flow and swirling flow test cases in an axisymmetric sudden expansion geometry and a two-phase flow test case in a cylindrical bluff body geometry. Results show that while the large eddy simulation (LES) performs best among all tested models in predicting both swirling and nonswirling flows, the shear stress transport (SST) k-ω model is the best choice among the commonly used Reynolds-averaged Navier-Stokes (RANS) models. The particle turbulent dispersion model is accurate enough in predicting particle trajectories in complex turbulent flows when the underlying turbulent flow is well predicted. Moreover, a commonly used modeling constant in the particle dispersion model is optimized on the basis of comparisons with particle-phase experimental data for the two-phase flow bluff body case. © 2011 American Chemical Society.

  19. A pseudo-compressible variational multiscale solver for turbulent incompressible flows

    Yang, Liang; Badia, Santiago; Codina, Ramon


    In this work, we design an explicit time-stepping solver for the simulation of the incompressible turbulent flow through the combination of VMS methods and artificial compressibility. We evaluate the effect of the artificial compressibility on the accuracy of the explicit formulation for under-resolved LES simulations. A set of benchmarks have been solved, e.g., the 3D Taylor-Green vortex problem in turbulent regimes. The resulting method is proven to be an effective alternative to implicit methods in some application ranges (in terms of problem size and computational resources), providing comparable results with very low memory requirements. As an example, with the explicit approach, we are able to solve accurately the Taylor-Green vortex benchmark in a fine mesh with 512^3 cells on a 12 cores 64 GB ram machine.

  20. A comparison of hyperbolic solvers for ideal and real gas flows

    R. M. L. Coelho


    Full Text Available Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to second-order by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. These methods require the so-called Roe's average state, which is frequently difficult and sometimes impossible to obtain. Other methods that do not require the average state are best suited for complex equations of state. Of these, the VFRoe, AUSM+ and Hybrid Lax-Friedrich-Lax-Wendroff methods were compared for one-dimensional compressible flows of a Van der Waals gas. All methods were evaluated regarding their accuracy for given mesh sizes and their computational cost for a given solution accuracy. It was shown that, even though they require more floating points and indirect addressing operations per time step, for a given time interval for integration the second-order methods are less-time consuming than the first-order methods for a required accuracy. It was also shown that AUSM+ and VFRoe are the most accurate methods and that AUSM+ is much faster than the others, and is thus recommended for nonideal one-phase gas flows.

  1. A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

    Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri


    Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variab...

  2. Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows

    Norris, Andrew T.; Hsu, Andrew T.


    In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.


    LI Jun; LIU Li-jun; FENG Zhen-ping


    Hydrodynamic optimization design of the bend pipe from pump using the Navier-Stokes solver and evolutionary algorithms was conducted. The minimization of the total pressure loss of the bend pipe was chosen as the design object in order to obtain the uniform exit flows through suppressing the secondary flows. The 3-D Navier-Stokes solver was applied to evaluate the hydrodynamic performance of the bend-pipe flows. A 7th-order Bezier curve was used to parameterize the meridional section and elliptic representation was adopted to represent the cross-section profiles of the bend pipe. Evolutionary algorithms were applied in optimization. The obtained results show that the designed bend pipe shape has much more uniform exit flows compared with the initial one and much weaker secondary flows, and that the evolutionary algorithms and CFD technique are the powerful optimization tools for the fluid machinery design.

  4. Multi-GPU three dimensional Stokes solver for simulating glacier flow

    Licul, Aleksandar; Herman, Frédéric; Podladchikov, Yuri; Räss, Ludovic; Omlin, Samuel


    Here we present how we have recently developed a three-dimensional Stokes solver on the GPUs and apply it to a glacier flow. We numerically solve the Stokes momentum balance equations together with the incompressibility equation, while also taking into account strong nonlinearities for ice rheology. We have developed a fully three-dimensional numerical MATLAB application based on an iterative finite difference scheme with preconditioning of residuals. Differential equations are discretized on a regular staggered grid. We have ported it to C-CUDA to run it on GPU's in parallel, using MPI. We demonstrate the accuracy and efficiency of our developed model by manufactured analytical solution test for three-dimensional Stokes ice sheet models (Leng et al.,2013) and by comparison with other well-established ice sheet models on diagnostic ISMIP-HOM benchmark experiments (Pattyn et al., 2008). The results show that our developed model is capable to accurately and efficiently solve Stokes system of equations in a variety of different test scenarios, while preserving good parallel efficiency on up to 80 GPU's. For example, in 3D test scenarios with 250000 grid points our solver converges in around 3 minutes for single precision computations and around 10 minutes for double precision computations. We have also optimized the developed code to efficiently run on our newly acquired state-of-the-art GPU cluster octopus. This allows us to solve our problem on more than 20 million grid points, by just increasing the number of GPU used, while keeping the computation time the same. In future work we will apply our solver to real world applications and implement the free surface evolution capabilities. REFERENCES Leng,W.,Ju,L.,Gunzburger,M. & Price,S., 2013. Manufactured solutions and the verification of three-dimensional stokes ice-sheet models. Cryosphere 7,19-29. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson,G.H., Hindmarsh, R

  5. Development of an Efficient Meso- scale Multi-phase Flow Solver in Nuclear Applications

    Lee, Taehun [City Univ. (CUNY), NY (United States)


    The proposed research aims at formulating a predictive high-order Lattice Boltzmann Equation for multi-phase flows relevant to nuclear energy related application - namely, saturated and sub-cooled boiling in reactors, and liquid- liquid mixing and extraction for fuel cycle separation. An efficient flow solver will be developed based on the Finite Element based Lattice Boltzmann Method (FE- LBM), accounting for phase-change heat transfer and capable of treating multiple phases over length scales from the submicron to the meter. A thermal LBM will be developed in order to handle adjustable Prandtl number, arbitrary specific heat ratio, a wide range of temperature variations, better numerical stability during liquid-vapor phase change, and full thermo-hydrodynamic consistency. Two-phase FE-LBM will be extended to liquid–liquid–gas multi-phase flows for application to high-fidelity simulations building up from the meso-scale up to the equipment sub-component scale. While several relevant applications exist, the initial applications for demonstration of the efficient methods to be developed as part of this project include numerical investigations of Critical Heat Flux (CHF) phenomena in nuclear reactor fuel bundles, and liquid-liquid mixing and interfacial area generation for liquid-liquid separations. In addition, targeted experiments will be conducted for validation of this advanced multi-phase model.

  6. MPSalsa a finite element computer program for reacting flow problems. Part 2 - user`s guide

    Salinger, A.; Devine, K.; Hennigan, G.; Moffat, H. [and others


    This manual describes the use of MPSalsa, an unstructured finite element (FE) code for solving chemically reacting flow problems on massively parallel computers. MPSalsa has been written to enable the rigorous modeling of the complex geometry and physics found in engineering systems that exhibit coupled fluid flow, heat transfer, mass transfer, and detailed reactions. In addition, considerable effort has been made to ensure that the code makes efficient use of the computational resources of massively parallel (MP), distributed memory architectures in a way that is nearly transparent to the user. The result is the ability to simultaneously model both three-dimensional geometries and flow as well as detailed reaction chemistry in a timely manner on MT computers, an ability we believe to be unique. MPSalsa has been designed to allow the experienced researcher considerable flexibility in modeling a system. Any combination of the momentum equations, energy balance, and an arbitrary number of species mass balances can be solved. The physical and transport properties can be specified as constants, as functions, or taken from the Chemkin library and associated database. Any of the standard set of boundary conditions and source terms can be adapted by writing user functions, for which templates and examples exist.

  7. MPSalsa a finite element computer program for reacting flow problems. Part 2 - user`s guide

    Salinger, A.; Devine, K.; Hennigan, G.; Moffat, H. [and others


    This manual describes the use of MPSalsa, an unstructured finite element (FE) code for solving chemically reacting flow problems on massively parallel computers. MPSalsa has been written to enable the rigorous modeling of the complex geometry and physics found in engineering systems that exhibit coupled fluid flow, heat transfer, mass transfer, and detailed reactions. In addition, considerable effort has been made to ensure that the code makes efficient use of the computational resources of massively parallel (MP), distributed memory architectures in a way that is nearly transparent to the user. The result is the ability to simultaneously model both three-dimensional geometries and flow as well as detailed reaction chemistry in a timely manner on MT computers, an ability we believe to be unique. MPSalsa has been designed to allow the experienced researcher considerable flexibility in modeling a system. Any combination of the momentum equations, energy balance, and an arbitrary number of species mass balances can be solved. The physical and transport properties can be specified as constants, as functions, or taken from the Chemkin library and associated database. Any of the standard set of boundary conditions and source terms can be adapted by writing user functions, for which templates and examples exist.

  8. Simulation of the Partially Ionized Reacting Plasma Flow in a Negative Hydrogen Ion Source

    Gatsonis, Nikolaos; Averkin, Sergey; Olson, Lynn


    A High Pressure Discharge Negative Ion Source (HPDNIS) operating on hydrogen is been under investigation. The Negative Ion Production (NIP) section of the HPDNIS attaches to the 10-100 Torr RF-discharge chamber with a micronozzle and ends with a grid that extracts the negative ion beam. The partially ionized and reacting plasma flow in the NIP section is simulated using an unstructured three-dimensional Direct Simulation Monte Carlo (U3DSMC) code. The NIP section contains a low-pressure plasma that includes H2, vibrationally-rotationally excited H2^*, negative hydrogen atoms H^-, and electrons. Primary reactions in the NIP section are dissociate attachment, H2^*+e->H^0+H^-and electron collisional detachment, e+H^-->H+2e. The U3DSMC computational domain includes the entrance to the NIP nozzle and the extraction grid at the exit. The flow parameters at the entrance are based on conditions in the RF-discharge chamber and are implemented in U3DSMC using a Kinetic-Moment subsonic boundary conditions method. The rotational and vibrational degrees of freedom in U3DSMC are implemented using the Larsen-Borgnakke model. Chemical reactions are implemented in U3DSMC using the Quantum-Kinetic model. Simulations cover the regime of operation of the HPDNIS and examine the flow characteristics inside the NIP section.

  9. Multiphase integral reacting flow computer code (ICOMFLO): User`s guide

    Chang, S.L.; Lottes, S.A.; Petrick, M.


    A copyrighted computational fluid dynamics computer code, ICOMFLO, has been developed for the simulation of multiphase reacting flows. The code solves conservation equations for gaseous species and droplets (or solid particles) of various sizes. General conservation laws, expressed by elliptic type partial differential equations, are used in conjunction with rate equations governing the mass, momentum, enthalpy, species, turbulent kinetic energy, and turbulent dissipation. Associated phenomenological submodels of the code include integral combustion, two parameter turbulence, particle evaporation, and interfacial submodels. A newly developed integral combustion submodel replacing an Arrhenius type differential reaction submodel has been implemented to improve numerical convergence and enhance numerical stability. A two parameter turbulence submodel is modified for both gas and solid phases. An evaporation submodel treats not only droplet evaporation but size dispersion. Interfacial submodels use correlations to model interfacial momentum and energy transfer. The ICOMFLO code solves the governing equations in three steps. First, a staggered grid system is constructed in the flow domain. The staggered grid system defines gas velocity components on the surfaces of a control volume, while the other flow properties are defined at the volume center. A blocked cell technique is used to handle complex geometry. Then, the partial differential equations are integrated over each control volume and transformed into discrete difference equations. Finally, the difference equations are solved iteratively by using a modified SIMPLER algorithm. The results of the solution include gas flow properties (pressure, temperature, density, species concentration, velocity, and turbulence parameters) and particle flow properties (number density, temperature, velocity, and void fraction). The code has been used in many engineering applications, such as coal-fired combustors, air

  10. Comment on "Flow-distributed oscillations: Stationary chemical waves in a reacting flow"

    Andresen, Peter Ragnar; Mosekilde, Erik; Dewel, G.;


    In a recent paper by Kern and Menzinger [Phys. Rev. E 60, R3471 (1999)] a successful verification of the stationary space-periodic structures predicted by Andresen et al. [Phys. Rev. E 60, 297 (1999)] was reported. Kaern and Menzinger suggest a mechanism for the formation of such structures...... that yields a linear relationship between the selected wavelength and the flow rate. We find this mechanism too simple and produce numerical simulations that support the original interpretation of these structures....

  11. Parallelization of Lower-Upper Symmetric Gauss-Seidel Method for Chemically Reacting Flow

    Yoon, Seokkwan; Jost, Gabriele; Chang, Sherry


    Development of technologies for exploration of the solar system has revived an interest in computational simulation of chemically reacting flows since planetary probe vehicles exhibit non-equilibrium phenomena during the atmospheric entry of a planet or a moon as well as the reentry to the Earth. Stability in combustion is essential for new propulsion systems. Numerical solution of real-gas flows often increases computational work by an order-of-magnitude compared to perfect gas flow partly because of the increased complexity of equations to solve. Recently, as part of Project Columbia, NASA has integrated a cluster of interconnected SGI Altix systems to provide a ten-fold increase in current supercomputing capacity that includes an SGI Origin system. Both the new and existing machines are based on cache coherent non-uniform memory access architecture. Lower-Upper Symmetric Gauss-Seidel (LU-SGS) relaxation method has been implemented into both perfect and real gas flow codes including Real-Gas Aerodynamic Simulator (RGAS). However, the vectorized RGAS code runs inefficiently on cache-based shared-memory machines such as SGI system. Parallelization of a Gauss-Seidel method is nontrivial due to its sequential nature. The LU-SGS method has been vectorized on an oblique plane in INS3D-LU code that has been one of the base codes for NAS Parallel benchmarks. The oblique plane has been called a hyperplane by computer scientists. It is straightforward to parallelize a Gauss-Seidel method by partitioning the hyperplanes once they are formed. Another way of parallelization is to schedule processors like a pipeline using software. Both hyperplane and pipeline methods have been implemented using openMP directives. The present paper reports the performance of the parallelized RGAS code on SGI Origin and Altix systems.

  12. Tomographic imaging of reacting flows in 3D by laser absorption spectroscopy

    Foo, J.; Martin, P. A.


    This paper describes the development of an infrared laser absorption tomography system for the 3D volumetric imaging of chemical species and temperature in reacting flows. The system is based on high-resolution near-infrared tunable diode laser absorption spectroscopy (TDLAS) for the measurement of water vapour above twin, mixed fuel gas burners arranged with an asymmetrical output. Four parallel laser beams pass through the sample region and are rotated rapidly in a plane to produce a wide range of projection angles. A rotation of 180° with 0.5° sampling was achieved in 3.6 s. The effects of changes to the burner fuel flow were monitored in real time for the 2D distributions. The monitoring plane was then moved vertically relative to the burners enabling a stack of 2D images to be produced which were then interpolated to form a 3D volumetric image of the temperature and water concentrations above the burners. The optical transmission of each beam was rapidly scanned around 1392 nm and the spectrum was fitted to find the integrated absorbance of the water transitions and although several are probed in each scan, two of these transitions possess opposite temperature dependencies. The projections of the integrated absorbances at each angle form the sinogram from which the 2D image of integrated absorbance of each line can be reconstructed by the direct Fourier reconstruction based on the Fourier slice theorem. The ratio of the integrated absorbances of the two lines can then be related to temperature alone in a method termed, two-line thermometry. The 2D temperature distribution obtained was validated for pattern and accuracy by thermocouple measurements. With the reconstructed temperature distribution, the temperature-dependent line strengths could be determined and subsequently the concentration distribution of water across the 2D plane whilst variations in burner condition were carried out. These results show that the measurement system based on TDLAS can be

  13. Reacting to "Reacting"

    Houle, Amanda


    This article describes the author's experiences as a student participating in a general education program called "Reacting to the Past," in which college students play elaborate games set at pivotal moments in the past, their roles informed by great texts. She found that the experience of reenacting pivotal historical moments produced an intensely…

  14. Prediction of engine and near-field plume reacting flows in low-thrust chemical rockets

    Weiss, Jonathan M.; Merkle, Charles L.


    A computational model is employed to study the reacting flow within the engine and near-field plumes of several small gaseous hydrogen-oxygen thrusters. The model solves the full Navier-Stokes equations coupled with species diffusion equations for a hydrogen-oxygen reaction kinetics system and includes a two-equation q-omega model for turbulence. Predictions of global performance parameters and localized flowfield variables are compared with experimental data in order to assess the accuracy with which these flowfields are modeled and to identify aspects of the model which require improvement. Predicted axial and radial velocities 3 mm downstream of the exit plane show reasonable agreement with the measurements. The predicted peak in axial velocity in the hydrogen film coolant along the nozzle wall shows the best agreement; however, predictions within the core region are roughly 15 percent below measured values, indicating an underprediction of the extent to which the hydrogen diffuses and mixes with the core flow. There is evidence that this is due to three-dimensional mixing processes which are not included in the axisymmetric model.

  15. High-Speed Turbulent Reacting Flows: Intrinsic Flame Instability and its Effects on the Turbulent Cascade

    Poludnenko, Alexei


    Turbulent reacting flows are pervasive both in our daily lives on Earth and in the Universe. They power modern society being at the heart of many energy generation and propulsion systems, such as gas turbines, internal combustion and jet engines. On astronomical scales, thermonuclear turbulent flames are the driver of some of the most powerful explosions in the Universe, knows as Type Ia supernovae. Despite this ubiquity in Nature, turbulent reacting flows still pose a number of fundamental questions often exhibiting surprising and unexpected behavior. In this talk, we will discuss several such phenomena observed in direct numerical simulations of high-speed, premixed, turbulent flames. We show that turbulent flames in certain regimes are intrinsically unstable even in the absence of the surrounding combustor walls or obstacles, which can support the thermoacoustic feedback. Such instability can fundamentally change the structure and dynamics of the turbulent cascade, resulting in a significant (and anisotropic) redistribution of kinetic energy from small to large scales. In particular, three effects are observed. 1) The turbulent burning velocity can develop pulsations with significant peak-to-peak amplitudes. 2) Unstable burning can result in pressure build-up and the formation of pressure waves or shocks when the flame speed approaches or exceeds the speed of a Chapman-Jouguet deflagration. 3) Coupling of pressure and density gradients across the flame can lead to the anisotropic generation of turbulence inside the flame volume and flame acceleration. We extend our earlier analysis, which relied on a simplified single-step reaction model, by demonstrating existence of these effects in realistic chemical flames (hydrogen and methane) and in thermonuclear flames in degenerate, relativistic plasmas found in stellar interiors. Finally, we discuss the implications of these results for subgrid-scale LES combustion models. This work was supported by the Air Force

  16. A feasibility Study: The Succinct Solver v2.0, XSB Prolog v2.6, and Flow-Logic Based Program Analysis for Carmel

    Pilegaard, Henrik


    We perform a direct comparison of the {Succinct Solver v2.0} and {XSB Prolog v2.6} based on experiments with {Control Flow Analyses} of scalable {Discretionary Ambient programs} and {Carmel programs}. To facilitate this comparison we expand ALFP clauses accepted by the Succinct Solver into more...

  17. Cerebral aneurysm blood flow simulations are sensitive to basic solver settings.

    Dennis, Kendall D; Kallmes, David F; Dragomir-Daescu, Dan


    Computational modeling of peri-aneurysmal hemodynamics is typically carried out with commercial software without knowledge of the sensitivity of the model to variation in input values. For three aneurysm models, we carried out a formal sensitivity analysis and optimization strategy focused on variation in timestep duration and model residual error values and their impact on hemodynamic outputs. We examined the solution sensitivity to timestep sizes of 10(-3)s, 10(-4)s, and 10(-5)s while using model residual error values of 10(-4), 10(-5), and 10(-6) using ANSYS Fluent to observe compounding errors and to optimize solver settings for computational efficiency while preserving solution accuracy. Simulations were compared qualitatively and quantitatively against the most rigorous combination of timestep and residual parameters, 10(-5)s and 10(-6), respectively. A case using 10(-4)s timesteps, with 10(-5) residual errors proved to be a converged solution for all three models with mean velocity and WSS difference RMS errors less than complex flow simulation. The worst case of our analysis, using 10(-3)s timesteps and 10(-4) residual errors, was still able to predict the dominant vortex in the aneurysm, but its velocity and WSS RMS errors reached 20%. Even with an appealing simulation time of 11h per cycle for the model with the most complex flow, the worst case analysis solution exhibited compounding errors from large timesteps and residual errors. To resolve time-dependent flow characteristics, CFD simulations of cerebral aneurysms require sufficiently small timestep size and residual error. Simulations with both insufficient timestep and residual resolution are vulnerable to compounding errors. Copyright © 2017 Elsevier Ltd. All rights reserved.

  18. Adding Complex Terrain and Stable Atmospheric Condition Capability to the OpenFOAM-based Flow Solver of the Simulator for On/Offshore Wind Farm Applications (SOWFA): Preprint

    Churchfield, M. J.; Sang, L.; Moriarty, P. J.


    This paper describes changes made to NREL's OpenFOAM-based wind plant aerodynamics solver such that it can compute the stably stratified atmospheric boundary layer and flow over terrain. Background about the flow solver, the Simulator for Off/Onshore Wind Farm Applications (SOWFA) is given, followed by details of the stable stratification/complex terrain modifications to SOWFA, along with somepreliminary results calculations of a stable atmospheric boundary layer and flow over a simply set of hills.

  19. A numerical scheme for modelling reacting flow with detailed chemistry and transport.

    Knio, Omar M. (The Johns Hopkins University, Baltimore, MD); Najm, Habib N.; Paul, Phillip H. (Eksigent Technologies LLC, Livermore, CA)


    An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C{sub 1}C{sub 2} methane-air mechanism and a detailed mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.

  20. Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows

    Givi, Peyman; Madnia, Cyrus K.; Steinberger, C. J.; Frankel, S. H.


    The principal objective is to extend the boundaries within which large eddy simulations (LES) and direct numerical simulations (DNS) can be applied in computational analyses of high speed reacting flows. A summary of work accomplished during the last six months is presented.

  1. Recent advances in coherent anti-Stokes Raman scattering spectroscopy: Fundamental developments and applications in reacting flows

    Roy, Sukesh [Spectral Energies, LLC, 5100 Springfield Street, Ste. 301, Dayton, OH 45431 (United States); Gord, James R. [Air Force Research Laboratory, Wright-Patterson AFB, OH 45433 (United States); Patnaik, Anil K. [Air Force Research Laboratory, Wright-Patterson AFB, OH 45433 (United States); Department of Physics, Wright State University, Dayton, OH 45435 (United States)


    Coherent anti-Stokes Raman scattering (CARS) spectroscopy is widely used for measuring temperature and species concentration in reacting flows. This paper reviews the advances made over the last twelve years in the development and application of CARS spectroscopy in gas-phase reacting flows. The advent of high-power nanosecond (ns) lasers and off-the-shelf compact picosecond (ps) and femtosecond (fs) lasers is enabling the rapid expansion of the application of single-shot or high-bandwidth CARS spectroscopy in a way that would have been quite unimaginable two decades ago. Furthermore, compact ps lasers are paving the way for the development of a fiber-based CARS system for use in harsh environments. The objective of this paper is to provide an overview of recent progresses in ns-, ps-, and fs-CARS spectroscopy for gas-phase thermometry and species-concentration measurements since the second edition of A.C. Eckbreth's book entitled Laser Diagnostics for Combustion Temperature and Species, which was published in 1996. During the last two decades, four encompassing issues have driven the fundamental development and application of CARS spectroscopy in reacting flows: 1) measurement of temperature and concentration of multiple species with one CARS system, 2) extension of the application of traditional ns-CARS to challenging reacting flow environments, 3) performance of nonresonant background-free and collision-free measurements in high-pressure reacting flows, and 4) measurement of temperature and species concentration at high bandwidth, typically 1 kHz or greater, to address the instability and transient phenomena associated with turbulent reacting flows in the combustors and augmentors of modern propulsion systems. This review is focused on identifying and discussing the recent results of gas-phase CARS spectroscopy related to the four issues mentioned above. The feasibility of performing high-bandwidth CARS spectroscopy with one laser beam as well as the

  2. A numerical study of mixing in stationary, nonpremixed, turbulent reacting flows

    Overholt, Matthew Ryan


    In this work a detailed numerical study is made of a statistically-stationary, non-premixed, turbulent reacting model flow known as Periodic Reaction Zones. The mixture fraction-progress variable approach is used, with a mean gradient in the mixture fraction and a model, single-step, reversible, finite-rate thermochemistry, yielding both stationary and local extinction behavior. The passive scalar is studied first, using a statistical forcing scheme to achieve stationarity of the velocity field. Multiple independent direct numerical simulations (DNS) are performed for a wide range of Reynolds numbers with a number of results including a bilinear model for scalar mixing jointly conditioned on the scalar and x2-component of velocity, Gaussian scalar probability density function tails which were anticipated to be exponential, and the quantification of the dissipation of scalar flux. A new deterministic forcing scheme for DNS is then developed which yields reduced fluctuations in many quantities and a more natural evolution of the velocity fields. This forcing method is used for the final portion of this work. DNS results for Periodic Reaction Zones are compared with the Conditional Moment Closure (CMC) model, the Quasi-Equilibrium Distributed Reaction (QEDR) model, and full probability density function (PDF) simulations using the Euclidean Minimum Spanning Tree (EMST) and the Interaction by Exchange with the Mean (IEM) mixing models. It is shown that CMC and QEDR results based on the local scalar dissipation match DNS wherever local extinction is not present. However, due to the large spatial variations of scalar dissipation, and hence local Damkohler number, local extinction is present even when the global Damkohler number is twenty-five times the critical value for extinction. Finally, in the PDF simulations the EMST mixing model closely reproduces CMC and DNS results when local extinction is not present, whereas the IEM model results in large error.

  3. Effect of the nature of vitiated crossflow on the flow-field of a transverse reacting jet

    Panda, Pratikash P.; Busari, Oluwatobi; Lucht, Robert P.; Laster, Walter R.


    The effect of the nature of vitiated crossflow on the structure and dynamics of non-reacting/reacting transverse jets is investigated. In this study, the vitiated crossflow is produced either by a low-swirl burner (LSB) that adds a swirling component to the crossflow or a bluff-body burner (BBB) that produces a uniform crossflow. The jet fluid is injected through a contoured injector, which provides a top-hat velocity profile. The swirling crossflow exhibits considerable swirl at the point of injection of the transverse jet. Two component high-repetition-rate PIV measurements demonstrate the influence of a vitiated crossflow generated by a low-swirl/bluff-body burner on the near-wake flow-field of the jet. Measurements at a plane below the injection location of the jet indicate that there is a continuous entrainment of PIV particles in case of swirling crossflow. The time-averaged flow-field shows that the velocity field for reacting/non-reacting jets in the LSB crossflow exhibits higher velocity gradients, in the measurement plane along jet cross section, as compared to BBB crossflow. It is found that the vorticity magnitude is lower in case of jets in the BBB crossflow and there is a delay in the formation of the wake vortex structure. The conditional turbulent statistics of the jet flow-field in the two crossflows shows that there is a higher degree of intermittency related to the wake vortex structure in case of a BBB crossflow, which results in a non-Gaussian distribution of the turbulent statistics. The wake Strouhal number calculation shows the influence of the nature of crossflow on the rate of wake vortex shedding. The wake Strouhal number for the jets in BBB crossflow is found to be lower than for the LSB crossflow. A decrease in the wake Strouhal number is observed with an increase in the nozzle separation distance. There is an increase in the dilatation rate owing to heat release which results in higher wake Strouhal number for reacting jets as compared

  4. Sound attenuation in rectangular and circular cross-section ducts with flow and bulk-reacting liner

    Bies, D. A.; Hansen, C. H.; Bridges, G. E.


    A generalized theory is presented for sound propagation in lined ducts of arbitrary cross-section where acoustic wave propagation in the lining is also taken into account. The effects of a mean fluid flow in the duct airway, an anisotropic bulk reacting liner and a limp, impervious membrane covering the liner are all taken into account. Simple extension of the formalism to include the effect of a perforated facing is also provided. Bulk reacting and locally reacting liners are treated as limiting cases. The general analysis is applied to ducts of both rectangular and circular cross-section, taking into account higher order modes as well as plane wave sound propagation. Design charts for duct attenuation in octave frequency band averages and in terms of dimensionless parameters are presented.

  5. Adding complex terrain and stable atmospheric condition capability to the OpenFOAM-based flow solver of the simulator for on/offshore wind farm applications (SOWFA

    Churchfield Matthew J.


    Full Text Available The National Renewable Energy Laboratory's Simulator for On/Offshore Wind Farm Applications contains an OpenFOAM-based flow solver for performing large-eddy simulation of flow through wind plants. The solver computes the atmospheric boundary layer flow and models turbines with actuator lines. Until recently, the solver was limited to flows over flat terrain and could only use the standard Smagorinsky subgrid-scale model. In this work, we present our improvements to the flow solver that enable us to 1 use any OpenFOAM-standard subgrid-scale model and 2 simulate flow over complex terrain. We used the flow solver to compute a stably stratified atmospheric boundary layer using both the standard and the Lagrangian-averaged scale-independent dynamic Smagorinsky models. Surprisingly, the results using the standard Smagorinsky model compare well to other researchers' results of the same case, although it is often said that the standard Smagorinsky model is too dissipative for accurate stable stratification calculations. The scale-independent dynamic subgrid-scale model produced poor results, probably due to the spikes in model constant with values as high as 4.6. We applied a simple bounding of the model constant to remove these spikes, which caused the model to produce results much more in line with other researchers' results. We also computed flow over a simple hilly terrain and performed some basic qualitative analysis to verify the proper operation of the terrain-local surface stress model we employed.

  6. A Study of Acoustic Forcing on Gas Centered Swirl Coaxial Reacting Flows (Conference Paper with Briefing Charts)


    other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a ...Conference Paper with Briefing Charts 3. DATES COVERED (From - To) 01 December 2016 – 11 January 2017 4. TITLE AND SUBTITLE A Study of collaboration with Sierra Lobo , Inc., UCLA; Conference Paper with Briefing Charts 14. ABSTRACT The reacting flow from a single gas-centered

  7. Optimal numerical solvers for transient simulations of ice flow using the Ice Sheet System Model (ISSM versions 4.2.5 and 4.11)

    Habbal, Feras; Larour, Eric; Morlighem, Mathieu; Seroussi, Helene; Borstad, Christopher P.; Rignot, Eric


    Identifying fast and robust numerical solvers is a critical issue that needs to be addressed in order to improve projections of polar ice sheets evolving in a changing climate. This work evaluates the impact of using advanced numerical solvers for transient ice-flow simulations conducted with the JPL-UCI Ice Sheet System Model (ISSM). We identify optimal numerical solvers by testing a broad suite of readily available solvers, ranging from direct sparse solvers to preconditioned iterative methods, on the commonly used Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models benchmark tests. Three types of analyses are considered: mass transport, horizontal stress balance, and incompressibility. The results of the fastest solvers for each analysis type are ranked based on their scalability across mesh size and basal boundary conditions. We find that the fastest iterative solvers are ˜ 1.5-100 times faster than the default direct solver used in ISSM, with speed-ups improving rapidly with increased mesh resolution. We provide a set of recommendations for users in search of efficient solvers to use for transient ice-flow simulations, enabling higher-resolution meshes and faster turnaround time. The end result will be improved transient simulations for short-term, highly resolved forward projections (10-100 year time scale) and also improved long-term paleo-reconstructions using higher-order representations of stresses in the ice. This analysis will also enable a new generation of comprehensive uncertainty quantification assessments of forward sea-level rise projections, which rely heavily on ensemble or sampling approaches that are inherently expensive.

  8. An object-oriented overland flow solver for watershed flood inundation predictions: case study of Ulus basin, Turkey

    Turan Burak


    Full Text Available This paper presents an object-oriented two-dimensional (2-D overland flow model and its application in simulating flood flows over Ulus basin, located in the north of Turkey adjacent to the Black Sea. A new coding implementation according to the class environment created in object oriented C++ programming language is carried out in structuring and building the solver. The model is based on the Godunov type finite volume scheme on unstructured triangular meshes. A mass balance preserving wet/dry boundary solution algorithm is integrated in the numerical scheme to satisfy the positive-depth condition and minimize the numerical instability when treating the propagation of wave front in regions of dry bed. The balance between bed slope and flux terms is also preserved for still water conditions on irregular topography. The 2-D solver is verified by simulating selected dam break cases, where good agreement with measured data is achieved. For the simulation of flood flows in the Ulus basin, in general, the simulated outflow hydrograph is found to compare well with the recorded data. A selected inundation map that is extracted from the model results is also presented to show the water surface level in the Floodplain.

  9. On the application of two-fluid flows solver to the casting problem

    Kamran, Kazem; Rossi, Riccardo; Dadvand, Pooyan; Idelsohn Barg, Sergio Rodolfo


    This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting...

  10. Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media

    Efendiev, Y.


    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.

  11. A 65+ Gflop/s unstructured finite element simulation of chemically reacting flows on the Intel Paragon

    Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K.; Hendrickson, B.; Leland, R.W. [Sandia National Labs., Albuquerque, NM (United States); Hennigan, G.L. [New Mexico State Univ., Las Cruces, NM (United States)


    Many scientific and engineering applications require a detailed analysis of complex systems with strongly coupled fluid flow, thermal energy transfer, mass transfer and non-equilibrium chemical reactions. Here they describe the performance of a newly developed application code, SALSA, designed to simulate these complex flows on large-scale parallel machines such as the Intel Paragon. SALSA uses 3D unstructure finite element methods to model geometrically complex flow systems. Fully implicit time integration multicomponent mass transport and general gas phase and surface species non-equilibrium chemical kinetics are employed. Using these techniques they have obtained over 65 Gflop/s on a 3D chemically reacting flow CVD problem for Silicon Carbide (SiC) deposition. This represents 46% of the peak performance of the 1904 node Intel Paragon, an outstanding computational rate in view of the required unstructured data communication.

  12. A Unified Gaskinetic Methodology for Full-Knudsen-Range Flows with Chemically Reacting Effects Project

    National Aeronautics and Space Administration — ZONA proposes a Unified Gas Kinetic Scheme (UGKS) to cover the full Knudsen number range from the continuum flow to free molecular flow that can simultaneously exist...

  13. An unstructured mesh arbitrary Lagrangian-Eulerian unsteady incompressible flow solver and its application to insect flight aerodynamics

    Su, Xiaohui; Cao, Yuanwei; Zhao, Yong


    In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.

  14. Blood damage through a bileaflet mechanical heart valve: a quantitative computational study using a multiscale suspension flow solver.

    Min Yun, B; Aidun, Cyrus K; Yoganathan, Ajit P


    Bileaflet mechanical heart valves (BMHVs) are among the most popular prostheses to replace defective native valves. However, complex flow phenomena caused by the prosthesis are thought to induce serious thromboembolic complications. This study aims at employing a novel multiscale numerical method that models realistic sized suspended platelets for assessing blood damage potential in flow through BMHVs. A previously validated lattice-Boltzmann method (LBM) is used to simulate pulsatile flow through a 23 mm St. Jude Medical (SJM) Regent™ valve in the aortic position at very high spatiotemporal resolution with the presence of thousands of suspended platelets. Platelet damage is modeled for both the systolic and diastolic phases of the cardiac cycle. No platelets exceed activation thresholds for any of the simulations. Platelet damage is determined to be particularly high for suspended elements trapped in recirculation zones, which suggests a shift of focus in blood damage studies away from instantaneous flow fields and toward high flow mixing regions. In the diastolic phase, leakage flow through the b-datum gap is shown to cause highest damage to platelets. This multiscale numerical method may be used as a generic solver for evaluating blood damage in other cardiovascular flows and devices.

  15. On Modeling the Response of Synovial Fluid: Unsteady Flow of a Shear-Thinning, Chemically-Reacting Fluid Mixture

    Bridges, Craig; Rajagopal, K R


    We study the flow of a shear-thinning, chemically-reacting fluid that could be used to model the flow of the synovial fluid. The actual geometry where the flow of the synovial fluid takes place is very complicated, and therefore the governing equations are not amenable to simple mathematical analysis. In order to understand the response of the model, we choose to study the flow in a simple geometry. While the flow domain is not a geometry relevant to the flow of the synovial fluid in the human body it yet provides a flow which can be used to assess the efficacy of different models that have been proposed to describe synovial fluids. We study the flow in the annular region between two cylinders, one of which is undergoing unsteady oscillations about their common axis, in order to understand the quintessential behavioral characteristics of the synovial fluid. We use the three models suggested by Hron et al. [ J. Hron, J. M\\'{a}lek, P. Pust\\v{e}jovsk\\'{a}, K. R. Rajagopal, On concentration dependent shear-thinni...

  16. CFD prediction of the reacting flow field inside a subscale scramjet combustor

    Chitsomboon, T.; Northam, G. B.; Rogers, R. C.; Diskin, G. S.


    A three-dimensional, Reynolds-averaged Navier-Stokes CFD code has been used to calculate the reacting flowfield inside a hydrogen-fueled, subscale scramjet combustor. Pilot fuel was injected transversely upstream of the combustor and the primary fuel was injected transversely downstream of a backward facing step. A finite rate combustion model with two-step kinetics was used. The CFD code used the explicit MacCormack algorithm with point-implicit treatment of the chemistry source terms. Turbulent mixing of the jets with the airstream was simulated by a simple mixing length scheme, whereas near wall turbulence was accounted for by the Baldwin-Lomax model. Computed results were compared with experimental wall pressure measurements.

  17. On a consistent high-order finite difference scheme with kinetic energy conservation for simulating turbulent reacting flows

    Trisjono, Philipp; Kang, Seongwon; Pitsch, Heinz


    The main objective of this study is to present an accurate and consistent numerical framework for turbulent reacting flows based on a high-order finite difference (HOFD) scheme. It was shown previously by Desjardins et al. (2008) [4] that a centered finite difference scheme discretely conserving the kinetic energy and an upwind-biased scheme for the scalar transport can be combined into a useful scheme for turbulent reacting flows. With a high-order spatial accuracy, however, an inconsistency among discretization schemes for different conservation laws is identified, which can disturb a scalar field spuriously under non-uniform density distribution. Various theoretical and numerical analyses are performed on the sources of the unphysical error. From this, the derivative of the mass-conserving velocity and the local Péclet number are identified as the primary factors affecting the error. As a solution, an HOFD stencil for the mass conservation is reformulated into a flux-based form that can be used consistently with an upwind-biased scheme for the scalar transport. The effectiveness of the proposed formulation is verified using two-dimensional laminar flows such as a scalar transport problem and a laminar premixed flame, where unphysical oscillations in the scalar fields are removed. The applicability of the proposed scheme is demonstrated in an LES of a turbulent stratified premixed flame.

  18. Fundamental Structure of High-Speed Reacting Flows: Supersonic Combustion and Detonation


    supersonic. Oblique Shock Interface Inert Reactants β θ P1 P2e P3eUCJ P1 UCJ P2i Detonation Figure 3. Idealized flow model of a detonation wave with an...Propagation With No Confinement But With Transvers Flow A consistent cross-flow was established by calibrating the height of the gases in time the controller commands, and then staggering the triggering of the gases such that each species – hydrogen, helium, and oxygen – independently

  19. SediFoam: A general-purpose, open-source CFD-DEM solver for particle-laden flow with emphasis on sediment transport

    Sun, Rui; Xiao, Heng


    With the growth of available computational resource, CFD-DEM (computational fluid dynamics-discrete element method) becomes an increasingly promising and feasible approach for the study of sediment transport. Several existing CFD-DEM solvers are applied in chemical engineering and mining industry. However, a robust CFD-DEM solver for the simulation of sediment transport is still desirable. In this work, the development of a three-dimensional, massively parallel, and open-source CFD-DEM solver SediFoam is detailed. This solver is built based on open-source solvers OpenFOAM and LAMMPS. OpenFOAM is a CFD toolbox that can perform three-dimensional fluid flow simulations on unstructured meshes; LAMMPS is a massively parallel DEM solver for molecular dynamics. Several validation tests of SediFoam are performed using cases of a wide range of complexities. The results obtained in the present simulations are consistent with those in the literature, which demonstrates the capability of SediFoam for sediment transport applications. In addition to the validation test, the parallel efficiency of SediFoam is studied to test the performance of the code for large-scale and complex simulations. The parallel efficiency tests show that the scalability of SediFoam is satisfactory in the simulations using up to O(107) particles.

  20. SediFoam: A general-purpose, open-source CFD-DEM solver for particle-laden flow with emphasis on sediment transport

    Sun, Rui


    With the growth of available computational resource, CFD-DEM (computational fluid dynamics-discrete element method) becomes an increasingly promising and feasible approach for the study of sediment transport. Several existing CFD-DEM solvers are applied in chemical engineering and mining industry. However, a robust CFD-DEM solver for the simulation of sediment transport is still desirable. In this work, the development of a three-dimensional, massively parallel, and open-source CFD-DEM solver SediFoam is detailed. This solver is built based on open-source solvers OpenFOAM and LAMMPS. OpenFOAM is a CFD toolbox that can perform three-dimensional fluid flow simulations on unstructured meshes; LAMMPS is a massively parallel DEM solver for molecular dynamics. Several validation tests of SediFoam are performed using cases of a wide range of complexities. The results obtained in the present simulations are consistent with those in the literature, which demonstrates the capability of SediFoam for sediment transport a...

  1. Reacting Flow of Hydrogen Chloride and Ammonia in Experimental and Numerical Modelling

    Dariusz Kardas; Katarzyna Falkowska


    The experimental and numerical investigations of the flow with reaction of two gases: hydrogen chloride HCl and ammonia NH_3 were performed.The article contains description of the visualisation method of the formation and flow of particles of ammonia chloride NH_4Cl.Analyses of mean concentration and variance of concentration fluctuations of dispersed phase were performed for different outputs of gases.Numerical calculations were performed for analysed phenomenon. Both numerical and visualisation results were matched and compared.

  2. Recent Enhancements To The FUN3D Flow Solver For Moving-Mesh Applications

    Biedron, Robert T,; Thomas, James L.


    An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been extended to handle general mesh movement involving rigid, deforming, and overset meshes. Mesh deformation is achieved through analogy to elastic media by solving the linear elasticity equations. A general method for specifying the motion of moving bodies within the mesh has been implemented that allows for inherited motion through parent-child relationships, enabling simulations involving multiple moving bodies. Several example calculations are shown to illustrate the range of potential applications. For problems in which an isolated body is rotating with a fixed rate, a noninertial reference-frame formulation is available. An example calculation for a tilt-wing rotor is used to demonstrate that the time-dependent moving grid and noninertial formulations produce the same results in the limit of zero time-step size.

  3. Combustion characteristics and turbulence modeling of swirling reacting flow in solid fuel ramjet

    Musa, Omer; Xiong, Chen; Changsheng, Zhou


    This paper reviews the historical studies have been done on the solid-fuel ramjet engine and difficulties associated with numerical modeling of swirling flow with combustible gases. A literature survey about works related to numerical and experimental investigations on solid-fuel ramjet as well as using swirling flow and different numerical approaches has been provided. An overview of turbulence modeling of swirling flow and the behavior of turbulence at streamline curvature and system rotation are presented. A new and simple curvature/correction factor is proposed in order to reduce the programming complexity of SST-CC turbulence model. Finally, numerical and experimental investigations on the impact of swirling flow on SFRJ have been carried out. For that regard, a multi-physics coupling code is developed to solve the problems of multi-physics coupling of fluid mechanics, solid pyrolysis, heat transfer, thermodynamics, and chemical kinetics. The connected-pipe test facility is used to carry out the experiments. The results showed a positive impact of swirling flow on SFRJ along with, three correlations are proposed.

  4. Numerical Simulations of Two-Phase Reacting Flow in a Single-Element Lean Direct Injection (LDI) Combustor Using NCC

    Liu, Nan-Suey; Shih, Tsan-Hsing; Wey, C. Thomas


    A series of numerical simulations of Jet-A spray reacting flow in a single-element lean direct injection (LDI) combustor have been conducted by using the National Combustion Code (NCC). The simulations have been carried out using the time filtered Navier-Stokes (TFNS) approach ranging from the steady Reynolds-averaged Navier-Stokes (RANS), unsteady RANS (URANS), to the dynamic flow structure simulation (DFS). The sub-grid model employed for turbulent mixing and combustion includes the well-mixed model, the linear eddy mixing (LEM) model, and the filtered mass density function (FDF/PDF) model. The starting condition of the injected liquid spray is specified via empirical droplet size correlation, and a five-species single-step global reduced mechanism is employed for fuel chemistry. All the calculations use the same grid whose resolution is of the RANS type. Comparisons of results from various models are presented.

  5. LES, DNS, and RANS for the Analysis of High-Speed Turbulent Reacting Flows

    Colucci, P. J.; Jaberi, F. A.; Givi, P.


    A filtered density function (FDF) method suitable for chemically reactive flows is developed in the context of large eddy simulation. The advantage of the FDF methodology is its inherent ability to resolve subgrid scales (SGS) scalar correlations that otherwise have to be modeled. Because of the lack of robust models to accurately predict these correlations in turbulent reactive flows, simulations involving turbulent combustion are often met with a degree of skepticism. The FDF methodology avoids the closure problem associated with these terms and treats the reaction in an exact manner. The scalar FDF approach is particularly attractive since it can be coupled with existing hydrodynamic computational fluid dynamics (CFD) codes.

  6. A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

    Krank, Benjamin; Wall, Wolfgang A; Kronbichler, Martin


    We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-...

  7. 1982 AFOSR Research Meeting on Diagnostics of Reacting Flow, 25-26 February 1982.


    observations and computer deconvolution methods. * COHERENT ANTI-STOKES RAMAN SPECTROSCOPY (Byer) - Development of tech- niques and measurements of species...of axial velocities for both cold and combusting flows, comparisons of velocity data with FREP and TEACH code predictions, the successful evalua- tion...of laser induced fluorescence and photoacoustic spectroscopy to measure trace species concentrations in flames. The Ramjet Division is also sponsoring

  8. AFOSR/ONR Contractors Meeting - Combustion, Rocket Propulsion, Diagnostics of Reacting Flow


    Section, The Combustion Institute, Oct. 1989. 5. McMillin, B. K., Lee, M. P., Palmer, J. L., Paul , P. H. and Hanson, R. K., "Planar Laser- Induced...K., Chang, A. Y., Seitzman, J. M., Lee, M. P., Paul , P. H. and Battles, B. E., "Laser-Induced Fluorescence Diagnostics for Supersonic Flows," AIAA-90...916)355-3087 289 I Dr Leanne Pitchford Dr Robert L Poeschel GTE Laboratories Plasma Physics Department 40 Sylvan Road Hughes Research Laboratories

  9. Effects of precursor heating on radiative and chemically reacting viscous flow around a Jovian entry body

    Tiwari, S. N.; Szema, K. Y.


    The influence of change in the precursor region flow properties on the entire shock layer flow phenomena around a Jovian entry body was investigated. The flow in the shock layer was assumed to be steady, axisymmetric, and viscous. Both the chemical equilibrium and the nonequilibrium composition of the shock layer gas were considered. The effects of transitional range behavior were included in the analysis of high altitude entry conditions. Realistic thermophysical and radiation models were used, and results were obtained by employing the implicit finite difference technique in the shock layer and an iterative procedure for the entire shock layer precursor zone. Results obtained for a 45 degree angle hyperboloid blunt body entering Jupiter's atmosphere at zero angle of attack indicates that preheating the gas significantly increases the static pressure and temperature ahead of the shock for entry velocities exceeding 36 km/sec. The nonequilibrium radiative heating rate to the body is found to be significantly higher than the corresponding equilibrium heating. The precursor heating generally increases the radiative and convective heating of a body. That increase is slightly higher for the nonequilibrium conditions.

  10. Development of Stokes flow solver against a large contrast in viscosity: toward plate-mantle simulation with free surface

    Furuichi, M.


    We are interested in solving a large-scale plate-mantle simulation enables capture of the large and complex deformation of a subducting plate. In our earlier study (Furuichi, et al 2008), we developed a numerical method toward plate-mantle simulation especially for the highly parallel vector supercomputer system (e.g. Earth Simulator). Our scheme is based on the finite volume method combines (i) the multigrid technique together with ACuTE smoother algorithm (Kameyama et al., 2005), and (ii) the low diffusive CIP-CSLR advection. The validity test of our simulation code by using a fluid rope coiling event (Furuichi, et al 2009) showed that our method enable us to reproduce large non-linear deformation problems of a rigid plate surrounded by soft material without serious quantitative errors. Then as a next step, I am trying to create a Stokes flow solver scalable against a large jump in a viscosity profile, for moving surface (geometrically free boundary) problems. It is for solving the Stokes flow motion under the same condition as real earth. In this presentation, I propose to apply BFBt preconditioner and AMG techniques for the problems of large viscosity contrast and moving free surface boundary condition respectively. I would like to show some numerical experiments for a self-gravitating motion of the layered Stokes flow.

  11. Parallel finite element method for modeling two-phase flow processes in porous media using PETSc solver

    Wang, W.; Zehner, B.; Böttcher, N.; Goerke, U.; Kolditz, O.


    Numerical modeling of the two-phase flow process in porous media for real applications, e.g. CO2 storage processes in saline aquifers, is computationally expensive due to the complexity and the non-linearity of the observed physical processes. In such modeling, a fine discretization of the considered domain is normally needed for a high degree of accuracy, and it leads to the requirement of extremely high computational resources. This work focuses on the parallel simulation of the two-phase flow process in porous media. The Galerkin finite element method is used to solve the governing equations. Based on the overlapping domain decomposition approach, the PETSc package is employed to parallelize the global equation assembly and the linear solver, respectively. A numerical model based on the real test site Ketzin in Germany is adopted for parallel computing. The model domain is discretized with more than four million tetrahedral elements. The parallel simulations are carried out on a Linux cluster with different number of cores. The obtained speedup shows a good scalability of the current parallel finite element approach of the two-phase flow modeling in geological CO2 storage applications.

  12. Chemically reacting dusty viscoelastic fluid flow in an irregular channel with convective boundary

    R. Sivaraj


    Full Text Available In this paper, we have studied the combined effects of free convective heat and mass transfer on an unsteady MHD dusty viscoelastic (Walters liquid model-B fluid flow between a vertical long wavy wall and a parallel flat wall saturated with porous medium subject to the convective boundary condition. The coupled partial differential equations are solved analytically using perturbation technique. The velocity, temperature and concentration fields have been studied for various combinations of physical parameters such as magnetic field, heat absorption, thermal radiation, radiation absorption, Biot number and chemical reaction parameters. The skin friction, Nusselt number and Sherwood number are also presented and displayed graphically. Further, it is observed that the velocity profiles of dusty fluid are higher than the dust particles.

  13. A Semi-Implicit, Fourier-Galerkin/B-Spline Collocation Approach for DNS of Compressible, Reacting, Wall-Bounded Flow

    Oliver, Todd; Ulerich, Rhys; Topalian, Victor; Malaya, Nick; Moser, Robert


    A discretization of the Navier-Stokes equations appropriate for efficient DNS of compressible, reacting, wall-bounded flows is developed and applied. The spatial discretization uses a Fourier-Galerkin/B-spline collocation approach. Because of the algebraic complexity of the constitutive models involved, a flux-based approach is used where the viscous terms are evaluated using repeated application of the first derivative operator. In such an approach, a filter is required to achieve appropriate dissipation at high wavenumbers. We formulate a new filter source operator based on the viscous operator. Temporal discretization is achieved using the SMR91 hybrid implicit/explicit scheme. The linear implicit operator is chosen to eliminate wall-normal acoustics from the CFL constraint while also decoupling the species equations from the remaining flow equations, which minimizes the cost of the required linear algebra. Results will be shown for a mildly supersonic, multispecies boundary layer case inspired by the flow over the ablating surface of a space capsule entering Earth's atmosphere. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].

  14. Examining the impact of ambient flow on biofilm and its feedback on the flow structure through a fluid-structure interaction (FSI) solver

    Hardy, R. J.; Sinha, S.; Sambrook Smith, G.; Kazemifar, F.; Christensen, K.; Best, J.


    Biofilms are ubiquitously present in fluvial systems, growing on almost all wetted surface. The local hydraulic conditions have a significant impact on the biofilm lifecycle as in order to sustain their growth biofilms draw essential nutrients either from the flow or from the surface on which they grow. This implies that in convection dominated flow, nutrient transfer from water, would nurture the growth of biofilms. However, at higher flow rates biofilms are subjected to higher stresses which may lead to their detachment. Furthermore, biofilms in ambient flow conditions oscillate and therefore alter the local flow conditions. There is, therefore, a complex feedback between biofilms and flow which have has implications for flow dynamics and water quality issues in riverine ecosystems. The research presented here describes a fluid-structure interaction solver to examine the coupled nature of biofilm oscillations due to the ambient flow and its feedback on the local flow structures. The fluid flow is modelled by the incompressible Navier-Stokes equations and structural deformation of the biofilm is modeled by applying a linear elastic model. The governing equations are numerically solved through Finite Volume methodology based on cell-centered scheme. Simulations are conducted in a laminar regime for a biofilm streamer modelled as moving slender plate. The temporal evolution of the pressure, flow structures are examined in the vicinity of the biofilm. Further investigations examine the impact of changing Reynolds number on the oscillation frequency as well as drag and lift forces experienced by the biofilm. The changing frequency of biofilm oscillation with varying Reynolds number is characterized by the Strouhal number (St). Our investigation reveals that as the flow separates around the biofilm attachment point, vortices are formed both above and beneath the biofilm which propagate downstream. As the vortex rolls off from the end of the biofilm, the interaction

  15. Experiments with Succinct Solvers

    Buchholtz, Mikael; Nielson, Hanne Riis; Nielson, Flemming


    time of the solver and the aim of this note is to provide some insight into which formulations are better than others. The experiments addresses three general issues: (i) the order of the parameters of relations, (ii) the order of conjuncts in preconditions and (iii) the use of memoisation....... The experiments are performed for Control Flow Analyses for Discretionary Ambients....

  16. Computational studies of reacting flows with applications to zinc selenide nanoparticle synthesis and methane/hydrogen separation

    Koutsona, Maria

    This work is a numerical study of the design and operation of two reacting flow systems, each with great potential in their fields. The design of reacting flow systems by computer simulations are successfully used in science and engineering to evaluate design geometries and operation, without resorting to experimental trial and error that is expensive, time consuming and, in some cases, dangerous. The models of the two systems described in this work are based on fundamental conservation equations for momentum and mass transfer coupled with chemical reaction kinetics and particle dynamics. The first part of this work is a study aiming to elucidate the transport phenomena and chemical reactions that control the size of ZnSe nanoparticles formed by a new vapor-phase synthesis route. The nanoparticles are synthesized by reacting vapors of (CH3)2Zn:N(C2H 5)3 adduct with H2Se gas (diluted in hydrogen) fed continuously from opposite sides into a counterflow jet reactor. The nuclei of the nanocrystals are formed by a direct condensation reaction near the stagnation point. The nuclei grow into nanoparticles by coalescence/coagulation and by surface growth reactions. A 2D model of an axially symmetric reactor was developed that includes descriptions of flow, mass transfer by convection and diffusion, chemical kinetics, particle nucleation, coagulation and surface growth. The coupled nonlinear partial differential equations of the model were solved using the Galerkin Finite Element Method. The model was used to study the relative importance of the underlying physical and chemical phenomena in controlling particle size and particle size distribution. Model predictions compared well with the limited experimental data available for this system. The model was also used for model-assisted design of the experimental counterflow jet reactor, where vapor-phase synthesis of ZnSe nanoparticles was demonstrated for the first time. The second part of this work involves the development of

  17. An efficient semi-implicit solver for direct numerical simulation of compressible flows at all speeds

    Modesti, Davide


    We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated with acoustic waves, in such a way to suppress, or at least mitigate the acoustic time step limitation. Together with replacement of the total energy equation with the entropy transport equation, this approach avoids the inversion of block-banded matrices involved in classical methods, which is replaced by less demanding inversion of standard banded matrices. The method is extended to deal with implicit integration of viscous terms and to multiple space dimensions through approximate factorization, and used as a building block of third-order Runge-Kutta time stepping scheme. Numerical experiments are carried out for isotropic turbulence, plane channel flow, and flow in a square duct. All available data support higher computational efficiency than existing methods, and saving ...

  18. Simulations of Spray Reacting Flows in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar PDF Method

    Shih, Tsan-Hsing; Liu, Nan-Suey


    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.

  19. Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media

    M. M. Rashidi


    Full Text Available The optimal homotopy analysis method (OHAM is employed to investigate the steady laminar incompressible free convective flow of a nanofluid past a chemically reacting upward facing horizontal plate in a porous medium taking into account heat generation/absorption and the thermal slip boundary condition. Using similarity transformations developed by Lie group analysis, the continuity, momentum, energy, and nanoparticle volume fraction equations are transformed into a set of coupled similarity equations. The OHAM solutions are obtained and verified by numerical results using a Runge-Kutta-Fehlberg fourth-fifth order method. The effect of the emerging flow controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction have been presented graphically and discussed. Good agreement is found between analytical and numerical results of the present paper with published results. This close agreement supports our analysis and the accuracy of the numerical computations. This paper also includes a representative set of numerical results for reduced Nusselt and Sherwood numbers in a table for various values of the parameters. It is concluded that the reduced Nusselt number increases with the Lewis number and reaction parameter whist it decreases with the order of the chemical reaction, thermal slip, and generation parameters.

  20. An unstructured parallel least-squares spectral element solver for incompressible flow problems

    Nool, M.; Proot, M.M.J.


    The parallelization of the least-squares spectral element formulation of the Stokes problem has recently been discussed for incompressible flow problems on structured grids. In the present work, the extension to unstructured grids is discussed. It will be shown that, to obtain an efficient and scala

  1. Recent developments of DSMC within the reactive plasma flow solver PICLas

    Reschke, W.; Binder, T.; Kleinert, J.; Mirza, A.; Nizenkov, P.; Pfeiffer, M.; Fasoulas, S.; Copplestone, S.; Ortwein, P.; Munz, C. D.


    In order to enable the numerical simulation of rarefied plasma flows in thermal and chemical non-equilibrium, electro-magnetic interactions as well as particle collisions have to be considered. A common approach is to use particle-based methods. The Particle-in-Cell (PIC) method simulates charged collisionless gas flows by solving the Vlasov-Maxwell equation system while particle collisions in neutral reactive flows are treated by the Direct Simulation Monte Carlo (DSMC) method. Therefore, PICLas is being developed, a coupled simulation code that enables three-dimensional particle-based simulations combining high-order PIC and DSMC schemes for the simulation of reactive, rarefied plasma flows. PICLas enables time-accurate simulations on unstructured hexahedral meshes and is parallelized for high-performance computing. In addition to an overview of PICLas, the current development status of the DSMC module is presented. This includes the relaxation of polyatomic gases, the extension of the chemical modeling to gas-surface interactions, and the implementation of steady-state detection routines.

  2. Development of a Three-Dimensional Unstructured Euler Solver for High-Speed Flows

    Tudorel Petronel AFILIPOAE


    Full Text Available This paper addresses the solution of the compressible Euler equations on hexahedral meshes for supersonic and hypersonic flows. Spatial discretization is accomplished by a cell-centered finite-volume formulation which employs two different upwind schemes for the computation of convective fluxes. Second-order solutions are attained through a linear state reconstruction technique that yields highly resolved flows in smooth regions while providing a sharp and clean resolution of shocks. The solution gradients required for the higher-order spatial discretization are estimated by a least-square method while Venkatakrishnan limiter is employed to preserve monotonicity and avoid oscillations in the presence of shocks. Furthermore, solutions are advanced in time by an explicit third-order Runge-Kutta scheme and convergence to steady state is accelerated using implicit residual smoothing. Flow around a circular arc in a channel and flow past a circular cylinder are studied and results are presented for various Mach numbers together with comparisons to theoretical and experimental data where possible.

  3. MEDUSA - An overset grid flow solver for network-based parallel computer systems

    Smith, Merritt H.; Pallis, Jani M.


    Continuing improvement in processing speed has made it feasible to solve the Reynolds-Averaged Navier-Stokes equations for simple three-dimensional flows on advanced workstations. Combining multiple workstations into a network-based heterogeneous parallel computer allows the application of programming principles learned on MIMD (Multiple Instruction Multiple Data) distributed memory parallel computers to the solution of larger problems. An overset-grid flow solution code has been developed which uses a cluster of workstations as a network-based parallel computer. Inter-process communication is provided by the Parallel Virtual Machine (PVM) software. Solution speed equivalent to one-third of a Cray-YMP processor has been achieved from a cluster of nine commonly used engineering workstation processors. Load imbalance and communication overhead are the principal impediments to parallel efficiency in this application.

  4. Chemically Reacting Turbulent Flow.


    two stages of gen I tubes equipped with P-47 phosphor screens The detector chosen for the camera was a Reticon RL128S* line detectoI- .,hich consists...the Stud’, of Turbulent Mixing," William M. Pitts, Nuclear Engineering Seminar of the Department of Chemical and Nuclear Engineering, University of

  5. A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

    Doisneau, François; Arienti, Marco; Oefelein, Joseph C.


    For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

  6. A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

    Doisneau, François, E-mail:; Arienti, Marco, E-mail:; Oefelein, Joseph C., E-mail:


    For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

  7. Coupled modelling of flow and biofilm in a laminar flow regime through a high-resolution fluid-structure interaction (FSI) solver

    Sinha, Sumit; Hardy, Richard; Smith, Gregory; Kazemifar, Farzan; Christensen, Kenneth; Best, Jim


    Biofilms are ubiquitously present in fluvial systems, growing on almost all wetted surface and has a significant impact on both water quantity, in terms of ambient flow condition, as well as water quality, biofilms growing in water distribution system leads to unwanted contamination. The local hydraulic conditions have a significant impact on the biofilm lifecycle as in order to sustain their growth biofilms draw essential nutrients either from the flow or from the surface on which they grow. This implies that in convection dominated flow, nutrient transfer from water, would nurture the growth of biofilms. However, at higher flow rates biofilms are subjected to higher stresses which may lead to their detachment. Furthermore, biofilms in ambient flow conditions oscillate and therefore alter the local flow conditions. There is, therefore, a complex feedback between biofilms and flow which have has implications for flow dynamics and water quality issues in riverine ecosystems. The research presented here describes a fluid-structure interaction solver to examine the coupled nature of biofilm oscillations due to the ambient flow and its feedback on the local flow structures. The fluid flow is modelled by the incompressible Navier-Stokes equations and structural deformation of the biofilm is modeled by applying a linear elastic model. The governing equations are numerically solved through Finite Volume methodology based on cell-centered scheme. Simulations are conducted in a laminar regime for a biofilm streamer modelled as moving slender plate. The temporal evolution of the pressure, flow structures are examined in the vicinity of the biofilm. Further investigations examine the impact of changing Reynolds number on the oscillation frequency as well as drag and lift forces experienced by the biofilm. The changing frequency of biofilm oscillation with varying Reynolds number is characterized by the Strouhal number (St). Our investigation reveals that as the flow separates

  8. Evaluation of two-phase flow solvers using Level Set and Volume of Fluid methods

    Bilger, C.; Aboukhedr, M.; Vogiatzaki, K.; Cant, R. S.


    Two principal methods have been used to simulate the evolution of two-phase immiscible flows of liquid and gas separated by an interface. These are the Level-Set (LS) method and the Volume of Fluid (VoF) method. Both methods attempt to represent the very sharp interface between the phases and to deal with the large jumps in physical properties associated with it. Both methods have their own strengths and weaknesses. For example, the VoF method is known to be prone to excessive numerical diffusion, while the basic LS method has some difficulty in conserving mass. Major progress has been made in remedying these deficiencies, and both methods have now reached a high level of physical accuracy. Nevertheless, there remains an issue, in that each of these methods has been developed by different research groups, using different codes and most importantly the implementations have been fine tuned to tackle different applications. Thus, it remains unclear what are the remaining advantages and drawbacks of each method relative to the other, and what might be the optimal way to unify them. In this paper, we address this gap by performing a direct comparison of two current state-of-the-art variations of these methods (LS: RCLSFoam and VoF: interPore) and implemented in the same code (OpenFoam). We subject both methods to a pair of benchmark test cases while using the same numerical meshes to examine a) the accuracy of curvature representation, b) the effect of tuning parameters, c) the ability to minimise spurious velocities and d) the ability to tackle fluids with very different densities. For each method, one of the test cases is chosen to be fairly benign while the other test case is expected to present a greater challenge. The results indicate that both methods can be made to work well on both test cases, while displaying different sensitivity to the relevant parameters.

  9. Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

    MacArt, Jonathan F.; Mueller, Michael E.


    Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

  10. Hypersonic simulations using open-source CFD and DSMC solvers

    Casseau, V.; Scanlon, T. J.; John, B.; Emerson, D. R.; Brown, R. E.


    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.


    王江峰; 伍贻兆


    A parallelized upwind flux splitting scheme for supersonic reacting flows on hybrid meshes is presented. The complexity of super/hyper-sonic combustion flows makes it necessary to establish solvers with higher resolution and efficiency for multi-component Euler/N-S equations. Hence, a spatial second-order van Leer type flux vector splitting scheme is established by introducing auxiliary points in interpolation, and a domain decomposition method used on unstructured hybrid meshes for obtaining high calculating efficiency. The numerical scheme with five-stage Runge-Kutta time step method is implemented to the simulation of combustion flows, including the supersonic hydrogen/air combustion and the normal injection of hydrogen into reacting flows. Satisfying results are obtained compared with limited references.%基于有限体积迎风格式对超声速燃烧流场进行了的数值模拟.由于超声速燃烧流场绕流的复杂性,要求对多组分Euler/N-S方程求解的数值模拟方法应具有较高的计算精度及效率.本文引用辅助点方法建立了具有空间二阶精度的van Leer迎风矢通量分裂格式,并应用于超声速燃烧流场绕流的数值模拟.化学反应为氢气/空气十反应模型,采用考虑了化学反应特征时间的当地时间步长显式Runge-Kutta时间推进格式.对钝头体模型爆轰现象、后向台阶氢气喷射及二维内外流超声速燃烧流场模型进行了区域分裂技术的并行计算.计算结果与参考文献作了对比,得到了满意的结果.

  12. Assessment of the Partially Resolved Numerical Simulation (PRNS) Approach in the National Combustion Code (NCC) for Turbulent Nonreacting and Reacting Flows

    Shih, Tsan-Hsing; Liu, Nan-Suey


    This paper describes an approach which aims at bridging the gap between the traditional Reynolds-averaged Navier-Stokes (RANS) approach and the traditional large eddy simulation (LES) approach. It has the characteristics of the very large eddy simulation (VLES) and we call this approach the partially-resolved numerical simulation (PRNS). Systematic simulations using the National Combustion Code (NCC) have been carried out for fully developed turbulent pipe flows at different Reynolds numbers to evaluate the PRNS approach. Also presented are the sample results of two demonstration cases: nonreacting flow in a single injector flame tube and reacting flow in a Lean Direct Injection (LDI) hydrogen combustor.

  13. Approximate Riemann solvers and flux vector splitting schemes for two-phase flow; Solveurs de Riemann approches et schemas de decentrement de flux pour les ecoulements diphasiques

    Toumi, I.; Kumbaro, A.; Paillere, H


    These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)

  14. DebrisInterMixing-2.3: a finite volume solver for three-dimensional debris-flow simulations with two calibration parameters - Part 1: Model description

    von Boetticher, Albrecht; Turowski, Jens M.; McArdell, Brian W.; Rickenmann, Dieter; Kirchner, James W.


    Here, we present a three-dimensional fluid dynamic solver that simulates debris flows as a mixture of two fluids (a Coulomb viscoplastic model of the gravel mixed with a Herschel-Bulkley representation of the fine material suspension) in combination with an additional unmixed phase representing the air and the free surface. We link all rheological parameters to the material composition, i.e., to water content, clay content, and mineral composition, content of sand and gravel, and the gravel's friction angle; the user must specify only two free model parameters. The volume-of-fluid (VoF) approach is used to combine the mixed phase and the air phase into a single cell-averaged Navier-Stokes equation for incompressible flow, based on code adapted from standard solvers of the open-source CFD software OpenFOAM. This effectively single-phase mixture VoF method saves computational costs compared to the more sophisticated drag-force-based multiphase models. Thus, complex three-dimensional flow structures can be simulated while accounting for the pressure- and shear-rate-dependent rheology.

  15. On applicability of the “thermalized potential” solver in simulations of the plasma flow in Hall thrusters

    Geng, Jinyue [School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191 (China); Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, District of Columbia 20052 (United States); Brieda, Lubos [Particle in Cell Consulting LLC, Falls Church, Virginia 22046 (United States); Rose, Laura; Keidar, Michael [Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, District of Columbia 20052 (United States)


    In Hall thrusters, the potential distribution plays an important role in discharge processes and ion acceleration. This paper presents a 2D potential solver in the Hall thruster instead of the “thermalized potential”, and compares equipotential contours solved by these two methods for different magnetic field conditions. The comparison results reveal that the expected “thermalized potential” works very well when the magnetic field is nearly uniform and electron temperature is constant along the magnetic field lines. However for the case with a highly non-uniform magnetic field or variable electron temperature along the magnetic field lines, the “thermalized potential” is not accurate. In some case with magnetic separatrix inside the thruster channel, the “thermalized potential” model cannot be applied at all. In those cases, a full 2D potential solver must be applied. Overall, this paper shows the limit of applicability of the “thermalized potential” model.

  16. Composing constraint solvers

    Zoeteweij, P.


    Composing constraint solvers based on tree search and constraint propagation through generic iteration leads to efficient and flexible constraint solvers. This was demonstrated using OpenSolver, an abstract branch-and-propagate tree search engine that supports a wide range of relevant solver configu

  17. Heterogeneous parallel compressible flow solver based on MPI+CUDA%基于MPI+CUDA的异构并行可压缩流求解器

    刘枫; 李桦; 田正雨; 潘沙


    A compressible flow heterogeneous parallel solver based on MPI+CUDA on CPU/GPU heterogeneous system was established.Then different parallel computing models and optimizing methods of compressible flow parallel computing algorithm were discussed.This solver runs different codes with difference resources:the codes which are complex or have low computing density are run on CPU,while the codes which are simple or have high computing density are run on GPU.The heterogeneous systems’computing results and the efficiencies with homogeneous systems were compared through several problems.Finally,the heterogeneous algorithm was applied to the hypersonic flow.The result shows that the algorithm is robust and the computing efficiency is improved ten times more than that of the homogeneous algorithm.%在CPU/GPU异构体系结构计算集群上,建立了基于MPI+CUDA的异构并行可压缩流求解器。讨论了异构结构上的可压缩流并行算法的并行模式,在CPU上执行计算密集度低、指令复杂的计算任务,在GPU上执行计算密集度高、指令单一的计算任务。通过数个算例,对比了异构并行计算和传统CPU并行计算计算结果和计算效率。将该算法运用于高超声速流动的数值模拟中,数值结果显示,基于MPI+CUDA的异构并行可压缩流求解器鲁棒性好,计算效率较CPU同构并行计算提高10倍以上。

  18. Comparing Spray Characteristics from Reynolds Averaged Navier-Stokes (RANS) National Combustion Code (NCC) Calculations Against Experimental Data for a Turbulent Reacting Flow

    Iannetti, Anthony C.; Moder, Jeffery P.


    Developing physics-based tools to aid in reducing harmful combustion emissions, like Nitrogen Oxides (NOx), Carbon Monoxide (CO), Unburnt Hydrocarbons (UHC s), and Sulfur Dioxides (SOx), is an important goal of aeronautics research at NASA. As part of that effort, NASA Glenn Research Center is performing a detailed assessment and validation of an in-house combustion CFD code known as the National Combustion Code (NCC) for turbulent reacting flows. To assess the current capabilities of NCC for simulating turbulent reacting flows with liquid jet fuel injection, a set of Single Swirler Lean Direct Injection (LDI) experiments performed at the University of Cincinnati was chosen as an initial validation data set. This Jet-A/air combustion experiment operates at a lean equivalence ratio of 0.75 at atmospheric pressure and has a 4 percent static pressure drop across the swirler. Detailed comparisons of NCC predictions for gas temperature and gaseous emissions (CO and NOx) against this experiment are considered in a previous work. The current paper is focused on detailed comparisons of the spray characteristics (radial profiles of drop size distribution and at several radial rakes) from NCC simulations against the experimental data. Comparisons against experimental data show that the use of the correlation for primary spray break-up implemented by Raju in the NCC produces most realistic results, but this result needs to be improved. Given the single or ten step chemical kinetics models, use of a spray size correlation gives similar, acceptable results

  19. Very Large Eddy Simulations of a Jet-A Spray Reacting Flow in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar DWFDF Method

    Shih, Tsan-Hsing; Liu, Nan-Suey


    This paper presents the very large eddy simulations (VLES) of a 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 DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the Eulerian scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the Eulerian scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.

  20. Zonal Detached Eddy Simulation of a simplified nose landing-gear for flow and noise predictions using an unstructured Navier-Stokes solver

    de la Puente Cerezo, Fernando; Sanders, Laurent; Vuillot, François; Druault, Philippe; Manoha, Eric


    A Zonal Detached Eddy Simulation has been performed on the simplified LAGOON nose landing gear geometry using a Navier-Stokes solver on a fully unstructured grid. The attached boundary layers have been finely resolved using Y+ values in the order of unity, while the high curvature zones have been intensively meshed in order to accurately solving adverse pressure gradients present in these regions. The mean and fluctuating flow fields have been compared with the experimental results, proving that both the mean flow field and the spectral content recorded at the wall are accurately reproduced. Following these comparisons, a detailed analysis of the topology of the flow has been carried out through the analysis of the skin friction coefficient and friction lines, coupled with three dimensional visualizations of the landing gear wake. The far-field acoustics, computed through the Ffowcs-Williams and Hawkings equation from the computed pressure on the landing gear skin, has been compared with the experimental results, obtaining a very good agreement for the different microphones and directions. Finally, the CFD methodology presented in this study proves to be a moderate cost approach, enabling an accurate flow and noise prediction for bluff bodies such as landing gears.

  1. rhoCentralRfFoam: An OpenFOAM solver for high speed chemically active flows - Simulation of planar detonations -

    Gutiérrez Marcantoni, L. F.; Tamagno, J.; Elaskar, S.


    A new solver developed within the framework of OpenFOAM 2.3.0, called rhoCentralRfFoam which can be interpreted like an evolution of rhoCentralFoam, is presented. Its use, performing numerical simulations on initiation and propagation of planar detonation waves in combustible mixtures H2-Air and H2-O2-Ar, is described. Unsteady one dimensional (1D) Euler equations coupled with sources to take into account chemical activity, are numerically solved using the Kurganov, Noelle and Petrova second order scheme in a domain discretized with finite volumes. The computational code can work with any number of species and its corresponding reactions, but here it was tested with 13 chemically active species (one species inert), and 33 elementary reactions. A gaseous igniter which acts like a shock-tube driver, and powerful enough to generate a strong shock capable of triggering exothermic chemical reactions in fuel mixtures, is used to start planar detonations. The following main aspects of planar detonations are here, treated: induction time of combustible mixtures cited above and required mesh resolutions; convergence of overdriven detonations to Chapman-Jouguet states; detonation structure (ZND model); and the use of reflected shocks to determine induction times experimentally. The rhoCentralRfFoam code was verified comparing numerical results and it was validated, through analytical results and experimental data.

  2. Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation

    Pushpalatha, K.; Ramana Reddy, J. V.; Sugunamma, V.; Sandeep, N.


    The problem of an unsteady MHD Casson fluid flow towards a stretching surface with cross diffusion effects is considered. The governing partial differential equations are converted into a set of nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. Further, these equations have been solved numerically by using Runge-Kutta fourth order method along with shooting technique. Finally, we studied the influence of various non-dimensional governing parameters on the flow field through graphs and tables. Results indicate that Dufour and Soret numbers have tendency to enhance the fluid velocity. It is also found that Soret number enhances the heat transfer rate where as an opposite result is observed with Casson parameter. A comparison of the present results with the previous literature is also tabulated to show the accuracy of the results.

  3. Staphylococcal enterotoxin B-specific electrochemiluminescence and lateral flow device assays cross-react with staphylococcal enterotoxin D.

    Tallent, Sandra M; Hait, Jennifer; Bennett, Reginald W


    Guam school children and faculty members experienced symptoms of vomiting, nausea, abdominal cramps, and diarrhea shortly after eating breakfast prepared by contracted caterers. The first illness was reported within an hour after breakfast, affecting 295 students and two faculty members. Local hospitals treated 130 people, and 61 were admitted for further treatment. Reported symptoms were consistent with staphylococcal food poisoning. Initial food testing using a lateral flow device and electrochemiluminescence method incorrectly implicated staphylococcal enterotoxin B as the causative agent, prompting partial activation of Guam's Emergency Response Center. Traditional ELISAs proved that the food poisoning agent was staphylococcal enterotoxin D. More specific and sensitive assays would have alleviated the issues and confusion that surrounded the reporting and investigation of this outbreak.

  4. Efficient partially implicit integration method for stiff chemistry in high-fidelity simulations of turbulent reacting flows

    Wu, Hao; Ihme, Matthias


    High-fidelity turbulent reactive flow simulations are typically associated with small time step sizes (h combustion simulations due to the reduced number of internal iterations and excessive implicitness. In this study, an improved 4th-order Rosenbrock-Krylov (ROK4L) scheme is developed for the system of chemical reactions. This class of schemes replaces the Jacobian matrix by its low-rank Krylov approximation, thus introducing partial implicitness. The scheme is improved in both accuracy and efficiency by fulfilling additional order conditions and reducing the number of function evaluations. The ROK4L scheme is demonstrated to possess superior efficiency in comparison to CVODE due to the minimal degree of implicitness for small time-step sizes and the avoidance of other overhead associated with the start-up process of multi-step methods. Financial support from NASA Transformational Tools and Technologies Project with Award No. NNX15AV04A.

  5. Investigations of Interaction of the Main Flow with Root and Tip Leakage Flows in an Axial Turbine Stage by Means of a Source/Sink Approach for a 3D Navier-Stokes Solver

    Piotr Lampart; Andrzej Gardzilewicz; Sergey Yershov; Andrey Rusanov


    The effect of interaction of the main flow with root and tip leakage flows on the performance of an high pressure (HP) stage of an impulse turbine is studied numerically. The flow in blade-to-blade channels and axial gaps is computed with the aid of a 3D Navier-Stokes solver FlowER. The numerical scheme is modified to include the some/sink-type boundary conditions in places at the endwalls referring to design locations of injection of leakage and windage flows into, or extract from, the blade-to-blade passage. The turbine stage is computed in three configurations. First, computations are made without tip leakage and windage flows with source/sink slots closed.Second, tip leakage slots are open. Third, both tip leakage and windage flow slots are open, and the obtained flow characteristics including kinetic energy losses in the stage are compared so as to estimate the interaction of the main and leakage flows.

  6. Chemically reacting micropolar fluid flow and heat transfer between expanding or contracting walls with ion slip, Soret and Dufour effects

    Odelu Ojjela


    Full Text Available The aim of the present study is to investigate the Hall and ion slip currents on an incompressible free convective flow, heat and mass transfer of a micropolar fluid in a porous medium between expanding or contracting walls with chemical reaction, Soret and Dufour effects. Assume that the walls are moving with a time dependent rate of the distance and the fluid is injecting or sucking with an absolute velocity. The walls are maintained at constant but different temperatures and concentrations. The governing partial differential equations are reduced into nonlinear ordinary differential equations by similarity transformations and then the resultant equations are solved numerically by quasilinearization technique. The results are analyzed for velocity components, microrotation, temperature and concentration with respect to different fluid and geometric parameters and presented in the form of graphs. It is noticed that with the increase in chemical reaction, Hall and ion slip parameters the temperature of the fluid is enhanced whereas the concentration is decreased. Also for the Newtonian fluid, the numerical values of axial velocity are compared with the existing literature and are found to be in good agreement.

  7. Differential equations problem solver

    Arterburn, David R


    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

  8. A parallel, state-of-the-art, least-squares spectral element solver for incompressible flow problems

    Nool, M.; Proot, M.M.J.


    The paper deals with the efficient parallelization of least-squares spectral element methods for incompressible flows. The parallelization of this sort of problems requires two different strategies. On the one hand, the spectral element discretization benefits from an element-by-element paralleli

  9. Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

    Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.


    This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

  10. Development and application of a dispersed two-phase flow capability in a general multi-block Navier Stokes solver

    Shah, Anant Pankaj


    Gas turbines for military applications, when operating in harsh environments like deserts often encounter unexpected operation faults. Such performance deterioration of the gas turbine decreases the mission readiness of the Air Force and simultaneously increases the maintenance costs. Some of the major factors responsible for the reduced performance are ingestion of debris during take off and landing, distorted intake flows during low altitude maneuvers, and hot gas ingestion during artillery...

  11. Advanced Diagnostics for Reacting Flows


    Ingeniera Mecanica , 17-19 Dec. 1990, Zaragosa, Spain; published in Congress Proceedings. 19. D. F. Davidson, A. Y. Chang, M. D. DiRosa and R. K. Hanson... Mecanica , 17-19 Dec. 1990, Zaragosa, Spain; published in Congress Proceedings. 14. D. F. Davidson, A. Y. Chang, M. D. DiRosa and R. K. Hanson

  12. Using conversions of chemically reacting tracers for numerical determination of temperature profiles in flowing systems and temperature histories in batch systems

    Brown, L.F.; Chemburkar, R.M.; Robinson, B.A.; Travis, B.J.


    This report presents the mathematical bases for measuring internal temperatures within batch and flowing systems using chemically reacting tracers. This approach can obtain temperature profiles of plug-flow systems and temperature histories within batch systems. The differential equations for reactant conversion can be converted into Fredholm integral equations of the first kind. The experimental variable is the tracer-reaction activation energy. When more than one tracer is used, the reactions must have different activation energies to gain information. In systems with temperature extrema, multiple solutions for the temperature profiles or histories can exist, When a single parameter in the temperature distribution is needed, a single-tracer test may furnish this information. For multi-reaction tracer tests, three Fredholm equations are developed. Effects of tracer-reaction activation energy, number of tracers used, and error in the data are evaluated. The methods can determine temperature histories and profiles for many existing systems, and can be a basis for analysis of the more complicated dispersed-flow systems. An alternative to using the Fredholm-equation approach is the use of an assumed temperature- distribution function and incorporation of this function into the basic integral equation describing tracer behavior. The function contains adjustable parameters which are optimized to give the temperature distribution. The iterative Fredholm equation method is tested to see what is required to discriminate between two models of the temperature behavior of Hot Dry Rock (HDR) geothermal reservoirs. Experimentally, ester and amide hydrolyses are valid HDR tracer reactions for measuring temperatures in the range 75-100{degrees}C. Hydrolyses of bromobenzene derivatives are valid HDR tracer reactions for measuring temperatures in the range 150-275{degrees}C.

  13. Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

    Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.


    The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

  14. Validation of the GPU-Accelerated CFD Solver ELBE for Free Surface Flow Problems in Civil and Environmental Engineering

    Christian F. Janßen


    Full Text Available This contribution is dedicated to demonstrating the high potential and manifold applications of state-of-the-art computational fluid dynamics (CFD tools for free-surface flows in civil and environmental engineering. All simulations were performed with the academic research code ELBE (efficient lattice boltzmann environment, The ELBE code follows the supercomputing-on-the-desktop paradigm and is especially designed for local supercomputing, without tedious accesses to supercomputers. ELBE uses graphics processing units (GPU to accelerate the computations and can be used in a single GPU-equipped workstation of, e.g., a design engineer. The code has been successfully validated in very different fields, mostly related to naval architecture and mechanical engineering. In this contribution, we give an overview of past and present applications with practical relevance for civil engineers. The presented applications are grouped into three major categories: (i tsunami simulations, considering wave propagation, wave runup, inundation and debris flows; (ii dam break simulations; and (iii numerical wave tanks for the calculation of hydrodynamic loads on fixed and moving bodies. This broad range of applications in combination with accurate numerical results and very competitive times to solution demonstrates that modern CFD tools in general, and the ELBE code in particular, can be a helpful design tool for civil and environmental engineers.

  15. Simulation of Thermo-fluid Interactions in Cryogenic Stage Turbine Startup System Using AUSM+-UP-based Higher-order Accurate Flow Solver

    Praveen Nair


    Full Text Available High-speed turbines are used in upper stage liquid engines of launch vehicles and the most common ones include LH2 and LOX turbines used in the cryogenic stages. The main constraints in the design of turbine system for a liquid engine are thermal loads, mass flow and pressure drops in various systems ahead of the turbine inlet. The temperature of the combustion products/gases reaching the turbine blades must be well below the melting point of the turbine blade material and the mass flow rate must be sufficient to generate the required power. Turbine can be started in two ways, by generating gases using a solid propellant-based spinner motor, and using compressed gases stored in gas bottles. The first method involves design challenges but requires less space and weight. On the other hand, second method is simple but requires more space. Because of the space and weight constraints associated with the upper stages, first method is preferred and discussed in this paper. It consists of a solid propellant-based spinner motor with a convergent-divergent nozzle, a guiding duct connecting nozzle exit, and the turbine inlet manifold in the form of a torroid with nozzle block having 39 guiding nozzles. The combustion products generated by the spinner motor are guided to the manifold through the guiding duct. Inlet manifold acts as a reservoir and supplies hot gases uniformly to the turbine through 39 nozzles. This study addresses the role of  computational fluid dynamics in the design of turbine startup system using unstructured cell-centered AUSM+-UP-based finite volume solver with the twoequation turbulence model. The flow and the thermal characteristics of the solid motor with a convergentdivergent nozzle were studied to evaluate the gas temperature, operating pressure, and flow velocities. The guiding duct along with the inlet manifold was analysed separately to find the drop in temperature and pressure within the system. From the simulation

  16. Assessment of Various Flow Solvers Used to Predict the Thermal Environment inside Space Shuttle Solid Rocket Motor Joints

    Wang, Qun-Zhen; Cash, Steve (Technical Monitor)


    It is very important to accurately predict the gas pressure, gas and solid temperature, as well as the amount of O-ring erosion inside the space shuttle Reusable Solid Rocket Motor (RSRM) joints in the event of a leak path. The scenarios considered are typically hot combustion gas rapid pressurization events of small volumes through narrow and restricted flow paths. The ideal method for this prediction is a transient three-dimensional computational fluid dynamics (CFD) simulation with a computational domain including both combustion gas and surrounding solid regions. However, this has not yet been demonstrated to be economical for this application due to the enormous amount of CPU time and memory resulting from the relatively long fill time as well as the large pressure and temperature rising rate. Consequently, all CFD applications in RSRM joints so far are steady-state simulations with solid regions being excluded from the computational domain by assuming either a constant wall temperature or no heat transfer between the hot combustion gas and cool solid walls.

  17. A totally Eulerian Finite Volume solver for multi-material fluid flows: Enhanced Natural Interface Positioning (ENIP)

    Loubère, Raphaël; Ghidaglia, Jean-Michel


    This work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally Eulerian since the mesh is not moving and a sharp interface, separating two materials, evolves through the grid. A sliding boundary condition is enforced at the interface and mass, momentum and total energy are conserved. Although this former method performs well on 1D test cases, the interface reconstruction suffers of poor accuracy in conserving shapes for instance in linear advection. This situation leads to spurious instabilities of the interface. The method Enhanced-NIP presented in the present paper cures an inconsistency in the former NIP method that improves strikingly the results. It takes advantage of a more consistent description of the interface in the numerical scheme. Results for linear advection and compressible Euler equations for inviscid fluids are presented ...

  18. A parallel PCG solver for MODFLOW.

    Dong, Yanhui; Li, Guomin


    In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree.

  19. Computed Verification of Drag Prediction for DLR-F6 Wing Body on Unstructured Grids Flow Solver%基于非结构平台的DLR-F6标模阻力预测

    章锦威; 戚姝妮; 郭承鹏; 董军


    This paper used the unstructured grids flow solver UNSMB to have a computed verification of the drag force for the DLR –F6 wing body configuration .Selective analysis on grid convergence , lift-drag curves and pressure distribute of the wing body configuration , and compare the computing results with the results of different solversand the wind tunnel data .The analysis results showsthat the computing results ofthe unstructured grids flow solver are close to the results of different solvers and the wind tunnel data ,to a certain extent it has a verification and validation forthe accuracy of computed drag of the solver .%采用自研的非结构网格解算器UNSMB进行了AIAA第三届阻力会议提供的DLR-F6翼身组合体的阻力计算验证。重点分析了模型的网格收敛特性、升阻力曲线以及压力分布等,并把计算结果与阻力预测会议上各个软件的计算结果以及试验数据进行比较,在此基础上分析计算结果。分析结果显示,非结构混合网格解算器的计算结果与各个软件的计算结果以及风洞试验数据吻合度较好,一定程度上验证与确认了解算器的阻力预测精度。

  20. Numerical Simulation of Interaction of Sonic Jet with High Speed Flow over a Blunt Body using Solution Mapped Higher Order Accurate AUSM+-UP Based Flow Solver

    P. Nair


    Full Text Available The development of a numerical procedure based on AUSM+-UP scheme using higher order accurate reconstruction method is presented. A code based on this is used for the simulation of film cooling for reentry module. Here the convective fluxes are evaluated using AUSM+-UP scheme. Least square based derivative evaluation is used to compute diffusive fluxes. The numerical code has been successfully validated using standard experimental data for counter flow injection. Analysis has been carried out for a simple axisymmetric reentry module with and without film cooling, for a free stream Mach number of 8.0. The predicted adiabatic wall temperatures were compared for both the cases. Film cooling is found to be effective for this configuration and injected coolant remains confined to the boundary layer formed by the free stream from nose tip to the aft end of the module. Numerical simulation of film cooling provides vital information required for design of effective cooling system such as number of counter flow injectors, their dimensions and locations, injection pressure and temperature, mass flow rate required etc.

  1. Turbulence Characteristics of Swirling Reacting Flow in a Combustor with Staged Air Injection%分级进风燃烧室内旋流反应流的湍流特性

    张健; 普勇; 周力行


    This paper presents an experimental investigation of the turbulent reacting flow in a swirl combustor with staged air injection. The air injected into the combustor is composed of the primary swirling jet and the secondary non-swirling jet. A three dimension-laser particle dynamic analyzer (PDA) was employed to measure the instantaneous gas velocity. The probability density functions (PDF) for the instantaneous gas axial and tangential velocities at each measuring location, as well as the radial profiles of the root mean square of fluctuating gas axial and tangential velocities and the second-order moment for the fluctuating gas axial and tangential velocities are obtained. The measured results delineate the turbulence properties of the swirling reacting flow under the conditions of staged combustion.

  2. Uncertainty Quantification for Production Navier-Stokes Solvers Project

    National Aeronautics and Space Administration — The uncertainty quantification methods developed under this program are designed for use with current state-of-the-art flow solvers developed by and in use at NASA....

  3. The REACT Project

    Bloch, Paul; Blystad, Astrid; Byskov, Jens;

    selected disease and programme interventions and services, within general care and on health systems management. Efforts to improve health sector performance have not yet been satisfactory, and adequate and sustainable improvements in health outcomes have not been shown. Priority setting in health systems...... decisions; and the provision of leadership and the enforcement of conditions. REACT - "REsponse to ACcountable priority setting for Trust in health systems" is an EU-funded five-year intervention study, which started in 2006 testing the application and effects of the AFR approach in one district each...... in Kenya, Tanzania and Zambia. Qualitative and quantitative methods are applied in an action research framework. The project baseline surveys have already been completed and indicate both a strong need and a high willingness for change in the study districts. REACT has developed active research...

  4. Parallel sparse direct solver for integrated circuit simulation

    Chen, Xiaoming; Yang, Huazhong


    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...

  5. Development of a numerical modelling tool for combined near field and far field wave transformations using a coupling of potential flow solvers

    Verbrugghe, Tim; Troch, Peter; Kortenhaus, Andreas;


    Wave energy converters (WECs) need to be deployed in large numbers in an array layout in order to have a significant power production. Each WEC has an impact on the incoming wave field, diffracting, reflecting and radiating waves. Simulating the wave transformations within and around a WEC farm...... is complex; it is difficult to simulate both near field and far field effects with a single numerical model, with relatively fast computing times. Within this research a numerical tool is developed to model near-field and far-field wave transformations caused by WECs. The tool is based on the coupling...... that the coupling of the two solvers is an efficient and promising numerical tool to perform simulations on near – and far field wave elevations and kinematics nearby WEC farms....

  6. Electric circuits problem solver

    REA, Editors of


    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

  7. Advanced calculus problem solver

    REA, Editors of


    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

  8. A Nonlinear Dynamic Subscale Model for Partially Resolved Numerical Simulation (PRNS)/Very Large Eddy Simulation (VLES) of Internal Non-Reacting Flows

    Shih, Tsan-Hsing; Liu, nan-Suey


    A brief introduction of the temporal filter based partially resolved numerical simulation/very large eddy simulation approach (PRNS/VLES) and its distinct features are presented. A nonlinear dynamic subscale model and its advantages over the linear subscale eddy viscosity model are described. In addition, a guideline for conducting a PRNS/VLES simulation is provided. Results are presented for three turbulent internal flows. The first one is the turbulent pipe flow at low and high Reynolds numbers to illustrate the basic features of PRNS/VLES; the second one is the swirling turbulent flow in a LM6000 single injector to further demonstrate the differences in the calculated flow fields resulting from the nonlinear model versus the pure eddy viscosity model; the third one is a more complex turbulent flow generated in a single-element lean direct injection (LDI) combustor, the calculated result has demonstrated that the current PRNS/VLES approach is capable of capturing the dynamically important, unsteady turbulent structures while using a relatively coarse grid.

  9. An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

    Thompson, Kyle B.; Gnoffo, Peter A.


    An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

  10. Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate in a Porous Medium with Suction



    Full Text Available A mathematical model is presented for a two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in a chemically reactive and porous medium in the presence of a transverse magnetic field. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with the forth order Runga-Kutta method. Pertinent results with respect to embedded parameters are displayed graphically for the velocity,temperature and concentration profiles and were discussed quantitatively.

  11. Heat and mass transfer effects on the mixed convective flow of chemically reacting nanofluid past a moving/stationary vertical plate

    B. Mahanthesh


    Full Text Available The problem of conjugate effects of heat and mass transfer over a moving/stationary vertical plate has been studied under the influence of applied magnetic field, thermal radiation, internal heat generation/absorption and first order chemical reaction. The fluid is assumed to be electrically conducting water based Cu-nanofluid. The Tiwari and Das model is used to model the nanofluid, whereas Rosseland approximation is used for thermal radiation effect. Unified closed form solutions are obtained for the governing equations using Laplace transform method. The velocity, temperature and concentration profiles are expressed graphically for different flow pertinent parameters. The physical quantities of engineering interest such as skin friction, Nusselt number and Sherwood number are also computed. The obtained analytical solutions satisfy all imposed initial and boundary conditions and they can be reduced to known previous results in some limiting cases. It is found that, by varying nanoparticle volume fraction, the flow and heat transfer characteristics could be controlled.

  12. Some topics of Navier-Stokes solvers

    Honma, H.; Nishikawa, N.


    The process of numerical simulation consists of selection of some items: a mathematical model, a numerical scheme, the level of the computer, and post processing. From this point of view, recent numerical studies of viscous flows are described especially for the fluid engineering laboratories in the Chiba University. The examples of simulations are Mach reflection on a wedge using a kinetic model equation and a cylinder-plate juncture flow using incompressible Navier Stokes equation. Some attempts at graphic monitoring of fluid mechanical calculations are also shown for some combinations of computers with Computational Fluid Dynamics (CFD) solvers.

  13. AFOSR/ONR Contractors’ Meeting on Combustion Rocket Propulsion Diagnostics of Reacting Flow Held in Ann Arbor, Michigan on 19-23 June 1989


    flow task: combined cycle engines, high performance turbine engines, safe compact nuclear rockets and space-based reusable orbital transfer vehicle...References 1. Chang, F. R., Fisher J. L., Nuclear Fusion, 22, No.8 (1982). 2. Chang, F. R., Krueger, W. A., Yang, T. F., AIAA/DBLR/JSASS International...and an EG&G OMA time-gated reticon array spectrometer are used to measure emissions near the center of the irradiated volume. A primary distinctive

  14. 1983 AFOSR/AFRPL Chemical Rocket Research Meeting, Abstracts and Agenda. Includes: Abstracts on Advanced Diagnostics of Reacting Flow, 28 February - 3 March 1983, Lancaster, California.


    past year, work continued on the build-up of the new ablation system, which will use a heliostat in conjuction with a solar concentrator to heat the...the velocity profile transitions towards a turbulent flow profile. Measurements with low amplitude pressure oscilla- tirns (0.05%) show heat transfer...FREQUENCY-DEPENDENT SURFACE DC-COMPONENT: ACOUSTIC STREAMING, HEAT TRANSFER (FIRST ORDER), WHEN U, V NOT OUT OF PHASE, NET WITH PHASE RELATIVE TO X

  15. Adaptive Kinetic-Fluid Solvers for Heterogeneous Computing Architectures

    Zabelok, Sergey; Kolobov, Vladimir


    This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. UFS is an adaptive kinetic-fluid simulation tool, which combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with AMR. Double digit speedups on single GPU and good scaling for multi-GPU have been demonstrated.


    Caughey, David


    A Symposium on Turbulence and Combustion was held at Cornell University on August 3-4, 2009. The overall goal of the Symposium was to promote future advances in the study of turbulence and combustion, through an unique forum intended to foster interactions between leading members of these two research communities. The Symposium program consisted of twelve invited lectures given by world-class experts in these fields, two poster sessions consisting of nearly 50 presentations, an open forum, and other informal activities designed to foster discussion. Topics covered in the lectures included turbulent dispersion, wall-bounded flows, mixing, finite-rate chemistry, and others, using experiment, modeling, and computations, and included perspectives from an international community of leading researchers from academia, national laboratories, and industry.

  17. Stability of compressible reacting mixing layer

    Shin, D. S.; Ferziger, J. H.


    Linear instability of compressible reacting mixing layers is analyzed with emphasis on the effects of heat release and compressibility. Laminar solutions of the compressible boundary-layer equations are used as the base flows. The parameters of this study are the adiabatic flame temperature, the Mach number of the upper stream, frequency, wavenumber, and the direction of propagation of the disturbance wave. Stability characteristics of the flow are presented. Three groups of unstable modes are found when the Mach number and/or heat release are large. Finally, it is shown that the unstable modes are two-dimensional for large heat release even in highly compressible flow.

  18. Quantum Electrodynamics vacuum polarization solver

    Carneiro, Pedro; Fonseca, Ricardo; Silva, Luís


    The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing scenarios of extreme energy density. We present a generalized finite-difference time-domain solver that can incorporate the modifications to Maxwells equations due to virtual vacuum polarization. Our multidimensional solver reproduced in one dimensional configurations the results for which an analytic treatment is possible, yielding vacuum harmonic generation and birefringence. The solver has also been tested for two-dimensional scenarios where finite laser beam spot sizes must be taken into account. We employ this solver to explore different types of counter-propagating configurations that can be relevant for future planned experiments aiming to detect quantum vacuum dynamics at ultra-high electromagnetic field intensities.

  19. Sherlock Holmes, Master Problem Solver.

    Ballew, Hunter


    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)

  20. Sherlock Holmes, Master Problem Solver.

    Ballew, Hunter


    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)

  1. European Reacting Flow Research: A Final Assessment.


    are in flame-front part of the laboratory of Molecular Ener- dynamics, premixed stabilized flames, get cis and Nacroscopic Combustion. The flame...Dedex FRANCE FRANCE Professor P. Clavin Professor Amable Lifian laboratoire de Recherche en Combustion Escuela Tecnica Suprior de Ingenieros Service 252

  2. Numerical Simulation of Chemically Reacting Flows


    constrained mechanical system in which the tiny hydrodynamic pressure can be interpreted as a Lagrange multiplier that imposes the proper divergence... house code generator based on the symbolic computing capabilities of Mathematica [31]. However, it proved extremely challenging to extend this software

  3. Turbulence-chemistry interactions in reacting flows

    Barlow, R.S.; Carter, C.D. [Sandia National Laboratories, Livermore, CA (United States)


    Interactions between turbulence and chemistry in nonpremixed flames are investigated through multiscalar measurements. Simultaneous point measurements of major species, NO, OH, temperature, and mixture fraction are obtained by combining spontaneous Raman scattering, Rayleigh scattering, and laser-induced fluorescence (LIF). NO and OH fluorescence signals are converted to quantitative concentrations by applying shot-to-shot corrections for local variations of the Boltzmann fraction and collisional quenching rate. These measurements of instantaneous thermochemical states in turbulent flames provide insights into the fundamental nature of turbulence-chemistry interactions. The measurements also constitute a unique data base for evaluation and refinement of turbulent combustion models. Experimental work during the past year has focused on three areas: (1) investigation of the effects of differential molecular diffusion in turbulent combustion: (2) experiments on the effects of Halon CF{sub 3}Br, a fire retardant, on the structure of turbulent flames of CH{sub 4} and CO/H{sub 2}/N{sub 2}; and (3) experiments on NO formation in turbulent hydrogen jet flames.

  4. Sensitive Diagnostics for Chemically Reacting Flows

    Farooq, Aamir


    This talk will feature latest diagnostic developments for sensitive detection of gas temperature and important combustion species. Advanced optical strategies, such as intrapulse chirping, wavelength modulation, and cavity ringdown are employed.

  5. Dynamics of High Pressure Reacting Shear Flows


    amplitude measurement described by Alenius (2014) • 1000-2000 sampled used Time average image subtracted from data Amplitude of mode at t = 0 Accounts for...and harmonics • Single modes can reconstruct convective processes (POD requires two modes) • Less efficient at reconstructing signal energy compared...Imaginary Receptivity mainly in the fundamental, some coherence at harmonics . DISTRIBUTION A: Approved for public release; distribution unlimited 22 Max

  6. Computational Fluid Dynamic Analyses for the High-Lift Common Research Model Using the USM3D and FUN3D Flow Solvers

    Rivers, Melissa; Hunter, Craig; Vatsa, Veer


    Two Navier-Stokes codes were used to compute flow over the High-Lift Common Research Model (HL-CRM) in preparation for a wind tunnel test to be performed at the NASA Langley Research Center 14-by-22-Foot Subsonic Tunnel in fiscal year 2018. Both flight and wind tunnel conditions were simulated by the two codes at set Mach numbers and Reynolds numbers over a full angle-of-attack range for three configurations: cruise, landing and takeoff. Force curves, drag polars and surface pressure contour comparisons are shown for the two codes. The lift and drag curves compare well for the cruise configuration up to 10deg angle of attack but not as well for the other two configurations. The drag polars compare reasonably well for all three configurations. The surface pressure contours compare well for some of the conditions modeled but not as well for others.

  7. Modern solvers for Helmholtz problems

    Tang, Jok; Vuik, Kees


    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...

  8. Performance evaluation of a parallel sparse lattice Boltzmann solver

    Axner, L.; Bernsdorf, J.; Zeiser, T.; Lammers, P.; Linxweiler, J.; Hoekstra, A.G.


    We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and

  9. Scalable Parallel Algebraic Multigrid Solvers

    Bank, R; Lu, S; Tong, C; Vassilevski, P


    The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

  10. Self-correcting Multigrid Solver

    Jerome L.V. Lewandowski


    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.

  11. Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation

    Mohamed A. El-Beltagy


    Full Text Available A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.

  12. Parallel Symmetric Eigenvalue Problem Solvers


    Plemmons G. Golub and A. Sameh. High-speed computing : scientific appli- cations and algorithm design. University of Illinois Press, Champaign, Illinois , 1988...16. SECURITY CLASSIFICATION OF: Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as...Eigenvalue Problem Solvers Report Title Sparse symmetric eigenvalue problems arise in many computational science and engineering applications such as

  13. A robust HLLC-type Riemann solver for strong shock

    Shen, Zhijun; Yan, Wei; Yuan, Guangwei


    It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipative flux can cure the shock instability, but also may lead to other problems, such as certain arbitrariness of choosing switching parameters or contact interface becoming smeared. In order to overcome these drawbacks, this paper proposes a simple and robust HLLC-type Riemann solver for inviscid, compressible gas flows, which is capable of preserving sharp contact surface and is free from instability. The main work is to construct a HLL-type Riemann solver and a HLLC-type Riemann solver by modifying the shear viscosity of the original HLL and HLLC methods. Both of the two new schemes are positively conservative under some typical wavespeed estimations. Moreover, a linear matrix stability analysis for the proposed schemes is accomplished, which illustrates the HLLC-type solver with shear viscosity is stable whereas the HLL-type solver with vorticity wave is unstable. Our arguments and numerical experiments demonstrate that the inadequate dissipation associated to the shear wave may be a unique reason to cause the instability.

  14. Development and validation of a local time stepping-based PaSR solver for combustion and radiation modeling

    Pang, Kar Mun; Ivarsson, Anders; Haider, Sajjad


    is henceforth addressed as radiationReactingLTSFoam (rareLTSFoam). A performance benchmarking exercise is here carried out to evaluate the effect of each LTS parameter on calculation stability, results accuracy and computational runtime. The model validation uses two test cases. The first test case presents...... 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...

  15. A constitutive theory of reacting electrolyte mixtures

    Costa Reis, Martina; Wang, Yongqi; Bono Maurizio Sacchi Bassi, Adalberto


    A constitutive theory of reacting electrolyte mixtures is formulated. The intermolecular interactions among the constituents of the mixture are accounted for through additional freedom degrees to each constituent of the mixture. Balance equations for polar reacting continuum mixtures are accordingly formulated and a proper set of constitutive equations is derived with basis in the Müller-Liu formulation of the second law of thermodynamics. Moreover, the non-equilibrium and equilibrium responses of the reacting mixture are investigated in detail by emphasizing the inner and reactive structures of the medium. From the balance laws and constitutive relations, the effects of molecular structure of constituents upon the fluid flow are studied. It is also demonstrated that the local thermodynamic equilibrium state can be reached without imposing that the set of independent constitutive variables is time independent, neither spatially homogeneous nor null. The resulting constitutive relations presented throughout this work are of relevance to many practical applications, such as swelling of clays, developing of bio and polymeric membranes, and use of electrorheological fluids in industrial processes. The first author acknowledges financial support from National Counsel of Technological and Scientific Development (CNPq) and German Academic Exchange Service (DAAD).

  16. Validation of a multi-block solver on aerospace test cases

    Gogoi, A.; Rao, K.V.L. [Aeronautical Development Agency, Bangalore (India)]. E-mail:


    The paper presents validation of a multi block solver on test cases of the aerospace industry like the RAE S duct, ONERA M6 wing and a delta wing. The flow features like curvature effects, cross flow vortices, overall diffusion of the S duct, {lambda} shock on the ONERA wing and leading edge vortex on the delta wing are well captured. These results demonstrate the robustness and versatility of the multi block solver. (author)

  17. High order Poisson Solver for unbounded flows

    Hejlesen, Mads Mølholm; Rasmussen, Johannes Tophøj; Chatelain, Philippe


    as regularisation we document an increased convergence rate up to tenth order. The method however, can easily be extended well beyond the tenth order. To show the full extend of the method we present the special case of a spectrally ideal regularisation of the velocity formulated integration kernel, which achieves......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...... or by performing the differentiation as a multiplication of the Fourier coefficients. In this way, differential operators such as the divergence or curl of the solution field could be solved to the same high order convergence without additional computational effort. The method was applied and validated using...

  18. Computation of two-phase reacting flows in solid-liquid rocket ramjets%固液火箭冲压发动机内两相反应流场数值计算

    马智博; 朱建士


    In order to compute three-dimens ional reacting flow fieldsestabl ished in the chambers of solid-liquid rocket ramjets,the block implicit algorit hm was used to solve the Navier-Stokes equations about gas,the Continuum Formul a tion Model and k-ε-Ap model were used to characterize the turbulent fl ow and vaporizatio n of droplets.The modified k-ε-g model was adopted to represent the combu stion of the fuels.Calculations were carried out under different chamber configuration s and initial droplet diameters,from which the effects of these conditions on t he combustion efficiency were analyzed.The numerical results reveal the p r ocesses of droplet vaporization and combustion.%为了计算固液混合式火箭冲压发动机补燃室内的三维反应流场,用块隐式法求解气相Navier-Stokes方程组,用连续介质模型和k-ε-Ap模型计算颗粒相的湍流流动与蒸发过程,用修正的k-ε-g模型描述燃料的燃烧。为了分析发动机设计参数对反应流场的影响,用不同的条件进行计算,并由此分析了补燃室几何结构和液体燃料初始颗粒直径对燃烧效率的影响。算例表明,计算方法有效可行,数值结果能够反映流场结构、液体燃料的蒸发和两种燃料的燃烧过程。

  19. A generalized gyrokinetic Poisson solver

    Lin, Z.; Lee, W.W.


    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.

  20. Turbulent diffusion of chemically reacting gaseous admixtures

    Elperin, T.; Kleeorin, N.; Liberman, M.; Rogachevskii, I.


    We study turbulent diffusion of chemically reacting gaseous admixtures in a developed turbulence. In our previous study [Phys. Rev. Lett. 80, 69 (1998), 10.1103/PhysRevLett.80.69] using a path-integral approach for a delta-correlated in a time random velocity field, we demonstrated a strong modification of turbulent transport in fluid flows with chemical reactions or phase transitions. In the present study we use the spectral τ approximation that is valid for large Reynolds and Peclet numbers and show that turbulent diffusion of the reacting species can be strongly depleted by a large factor that is the ratio of turbulent and chemical times (turbulent Damköhler number). We have demonstrated that the derived theoretical dependence of a turbulent diffusion coefficient versus the turbulent Damköhler number is in good agreement with that obtained previously in the numerical modeling of a reactive front propagating in a turbulent flow and described by the Kolmogorov-Petrovskii-Piskunov-Fisher equation. We have found that turbulent cross-effects, e.g., turbulent mutual diffusion of gaseous admixtures and turbulent Dufour effect of the chemically reacting gaseous admixtures, are less sensitive to the values of stoichiometric coefficients. The mechanisms of the turbulent cross-effects differ from the molecular cross-effects known in irreversible thermodynamics. In a fully developed turbulence and at large Peclet numbers the turbulent cross-effects are much larger than the molecular ones. The obtained results are applicable also to heterogeneous phase transitions.

  1. High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

    Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.


    Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.

  2. An immersed interface vortex particle-mesh solver

    Marichal, Yves; Chatelain, Philippe; Winckelmans, Gregoire


    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.

  3. PSH3D fast Poisson solver for petascale DNS

    Adams, Darren; Dodd, Michael; Ferrante, Antonino


    Direct numerical simulation (DNS) of high Reynolds number, Re >= O (105) , turbulent flows requires computational meshes >= O (1012) grid points, and, thus, the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the solver. We have developed a parallel solver of the Helmholtz equation in 3D, PSH3D. The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform in two spatial directions, and a parallel linear solver in the third direction. For computational meshes up to 81923 grid points, our numerical results show that PSH3D scales up to at least 262k cores of Cray XT5 (Blue Waters). PSH3D has a peak performance 6 × faster than 3D FFT-based methods when used with the 'partial-global' optimization, and for a 81923 mesh solves the Poisson equation in 1 sec using 128k cores. Also, we have verified that the use of PSH3D with the 'partial-global' optimization in our DNS solver does not reduce the accuracy of the numerical solution of the incompressible Navier-Stokes equations.

  4. Error Control of Iterative Linear Solvers for Integrated Groundwater Models

    Dixon, Matthew; Brush, Charles; Chung, Francis; Dogrul, Emin; Kadir, Tariq


    An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a prac...

  5. A survey of SAT solver

    Gong, Weiwei; Zhou, Xu


    In Computer Science, the Boolean Satisfiability Problem(SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. SAT is one of the first problems that was proven to be NP-complete, which is also fundamental to artificial intelligence, algorithm and hardware design. This paper reviews the main algorithms of the SAT solver in recent years, including serial SAT algorithms, parallel SAT algorithms, SAT algorithms based on GPU, and SAT algorithms based on FPGA. The development of SAT is analyzed comprehensively in this paper. Finally, several possible directions for the development of the SAT problem are proposed.

  6. An Energy Conserving Parallel Hybrid Plasma Solver

    Holmstrom, M


    We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is done in the FLASH software framework. It is shown that the solver conserves energy well over time, and that the parallelization is efficient (it exhibits weak scaling).

  7. Predicting SMT Solver Performance for Software Verification

    Andrew Healy


    Full Text Available The Why3 IDE and verification system facilitates the use of a wide range of Satisfiability Modulo Theories (SMT solvers through a driver-based architecture. We present Where4: a portfolio-based approach to discharge Why3 proof obligations. We use data analysis and machine learning techniques on static metrics derived from program source code. Our approach benefits software engineers by providing a single utility to delegate proof obligations to the solvers most likely to return a useful result. It does this in a time-efficient way using existing Why3 and solver installations - without requiring low-level knowledge about SMT solver operation from the user.

  8. A Survey of Solver-Related Geometry and Meshing Issues

    Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris


    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.

  9. Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

    Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em


    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).

  10. Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

    Tang, Yu-Hang, E-mail: [Division of Applied Mathematics, Brown University, Providence, RI (United States); Kudo, Shuhei, E-mail: [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501 (Japan); Bian, Xin, E-mail: [Division of Applied Mathematics, Brown University, Providence, RI (United States); Li, Zhen, E-mail: [Division of Applied Mathematics, Brown University, Providence, RI (United States); Karniadakis, George Em, E-mail: [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)


    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)

  11. A Fast Poisson Solver with Periodic Boundary Conditions for GPU Clusters in Various Configurations

    Rattermann, Dale Nicholas

    Fast Poisson solvers using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fast Poisson solver for periodic boundary conditions for use on a variety of GPU configurations. The solver used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these solvers are still computationally costly to employ, and the total solver time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid solvers by integrating a parallel FFT solver on a uniform grid during a coarse level. This hybrid solver could then be theoretically improved by replacing the highly-parallelizable FFT solver with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT solver (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poisson solver that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in

  12. A Novel High-Order, Entropy Stable, 3D AMR MHD Solver with Guaranteed Positive Pressure

    Derigs, Dominik; Gassner, Gregor J; Walch, Stefanie


    We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code $\\texttt{FLASH}$ ( The accuracy, robustness and computational efficiency is demonstrated with a number of tests, including comparisons to available MHD implementations in $\\texttt{FLASH}$.

  13. A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure

    Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie


    We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (

  14. State of the Art of Multi-Dimensional Modeling of Engine Reacting Flows État de l'art de la modélisation multidimensionnelle pour les écoulements réactifs dans les moteurs

    Gosman A. D.


    Full Text Available An overview is provided of the state of art and future prospects for the use of CFD simulation in engine analysis and design. The aspects covered include geometry handling and mesh generation, numerical solvers, mathematical modeling of key physical phenomena, exploitation of parallel computers and industrial application. The main conclusions are that:- solver and mesh generation methodology developments, allied to parallel computing technology, now enable much more rapid turnaround in CFD simulations than hitherto;- physics modeling is at an advanced stage for most aspects of SI combustion simulation, but less so for Diesel combustion and for spray-related processes generally;- the overall picture is one of rapidly-increasing use of CFD for engine design;- future developments, including the use of LES, promise even better results. Cet article dresse un aperçu de l'état de l'art et des perspectives de l'utilisation de la modélisation 3D pour l'analyse et le développement des moteurs. Les aspects abordés comprennent l'acquisition des géométries, la génération des maillages, les méthodologies numériques, la modélisation mathématique des phénomènes physiques importants, l'exploitation des calculateurs parallèles et l'application industrielle. Les conclusions principales de cette analyse font apparaître les points suivants : - les méthodologies numériques et la génération des maillages, associées au calcul parallèle, permettent maintenant de raccourcir notablement le cycle total de simulation ; - la modélisation physique a atteint sa maturité dans la plupart des aspects relatifs à la simulation de la combustion en allumage commandé ; en revanche, elle reste encore à acquérir en ce qui concerne la combustion Diesel et certains aspects des processus reliés aux sprays ; - globalement, l'utilisation de la simulation 3D pour la conception des moteurs est en forte augmentation ; - les développements futurs, dont l




    Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully

  16. SIERRA framework version 4 : solver services.

    Williams, Alan B.


    Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.

  17. Experimental Vortex Identification and Characterization in Reacting Jets in Crossflow

    Nair, Vedanth; Emerson, Ben; Lieuwen, Timothy


    Reacting jets in crossflow (JICF) is an important canonical flow field in combustion problems where there is strong coupling between heat release and the evolution of vortical structures. We use vortex identification studies to experimentally characterize the spatial evolution of vortex dynamics in a reacting JICF. A vortex identification algorithm was designed to operate on particle image velocimetry (PIV) data and its raw Mie scattering images. The algorithm uses the velocity fields to obtain comparisons between the strain rate and the rotation rate. Additionally, the algorithm uses the raw Mie scattering data to identify regions where the high acceleration at vortex cores has centrifuged seeding particles out of the vortex cores. Together, these methods are used to estimate the vortex location and circulation. Analysis was done on 10 kHz PIV data from a reacting JICF experiment, and the resulting vortex trajectory, and growth rate statistics are presented. Results are compared between non-reacting JICF and reacting studies performed with different jet density ratios and different levels of acoustic forcing. We observed how the density ratio, the frequency and amplitude of the acoustic forcing affected the vortex characteristics and growth rate.

  18. On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

    Weston, Brian T. [Univ. of California, Davis, CA (United States)


    This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser

  19. IGA-ADS: Isogeometric analysis FEM using ADS solver

    Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav


    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).

  20. Benchmarking optimization solvers for structural topology optimization

    Rojas Labanda, Susana; Stolpe, Mathias


    The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different...... sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point...... profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving...

  1. An advanced implicit solver for MHD

    Udrea, Bogdan

    A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel

  2. Phase Selection Heuristics for Satisfiability Solvers

    Chen, Jingchao


    In general, a SAT Solver based on conflict-driven DPLL consists of variable selection, phase selection, Boolean Constraint Propagation, conflict analysis, clause learning and its database maintenance. Optimizing any part of these components can enhance the performance of a solver. This paper focuses on optimizing phase selection. Although the ACE (Approximation of the Combined lookahead Evaluation) weight is applied to a lookahead SAT solver such as March, so far, no conflict-driven SAT solver applies successfully the ACE weight, since computing the ACE weight is time-consuming. Here we apply the ACE weight to partial phase selection of conflict-driven SAT solvers. This can be seen as an improvement of the heuristic proposed by Jeroslow-Wang (1990). We incorporate the ACE heuristic and the existing phase selection heuristics in the new solver MPhaseSAT, and select a phase heuristic in a way similar to portfolio methods. Experimental results show that adding the ACE heuristic can improve the conflict-driven so...

  3. Improved Stiff ODE Solvers for Combustion CFD

    Imren, A.; Haworth, D. C.


    Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. In this work, a fresh look at stiff ODE solvers is taken that includes how the solver is integrated into a turbulent combustion CFD code, and the advantages of extrapolation-based solvers in this regard are demonstrated. Benefits in CPU time and accuracy are demonstrated for homogeneous systems and compression-ignition engines, for chemical mechanisms that range in size from fewer than 50 to more than 7,000 species.

  4. A solver for the two-phase two-fluid model based on high-resolution total variation diminishing scheme

    Abu Saleem, Rabie A., E-mail: [Nuclear Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110 (Jordan); Kozlowski, Tomasz, E-mail: [Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 216 Talbot Laboratory, 104 S. Wright St., Urbana, IL 61801 (United States); Shrestha, Rijan, E-mail: [Portland Technology Development, Intel Corporation, 2501 NW 229th Ave Hillsboro OR 97124 (United States)


    Highlights: • The two-fluid model and the challenges associated with its numerical modeling are investigated. • A high-order solver based on flux limiter schemes and the theta method was developed. • The solver was compared to existing thermal hydraulics codes used in nuclear industry. • The solver was shown to handle fast transients with discontinuities and phase change. - Abstract: Finite volume techniques with staggered mesh are used to develop a new numerical solver for the one-dimensional two-phase two-fluid model using a high-resolution, Total Variation Diminishing (TVD) scheme. The solver is implemented to analyze numerical benchmark problems for verification and testing its abilities to handle discontinuities and fast transients with phase change. Convergence rates are investigated by comparing numerical results to analytical solutions available in literature for the case of the faucet flow problem. The solver based on a new TVD scheme is shown to exhibit higher-order of accuracy compared to other numerical schemes. Mass errors are also examined when phase change occurs for the shock tube problem, and compared to those of the 1st-order upwind scheme implemented in the nuclear thermal-hydraulics code TRACE. The solver is shown to exhibit numerical stability when applied to problems with discontinuous solutions and results of the new solver are free of spurious oscillations.

  5. Advances in the hydrodynamics solver of CO5BOLD

    Freytag, Bernd

    Many features of the Roe solver used in the hydrodynamics module of CO5BOLD have recently been added or overhauled, including the reconstruction methods (by adding the new second-order ``Frankenstein's method''), the treatment of transversal velocities, energy-flux averaging and entropy-wave treatment at small Mach numbers, the CTU scheme to combine the one-dimensional fluxes, and additional safety measures. All this results in a significantly better behavior at low Mach number flows, and an improved stability at larger Mach numbers requiring less (or no) additional tensor viscosity, which then leads to a noticeable increase in effective resolution.

  6. Physical gasdynamics of reacting media. Fizicheskaia gazodinamika reagiruiushchikh sred

    Alekseev, B.V.; Grishin, A.M.


    The fundamentals of the mechanics of reacting gases (aerothermochemistry) are presented in a systematic manner. Topics discussed include the kinetic theory of gases, elements of thermodynamics and chemical kinetics, transfer coefficients and mathematical models of gas flows, and transfer processes in a radiating gas. Attention is also given to similarity criteria and classification of aerothermochemical phenomena, elements of combustion theory, and some aspects of boundary layer theory. 81 references.

  7. Flutter and Forced Response Analyses of Cascades using a Two-Dimensional Linearized Euler Solver

    Reddy, T. S. R.; Srivastava, R.; Mehmed, O.


    Flutter and forced response analyses for a cascade of blades in subsonic and transonic flow is presented. The structural model for each blade is a typical section with bending and torsion degrees of freedom. The unsteady aerodynamic forces due to bending and torsion motions. and due to a vortical gust disturbance are obtained by solving unsteady linearized Euler equations. The unsteady linearized equations are obtained by linearizing the unsteady nonlinear equations about the steady flow. The predicted unsteady aerodynamic forces include the effect of steady aerodynamic loading due to airfoil shape, thickness and angle of attack. The aeroelastic equations are solved in the frequency domain by coupling the un- steady aerodynamic forces to the aeroelastic solver MISER. The present unsteady aerodynamic solver showed good correlation with published results for both flutter and forced response predictions. Further improvements are required to use the unsteady aerodynamic solver in a design cycle.

  8. An approximate Riemann solver for real gas parabolized Navier-Stokes equations

    Urbano, Annafederica, E-mail: [Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universita di Roma, Via Eudossiana 18, Roma 00184 (Italy); Nasuti, Francesco, E-mail: [Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universita di Roma, Via Eudossiana 18, Roma 00184 (Italy)


    Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finite volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.

  9. Inductive ionospheric solver for magnetospheric MHD simulations

    H. Vanhamäki


    Full Text Available We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances and similar output is produced (ionospheric electric field. The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km−1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981.

  10. Inductive ionospheric solver for magnetospheric MHD simulations

    Vanhamäki, H.


    We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).

  11. Direct simulations of chemically reacting turbulent mixing layers, part 2

    Metcalfe, Ralph W.; Mcmurtry, Patrick A.; Jou, Wen-Huei; Riley, James J.; Givi, Peyman


    The results of direct numerical simulations of chemically reacting turbulent mixing layers are presented. This is an extension of earlier work to a more detailed study of previous three dimensional simulations of cold reacting flows plus the development, validation, and use of codes to simulate chemically reacting shear layers with heat release. Additional analysis of earlier simulations showed good agreement with self similarity theory and laboratory data. Simulations with a two dimensional code including the effects of heat release showed that the rate of chemical product formation, the thickness of the mixing layer, and the amount of mass entrained into the layer all decrease with increasing rates of heat release. Subsequent three dimensional simulations showed similar behavior, in agreement with laboratory observations. Baroclinic torques and thermal expansion in the mixing layer were found to produce changes in the flame vortex structure that act to diffuse the pairing vortices, resulting in a net reduction in vorticity. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers were shown to result from vorticity generation by baroclinic torques.

  12. A Novel Preconditioner for Electromagnetic Solvers


    A novel preconditioning scheme for electromagnetic scattering solver is presented to improve the convergence of the iterative solver for the linear system resulted by the integral quations. Its kernel idea is the selection of the main contribution of the matrix elements, which affect the matrix condition number the most. We employ the important part similar to the near-field to build the preconditioning matrix. A parameter delta is given to control the balance between the computational expense to get the preconditioner and the effectiveness of the preconditioner. A practical selection of the control parameter delta of the preconditioner is discussed, which indicates the preconditioner is effective in conjunction with a BiCGstab(l) solver.

  13. New iterative solvers for the NAG Libraries

    Salvini, S.; Shaw, G. [Numerical Algorithms Group Ltd., Oxford (United Kingdom)


    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.

  14. Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

    Atanasov, Atanas


    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.

  15. Development of a multigrid finite difference solver for benchmark permeability analysis

    Loendersloot, Richard; Grouve, Wouter J.B.; Akkerman, Remko; Boer, de André; Michaud, V.


    A finite difference solver, dedicated to flow around fibre architectures is currently being developed. The complexity of the internal geometry of textile reinforcements results in extreme computation times, or inaccurate solutions. A compromise between the two is found by implementing a multigrid al

  16. Modification of Ordinary Differential Equations MATLAB Solver

    E. Cocherova


    Full Text Available Various linear or nonlinear electronic circuits can be described bythe set of ordinary differential equations (ODEs. The ordinarydifferential equations can be solved in the MATLAB environment inanalytical (symbolic toolbox or numerical way. The set of nonlinearODEs with high complexity can be usually solved only by use ofnumerical integrator (solver. The modification of ode23 MATLABnumerical solver has been suggested in this article for the applicationin solution of some special cases of ODEs. The main feature of thismodification is that the solution is found at every prescribed point,in which the special behavior of system is anticipated. Theextrapolation of solution is not allowed in those points.

  17. Acoustic imaging for diagnostics of chemically reacting systems

    Ramohalli, K.; Seshan, P.


    The concept of local diagnostics, in chemically reacting systems, with acoustic imaging is developed. The elements of acoustic imaging through ellipsoidal mirrors are theoretically discussed. In a general plan of the experimental program, the first system is chosen in these studies to be a simple open jet, non premixed turbulent flame. Methane is the fuel and enriched air is the oxidizer. This simple chemically reacting flow system is established at a Reynolds number (based on cold viscosity) of 50,000. A 1.5 m diameter high resolution acoustic mirror with an f-number of 0.75 is used to map the acoustic source zone along the axis of the flame. The results are presented as acoustic power spectra at various distances from the nozzle exit. It is seen that most of the reaction intensity is localized in a zone within 8 diameters from the exit. The bulk reactions (possibly around the periphery of the larger eddies) are evenly distributed along the length of the flame. Possibilities are seen for locally diagnosing single zones in a multiple cluster of reaction zones that occur frequently in practice. A brief outline is given of the future of this work which will be to apply this technique to chemically reacting flows not limited to combustion.

  18. Computation of non-equilibrium flow downstream of a plasma torch

    Harle, Christophe; Varghese, Philip L.; Carey, Graham F.


    Numerical solutions of the Navier-Stokes equations for compressible reacting flow in an axisymmetric geometry are presented for a nitrogen plasma torch with both thermal and chemical nonequilibrium. The Navier-Stokes equations are solved using a new axisymmetric finite element/finite volume formulation in which the convective flux is treated by an extension of the approximate Riemann solver due to Osher. The numerical scheme is validated by comparison with a previous solution of the same problem using a different computational scheme. Results obtained using two different models of nonthermal dissociation rates are compared to experimental data.

  19. Code Verification of the HIGRAD Computational Fluid Dynamics Solver

    Van Buren, Kendra L. [Los Alamos National Laboratory; Canfield, Jesse M. [Los Alamos National Laboratory; Hemez, Francois M. [Los Alamos National Laboratory; Sauer, Jeremy A. [Los Alamos National Laboratory


    The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.

  20. Novel Scalable 3-D MT Inverse Solver

    Kuvshinov, A. V.; Kruglyakov, M.; Geraskin, A.


    We present a new, robust and fast, three-dimensional (3-D) magnetotelluric (MT) inverse solver. As a forward modelling engine a highly-scalable solver extrEMe [1] is used. The (regularized) inversion is based on an iterative gradient-type optimization (quasi-Newton method) and exploits adjoint sources approach for fast calculation of the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT (single-site and/or inter-site) responses, and supports massive parallelization. Different parallelization strategies implemented in the code allow for optimal usage of available computational resources for a given problem set up. To parameterize an inverse domain a mask approach is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to high-performance clusters demonstrate practically linear scalability of the code up to thousands of nodes. 1. Kruglyakov, M., A. Geraskin, A. Kuvshinov, 2016. Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method, Computers and Geosciences, in press.

  1. vZ - An Optimizing SMT Solver

    Bjørner, Nikolaj; Dung, Phan Anh; Fleckenstein, Lars


    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...

  2. Quantitative visualization of the chemical reacting JET

    Okamoto, K.; Arata, Y.; Sasaki, T.; Madarame, H. [Nuclear Engineering Research Laboratory, Tokyo Univ., Tokai, Ibaraki (Japan)


    The sodium-water reaction should be precisely evaluated for the safety analysis of the sodium-cooled nuclear power plant. To evaluate these chemical reacting jet, the characteristics of the reaction and the mole fraction distributions of the reacting material should be known. In this study, to evaluate the basic characteristics, two fluid jet and chemical reacting jet was measured by the PIV and DELIF. The new dye pair for the dual emission LIF technique was proposed to measure the pH distribution. The Quinine for pH sensitive dye with blue emission and Rhodamine 6G for non-sensitive dye with orange emission, were excited by the third harmonic of Nd:YAG laser (355nm). The high accurate measurement could be achieved for the range of pH 4.0 to 5.5. The ammonia jet into acetic acid was measured using the proposed dye. The effectiveness of the present method was demonstrated. (author)

  3. Advanced validation of CFD-FDTD combined method using highly applicable solver for reentry blackout prediction

    Takahashi, Yusuke


    An analysis model of plasma flow and electromagnetic waves around a reentry vehicle for radio frequency blackout prediction during aerodynamic heating was developed in this study. The model was validated based on experimental results from the radio attenuation measurement program. The plasma flow properties, such as electron number density, in the shock layer and wake region were obtained using a newly developed unstructured grid solver that incorporated real gas effect models ...

  4. Calorimetry of non-reacting systems

    McCullough, John P


    Experimental Thermodynamics, Volume 1: Calorimetry of Non-Reacting Systems covers the heat capacity determinations for chemical substances in the solid, liquid, solution, and vapor states, at temperatures ranging from near the absolute zero to the highest at which calorimetry is feasible.This book is divided into 14 chapters. The first four chapters provide background information and general principles applicable to all types of calorimetry of non-reacting systems. The remaining 10 chapters deal with specific types of calorimetry. Most of the types of calorimetry treated are developed over a c

  5. [Analysis on the removal efficiency and mechanisms of phosphorus by modified zeolites substrates coated with LDHs reacted by different metal compounds in laboratory-scale vertical-flow constructed wetlands].

    Zhang, Xiang-Ling; Chen, Jun-Jie; Guo, Lu; Chen, Qiao-Zhen; Wang, Xiao-Xiao


    Six kinds of metal compounds which were CaCl2 , ZnCl2, MgCl2, FeCl3, AlCl3, and CoCl3 were formed nine kinds of different combinations in the alkaline conditions to synthesized LDHs (Layered Double Hydroxides), which were in-situ coated on the surface of zeolites. With the filling of the original and nine kinds of modified zeolites in the columns to simulate a laboratory-scale vertical-flow constructed wetland system, the experiments of purified phosphorus were conducted. Combined removal efficiency with adsorption isotherm data of the ten kinds of zeolites, mechanism for strengthening the removal rates of the phosphorus by the modified zeolites was studied. The results showed that compared with the original zeolites, the removal rates of the phosphorus by nine kinds of modified zeolites were enhanced with various degrees. In the cases of Zn involved in the modified zeolites, the removal efficiencies of phosphorus reached a high quality. Especially, the ZnFe-LDHs had the average removal rates of the total phosphorus, the dissolved phosphorus and the phosphate were over 90%, and its maximum adsorption capacity of the phosphorus was three times higher than that of the original zeolites. Therefore, by means of increasing the adsorption capacity and improving the chemical adsorption ability of phosphorus, the modification to coated LDHs on the zeolites reached the aim of strengthening the purification of the phosphorus.

  6. Transonic Drag Prediction on a DLR-F6 Transport Configuration Using Unstructured Grid Solvers

    Lee-Rausch, E. M.; Frink, N. T.; Mavriplis, D. J.; Rausch, R. D.; Milholen, W. E.


    A second international AIAA Drag Prediction Workshop (DPW-II) was organized and held in Orlando Florida on June 21-22, 2003. The primary purpose was to inves- tigate the code-to-code uncertainty. address the sensitivity of the drag prediction to grid size and quantify the uncertainty in predicting nacelle/pylon drag increments at a transonic cruise condition. This paper presents an in-depth analysis of the DPW-II computational results from three state-of-the-art unstructured grid Navier-Stokes flow solvers exercised on similar families of tetrahedral grids. The flow solvers are USM3D - a tetrahedral cell-centered upwind solver. FUN3D - a tetrahedral node-centered upwind solver, and NSU3D - a general element node-centered central-differenced solver. For the wingbody, the total drag predicted for a constant-lift transonic cruise condition showed a decrease in code-to-code variation with grid refinement as expected. For the same flight condition, the wing/body/nacelle/pylon total drag and the nacelle/pylon drag increment predicted showed an increase in code-to-code variation with grid refinement. Although the range in total drag for the wingbody fine grids was only 5 counts, a code-to-code comparison of surface pressures and surface restricted streamlines indicated that the three solvers were not all converging to the same flow solutions- different shock locations and separation patterns were evident. Similarly, the wing/body/nacelle/pylon solutions did not appear to be converging to the same flow solutions. Overall, grid refinement did not consistently improve the correlation with experimental data for either the wingbody or the wing/body/nacelle pylon configuration. Although the absolute values of total drag predicted by two of the solvers for the medium and fine grids did not compare well with the experiment, the incremental drag predictions were within plus or minus 3 counts of the experimental data. The correlation with experimental incremental drag was not

  7. Mathematical programming solver based on local search

    Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain


    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...

  8. Aleph Field Solver Challenge Problem Results Summary

    Hooper, Russell [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)


    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.

  9. Integrating Standard Dependency Schemes in QCSP Solvers

    Ji-Wei Jin; Fei-Fei Ma; Jian Zhang


    Quantified constraint satisfaction problems (QCSPs) are an extension to constraint satisfaction problems (CSPs) with both universal quantifiers and existential quantifiers.In this paper we apply variable ordering heuristics and integrate standard dependency schemes in QCSP solvers.The technique can help to decide the next variable to be assigned in QCSP solving.We also introduce a new factor into the variable ordering heuristics:a variable's dep is the number of variables depending on it.This factor represents the probability of getting more candidates for the next variable to be assigned.Experimental results show that variable ordering heuristics with standard dependency schemes and the new factor dep can improve the performance of QCSP solvers.

  10. High Resolution Euler Solvers Based on the Space-Time Conservation Element and Solution Element Method

    Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung


    The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.

  11. Chemical Mechanism Solvers in Air Quality Models

    John C. Linford


    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.

  12. A multigrid solver for the semiconductor equations

    Bachmann, Bernhard


    We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

  13. RANS solver for microscale pollution dispersion problems in areas with vegetation: Development and validation

    Šíp, Viktor


    We present a description and validation of a finite volume solver aimed at solving the problems of microscale urban flows where vegetation is present. The solver is based on the five equation system of Reynolds-averaged Navier-Stokes equations for atmospheric boundary layer flows, which are complemented by the k-epsilon turbulence model. The vegetation is modelled as a porous zone, and the effects of the vegetation are included in the momentum and turbulence equations. A detailed dry deposition model is incorporated in the pollutant transport equation, allowing the investigation of the filtering properties of urban vegetation. The solver is validated on four test cases to assess the components of the model: the flow and pollutant dispersion around the 2D hill, the temporal evolution of the rising thermal bubble, the flow through and around the forest canopy, and a hedgerow filtering the particle-laden flow. Generally good agreement with the measured values or previously computed numerical solution is observed...

  14. Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver

    Livne, Oren E


    Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and an energy correction of the coarse-level systems. This results in fast convergence and substantial overhead and memory s...

  15. Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties

    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...... 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), were less successful due to lack of such good approximation...... 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...

  16. Development and acceleration of unstructured mesh-based cfd solver

    Emelyanov, V.; Karpenko, A.; Volkov, K.


    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.

  17. Algorithmic Enhancements to the VULCAN Navier-Stokes Solver

    Litton, D. K.; Edwards, J. R.; White, J. A.


    VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.

  18. Simulation Experiments of Reacting Two-Phase Flow


    Simulation Experiments 16 2.8 Lord’s Work Done in the 1960’s 17 2.9 Investigations Performed by Wilkins and Carros in the 1960’s 19 2.10 Statement of Work 20...the fundamental research work described here. A gas gun facility, based on the studies of Lord (21 and Wilkins and Carros [3] was built at that the calculations of Lord [2] are in error (see Section 4.). ’i 3-X: 2.9 Investigations Performed by Wilkins and Carros inthe 196o’s- Wilkins

  19. Investigation of Highly Pressurized Two-Phase, Reacting Flow


    single-stage gas gun built at the Ernst-Mach-lnstitut [101 is based upon earlier developments of Lord [14] and Wilkins and Carros [15]. A detailed...conditions approaching those of real guns are within reach of such gas guns [141. In 1963, Wilkins and Carros [151 reported on combustion tests performed with...and unmixed hydrogen and hydrogen resulted in severe pressure oscillations or even detonation corroborating the findings of Wilkins and Carros [15

  20. On unsteady reacting flow in a channel with a cavity

    Ivar Ø. Sand


    Full Text Available The problem investigated is the stability of a flame anchored by recirculation within a channel with a cavity, acting as a two-dimensional approximation to a gas turbine combustion chamber. This is related to experiments of Vaneveld, Hom and Oppenheim (1982. The hypothesis studied is that hydrodynamic oscillations within the cavity can lead to flashback.

  1. Chemically reacting fluid flow in exoplanet and brown dwarf atmospheres

    Bordwell, Baylee; Brown, Benjamin P.; Oishi, Jeffrey S.


    In the past few decades, spectral observations of planets and brown dwarfs have demonstrated significant deviations from predictions in certain chemical abundances. Starting with Jupiter, these deviations were successfully explained to be the effect of fast dynamics on comparatively slow chemical reactions. These dynamical effects are treated using mixing length theory in what is known as the "quench" approximation. In these objects, however, both radiative and convective zones are present, and it is not clear that this approximation applies. To resolve this issue, we solve the fully compressible equations of fluid dynamics in a matched polytropic atmosphere using the state-of-the-art pseudospectral simulation framework Dedalus. Through the inclusion of passive tracers, we explore the transport properties of convective and radiative zones, and verify the classical eddy diffusion parameterization. With the addition of active tracers, we examine the interactions between dynamical and chemical processes using abstract chemical reactions. By locating the quench point (the point at which the dynamical and chemical timescales are the same) in different dynamical regimes, we test the quench approximation, and generate prescriptions for the exoplanet and brown dwarf communities.

  2. Nitramine Monopropellant Deflagration and General Nonsteady Reacting Rocket Chamber Flows.


    University, Department of Aerospace, Princeton, NJ, 1973. 68. Maltsev , V. M. Law, R. J., Ryan, N. W., Bare, A. D., and Summerfield, M., "on the...closeness of the HMX and RDX points; no attempt was made to correlate the HMX results. -189- DB, LUMINOUS FLAMtE FRONT, MEASURED BY MALTSEV MEASURED

  3. Reacting Flows Simulation with Applications to Ground to Flight Extrapolation


    P.zza Leonardo da Vinci 32, 20133 Milano, Italy Abstract The development of next generation reusable space vehicles requires a...Politecnico di Milano, Dept. of Mathematics P.zza Leonardo da Vinci 32, 20133 Milano, Italy 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING

  4. Improved Modeling Tools For High Speed Reacting Flows


    putting the tools in place and operating them as a single system on the Beowulf cluster which was purposely built by Blue Blanket LLC (BBLLC) for this...a commercial tool, available from the Program Development Company (PDC). Computational Cluster An eight processor cluster was leased from BBLLC...SBIR I - FA8650-05-M-2594 3 Software Installation Once this cluster was in place, the off-the-shelf software was installed and tested

  5. Development of Implicit Compact Methods for Chemically Reacting Flows


    CPtHEATr .. CPt 2 LACP r Tr2 CPttLACPrTr2 d F4 / d (T) = = LACPt Tr < CP2 CP2 CP CPt LACPt rTr2...rRHOTt CPt2 LACP r Tz2 LACPt t r Tr2 - LACPt r Trr CP T CP2 CPttLACPrTz2 CPt LACPt r Tz2 , r RHO Tr U r RHO Tz W

  6. A new computational method for reacting hypersonic flows

    Niculescu, M. L.; Cojocaru, M. G.; Pricop, M. V.; Fadgyas, M. C.; Pepelea, D.; Stoican, M. G.


    Hypersonic gas dynamics computations are challenging due to the difficulties to have reliable and robust chemistry models that are usually added to Navier-Stokes equations. From the numerical point of view, it is very difficult to integrate together Navier-Stokes equations and chemistry model equations because these partial differential equations have different specific time scales. For these reasons, almost all known finite volume methods fail shortly to solve this second order partial differential system. Unfortunately, the heating of Earth reentry vehicles such as space shuttles and capsules is very close linked to endothermic chemical reactions. A better prediction of wall heat flux leads to smaller safety coefficient for thermal shield of space reentry vehicle; therefore, the size of thermal shield decreases and the payload increases. For these reasons, the present paper proposes a new computational method based on chemical equilibrium, which gives accurate prediction of hypersonic heating in order to support the Earth reentry capsule design.

  7. Experimental and numerical investigation of reacting stagnation flow

    Bergthorson, Jeff; Dimotakis, Paul


    Planar laminar premixed flames are stabilized in the stagnation flowfield of an impinging jet. These flames are studied experimentally through measurements of the axial velocity and CH radical profiles, the equivalence ratio, plate temperature, and the static (Bernoulli) pressure drop across the nozzle. The velocity measurements are performed using Particle Streak Velocimetry (PSV), a technique valuable in flame measurements due to the low particle-mass loading, high accuracy and short run times possible. The CH radical profile is measured using Planar Laser Induced Fluorescence (PLIF), which provides a very accurate marker for the reaction zone location. The experimental results are compared to predictions by a one-dimensional simulation which incorporates full chemistry. Difficulties in performing detailed comparisons between one-dimensional simulations and finite-nozzle-diameter experiments are discussed in the context of validating chemical kinetics models. To further investigate the validity of these chemical kinetics models, global flame properties such as extinction strain-rates are also investigated.

  8. 双向分布水翼周围有势流动时的耗散自由表面解%Dissipative Free-Surface Solver for the Potential Flow Around a Hydrofoil Distributed With Doublets

    陈志敏; W·G·普莱斯; 海治


    A doublet integral equation was formulated for a two-dimensional dissipative potential flow around a hydrofoil submerged below the free-water surface. The free-water surface was assumed to involve energy dissipation and thus was source of damping. A doublet panel method was developed from incorporation of dissipative Green function approach and doublets distribution on the hydrofoil surface. Numerical computations were implemented and derived numerical results were in good agreement with analytic solutions and experimental measurements.%为浸没于自由表面下部的2维水翼,建立水翼周围作耗散有势流动时的二次积分方程.假设自由表面具有能量的耗散,也就是阻尼的来源.根据耗散Green函数的无旋性近似和水翼表面的双向分布,提出了双向的面元法( doublet panel method).数值计算后得到的结果,与分析解和已有实验数据均吻合得很好.

  9. Solvers for large-displacement fluid structure interaction problems: segregated versus monolithic approaches

    Heil, Matthias; Hazel, Andrew L.; Boyle, Jonathan


    We compare the relative performance of monolithic and segregated (partitioned) solvers for large- displacement fluid structure interaction (FSI) problems within the framework of oomph-lib, the object-oriented multi-physics finite-element library, available as open-source software at . Monolithic solvers are widely acknowledged to be more robust than their segregated counterparts, but are believed to be too expensive for use in large-scale problems. We demonstrate that monolithic solvers are competitive even for problems in which the fluid solid coupling is weak and, hence, the segregated solvers converge within a moderate number of iterations. The efficient monolithic solution of large-scale FSI problems requires the development of preconditioners for the iterative solution of the linear systems that arise during the solution of the monolithically coupled fluid and solid equations by Newton’s method. We demonstrate that recent improvements to oomph-lib’s FSI preconditioner result in mesh-independent convergence rates under uniform and non-uniform (adaptive) mesh refinement, and explore its performance in a number of two- and three-dimensional test problems involving the interaction of finite-Reynolds-number flows with shell and beam structures, as well as finite-thickness solids.

  10. Courant Number and Mach Number Insensitive CE/SE Euler Solvers

    Chang, Sin-Chung


    It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.

  11. On the verification of polynomial system solvers

    Changbo CHEN; Marc MORENO MAZA; Wei PAN; Yuzhen XI


    We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which manipulates constructible sets represented by regular systems. We provide comparative benchmarks of different verification procedures applied to four solvers on a large set of well-known polynomial systems. Our experimental results illustrate the high effi-ciency of our new approach. In particular, we are able to verify triangular decompositions of polynomial systems which are not easy to solve.

  12. Input-output-controlled nonlinear equation solvers

    Padovan, Joseph


    To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.

  13. Preconditioners for Incompressible Navier-Stokes Solvers

    A.Segal; M.ur Rehman; C.Vuik


    In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block precon- ditioners form an excellent approach for the solution, however if the grids are not to fine preconditioning with a Saddle point ILU matrix (SILU) may be an attractive al- ternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

  14. DPS--a computerised diagnostic problem solver.

    Bartos, P; Gyárfas, F; Popper, M


    The paper contains a short description of the DPS system which is a computerized diagnostic problem solver. The system is under development of the Research Institute of Medical Bionics in Bratislava, Czechoslovakia. Its underlying philosophy yields from viewing the diagnostic process as process of cognitive problem solving. The implementation of the system is based on the methods of Artificial Intelligence and utilisation of production systems and frame theory should be noted in this context. Finally a list of program modules and their characterisation is presented.

  15. Metaheuristics progress as real problem solvers

    Nonobe, Koji; Yagiura, Mutsunori


    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.

  16. Predictions of a Supersonic Jet-in-Crossflow: Comparisons Among CFD Solvers and with Experiment


    outflow boundaries were specified as modified Riemann invariants conditions at the freestream flow conditions. The computational inlet is a planar face and...jet-on cases. Figure 6. ARL computational mesh. Figure 7. ARL geometry and mesh in jet nozzle area. D ow nl oa de d by J am es D...The inviscid flux function was a second-order, upwind scheme using a Harten-Lax-van Leer-Contact (HLLC) Riemann solver and a multi- dimensional Total

  17. Three-dimensional incompressible Navier-Stokes solver using lower-upper symmetric-Gauss-Seidel algorithm

    Yoon, Seokkwan; Kwak, Dochan


    A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

  18. A set of strongly coupled, upwind algorithms for computing flows in chemical nonequilibrium

    Molvik, Gregory A.; Merkle, Charles L.


    Two new algorithms have been developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both take advantage of the benefits of upwind differencing, Total Variation Diminishing (TVD) techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithym is a time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a new temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms.

  19. Framework for a Robust General Purpose Navier-Stokes Solver on Unstructured Meshes

    Xiao, Cheng-Nian; Denner, Fabian; van Wachem, Berend G. M.


    A numerical framework for a pressure-based all-speeds flow solver operating on unstructured meshes, which is robust for a broad range of flow configurations, is proposed. The distinct features of our framework are the full coupling of the momentum and continuity equations as well as the use of an energy equation in conservation form to relate the thermal quantities with the flow field. In order to overcome the well-documented instability occurring while coupling the thermal energy to the remaining flow variables, a multistage iteration cycle has been devised which exhibits excellent convergence behavior without requiring any numerical relaxation parameters. Different spatial schemes for accurate shock resolution as well as complex thermodynamic gas models are also seamlessly incorporated into the framework. The solver is directly applicable to stationary and transient flows in all Mach number regimes (sub-, trans-, supersonic), exhibits strong robustness and accurately predicts flow and thermal variables at all speeds across shocks of different strengths. We present a wide range of results for both steady and transient compressible flows with vastly different Mach numbers and thermodynamic conditions in complex geometries represented by different types of unstructured meshes. The authors are grateful for the financial support provided by Shell.

  20. Time Domain Surface Integral Equation Solvers for Quantum Corrected Electromagnetic Analysis of Plasmonic Nanostructures

    Uysal, Ismail Enes


    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

  1. Analysis on capabilities of density-based solvers within OpenFOAM to distinguish aerothermal variables in diffusion boundary layer

    Shen Chun; Sun Fengxian; Xia Xinlin


    Open source field operation and manipulation (OpenFOAM) is one of the most preva-lent open source computational fluid dynamics (CFD) software. It is very convenient for researchers to develop their own codes based on the class library toolbox within OpenFOAM. In recent years, several density-based solvers within OpenFOAM for supersonic/hypersonic compressible flow are coming up. Although the capabilities of these solvers to capture shock wave have already been ver-ified by some researchers, these solvers still need to be validated comprehensively as commercial CFD software. In boundary layer where diffusion is the dominant transportation manner, the con-vective discrete schemes’ capability to capture aerothermal variables, such as temperature and heat flux, is different from each other due to their own numerical dissipative characteristics and from viewpoint of this capability, these compressible solvers within OpenFOAM can be validated further. In this paper, firstly, the organizational architecture of density-based solvers within OpenFOAM is analyzed. Then, from the viewpoint of the capability to capture aerothermal vari-ables, the numerical results of several typical geometrical fields predicted by these solvers are com-pared with both the outcome obtained from the commercial software Fastran and the experimental data. During the computing process, the Roe, AUSM+(Advection Upstream Splitting Method), and HLLC(Harten-Lax-van Leer-Contact) convective discrete schemes of which the spatial accu-racy is 1st and 2nd order are utilized, respectively. The compared results show that the aerothermal variables are in agreement with results generated by Fastran and the experimental data even if the 1st order spatial precision is implemented. Overall, the accuracy of these density-based solvers can meet the requirement of engineering and scientific problems to capture aerothermal variables in diffusion boundary layer.

  2. Facilities GIS Modeling for the REACT System Project

    National Aeronautics and Space Administration — The Real-Time Emergency Action Coordination Tool (REACT) was developed under contract to NASA and deployed for use by the entire agency.  NASA REACT is a...

  3. A Novel Interactive MINLP Solver for CAPE Applications

    Henriksen, Jens Peter; Støy, S.; Russel, Boris Mariboe;


    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...

  4. Efficient use of iterative solvers in nested topology optimization

    Amir, Oded; Stolpe, Mathias; Sigmund, Ole


    by a Krylov subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence...

  5. Experiences with linear solvers for oil reservoir simulation problems

    Joubert, W.; Janardhan, R. [Los Alamos National Lab., NM (United States); Biswas, D.; Carey, G.


    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.

  6. Mathematical aspects of reacting and diffusing systems

    Fife, Paul C


    Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...

  7. Quick-Mixing Studies Under Reacting Conditions

    Leong, May Y.; Samuelsen, G. S.


    The low-NO(x) emitting potential of rich-burn/quick-mix/lean-burn )RQL) combustion makes it an attractive option for engines of future stratospheric aircraft. Because NO(x) formation is exponentially dependent on temperature, the success of the RQL combustor depends on minimizing high temperature stoichiometric pocket formation in the quick-mixing section. An experiment was designed and built, and tests were performed to characterize reaction and mixing properties of jets issuing from round orifices into a hot, fuel-rich crossflow confined in a cylindrical duct. The reactor operates on propane and presents a uniform, non-swirling mixture to the mixing modules. Modules consisting of round orifice configurations of 8, 9, 10, 12, 14, and 18 holes were evaluated at a momentum-flux ratio of 57 and jet-to-mainstream mass-flaw ratio of 2.5. Temperatures and concentrations of O2, CO2, CO, HC, and NO(x) were obtained upstream, down-stream, and within the orifice plane to determine jet penetration as well as reaction processes. Jet penetration was a function of the number of orifices and affected the mixing in the reacting system. Of the six configurations tested, the 14-hole module produced jet penetration close to the module half-radius and yielded the best mixing and most complete combustion at a plane one duct diameter from the orifice leading edge. The results reveal that substantial reaction and heat release occur in the jet mixing zone when the entering effluent is hot and rich, and that the experiment as designed will serve to explore satisfactorily jet mixing behavior under realistic reacting conditions in future studies.

  8. Scalable Adaptive Multilevel Solvers for Multiphysics Problems

    Xu, Jinchao


    In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.

  9. Integrating advanced reasoning into a SAT solver

    DING Min; TANG Pushan; ZHOU Dian


    In this paper, we present a SAT solver based on the combination of DPLL (Davis Putnam Logemann and Loveland) algorithm and Failed Literal Detection (FLD), one of the advanced reasoning techniques. We propose a Dynamic Filtering method that consists of two restriction rules for FLD: internal and external filtering. The method reduces the number of tested literals in FLD and its computational time while maintaining the ability to find most of the failed literals in each decision level. Unlike the pre-defined criteria, literals are removed dynamically in our approach. In this way, our FLD can adapt itself to different real-life benchmarks. Many useless tests are therefore avoided and as a consequence it makes FLD fast. Some other static restrictions are also added to further improve the efficiency of FLD. Experiments show that our optimized FLD is much more efficient than other advanced reasoning techniques.

  10. Optimising a parallel conjugate gradient solver

    Field, M.R. [O`Reilly Institute, Dublin (Ireland)


    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.

  11. Asynchronous Parallelization of a CFD Solver

    Daniel S. Abdi


    Full Text Available 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 in CFD codes; however, it has a potential to alleviate scaling bottlenecks incurred due to processors having to wait for each other at designated synchronization points. A common way to avoid this idle time is to overlap asynchronous communication with computation. For this to work, however, there must be something useful and independent a processor can do while waiting for messages to arrive. We investigate an alternative approach of computation, namely, conducting asynchronous iterations to improve local subdomain solution while communication is in progress. An in-house CFD code is parallelized using message passing interface (MPI, and scalability tests are conducted that suggest asynchronous iterations are a viable way of parallelizing CFD code.

  12. An experimental and numerical study of confined non-reacting and reacting turbulent jets to facilitate homogeneous combustion in industrial furnaces

    Lee, Insu

    Confined non-reacting turbulent jets are ideal for recirculating the hot flue gas back into the furnace from an external exhaust duct. Such jets are also used inside the furnace to internally entrain and recirculate the hot flue gas to preheat and dilute the reactants. Both internal and external implementation of confined turbulent jets increase the furnace thermal efficiency. For external implementation, depending on the circumstances, the exhaust gas flow may be co- or counter-flow relative to the jet flow. Inside the furnaces, fuel and air jets are injected separately. To create a condition which can facilitate near homogeneous combustion, these jets have to first mix with the burned gas inside the furnace and simultaneously being heated and diluted prior to combustion. Clearly, the combustion pattern and emissions from reacting confined turbulent jets are affected by jet interactions, mixing and entrainment of hot flue gas. In this work, the flow and mixing characteristics of a non-reacting and reacting confined turbulent jet are investigated experimentally and numerically. This work consists of two parts: (i) A study of flow and mixing characteristics of non-reacting confined turbulent jets with co- or counter-flowing exhaust/flue gas. Here the axial and radial distributions of temperature, velocity and NO concentration (used as a tracer gas) were measured. FLUENT was used to numerically simulate the experimental results. This work provides the basic understanding of the flow and mixing characteristics of confined turbulent jets and develops some design considerations for recirculating flue gas back into the furnace as expressed by the recirculation zone and the stagnation locations. (ii) Numerical calculations of near homogeneous combustion are performed for the existing furnace. The exact geometry of the furnace in the lab is used and the real dimensional boundary conditions are considered. The parameters such as air nozzle diameter (dair), fuel nozzle

  13. Linear models for sound from supersonic reacting mixing layers

    Chary, P. Shivakanth; Samanta, Arnab


    We perform a linearized reduced-order modeling of the aeroacoustic sound sources in supersonic reacting mixing layers to explore their sensitivities to some of the flow parameters in radiating sound. Specifically, we investigate the role of outer modes as the effective flow compressibility is raised, when some of these are expected to dominate over the traditional Kelvin-Helmholtz (K-H) -type central mode. Although the outer modes are known to be of lesser importance in the near-field mixing, how these radiate to the far-field is uncertain, on which we focus. On keeping the flow compressibility fixed, the outer modes are realized via biasing the respective mean densities of the fast (oxidizer) or slow (fuel) side. Here the mean flows are laminar solutions of two-dimensional compressible boundary layers with an imposed composite (turbulent) spreading rate, which we show to significantly alter the growth of instability waves by saturating them earlier, similar to in nonlinear calculations, achieved here via solving the linear parabolized stability equations. As the flow parameters are varied, instability of the slow modes is shown to be more sensitive to heat release, potentially exceeding equivalent central modes, as these modes yield relatively compact sound sources with lesser spreading of the mixing layer, when compared to the corresponding fast modes. In contrast, the radiated sound seems to be relatively unaffected when the mixture equivalence ratio is varied, except for a lean mixture which is shown to yield a pronounced effect on the slow mode radiation by reducing its modal growth.

  14. Simulation of filtration processes in deformable media Part 3.1: Basic concepts and particle-fluid force implementation of a non-spherical dirt particle solver

    G Boiger


    Full Text Available A Lagrangian solver to realistically model large, non-spherical dirt particlesand their behaviour in the vicinity of deformable filtration fibres has beenprogrammed. While this paper focuses on basic solver concepts as well asdrag force implementations, a related article, concerning the realisation ofinteraction effects and result verification, is forthcoming, [3].Within the framework of a digitally reconstructed, deformable filter fibregeometry, the solver traces the governing multi physics effects down to theoccurrence of single force- and torque vectors. In order to go from an initial,spherical particle model [2], to a more sophisticated, non-spherical model,the capabilities of a Six Degrees of Freedom Solver have been included inthe programming. A panel model and the concept of satellite help points areused to handle particles that encompass several fluid calculation cells.An innovative drag force implementation allows the consideration ofrotational- and shear flow effects on particle motion. Results are evaluatedand compared to an analytical formulation.

  15. High-Performance Solvers for Dense Hermitian Eigenproblems

    Petschow, Matthias; Bientinesi, Paolo


    We introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the Algorithm of Multiple Relatively Robust Representations - referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is designed to fully support both message-passing (MPI) and multithreading parallelism (SMP). As a result, the solvers can equally be used in pure MPI or in hybrid MPI-SMP fashion. We conducted a thorough performance study of EleMRRR and ScaLAPACK's solvers on two supercomputers. Such a study, performed with up to 8,192 cores, provides precise guidelines to assemble the fastest solver within the ScaLAPACK framework; it also ind...

  16. Comparison of open-source linear programming solvers.

    Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph


    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.

  17. An optimal iterative solver for the Stokes problem

    Wathen, A. [Univ. of Bristol (United Kingdom); Silvester, D.


    Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.

  18. Parallelizable approximate solvers for recursions arising in preconditioning

    Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)


    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.

  19. An iterative solver for the 3D Helmholtz equation

    Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir


    We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

  20. Adjoint based sensitivity analysis of a reacting jet in crossflow

    Sashittal, Palash; Sayadi, Taraneh; Schmid, Peter


    With current advances in computational resources, high fidelity simulations of reactive flows are increasingly being used as predictive tools in various industrial applications. In order to capture the combustion process accurately, detailed/reduced chemical mechanisms are employed, which in turn rely on various model parameters. Therefore, it would be of great interest to quantify the sensitivities of the predictions with respect to the introduced models. Due to the high dimensionality of the parameter space, methods such as finite differences which rely on multiple forward simulations prove to be very costly and adjoint based techniques are a suitable alternative. The complex nature of the governing equations, however, renders an efficient strategy in finding the adjoint equations a challenging task. In this study, we employ the modular approach of Fosas de Pando et al. (2012), to build a discrete adjoint framework applied to a reacting jet in crossflow. The developed framework is then used to extract the sensitivity of the integrated heat release with respect to the existing combustion parameters. Analyzing the sensitivities in the three-dimensional domain provides insight towards the specific regions of the flow that are more susceptible to the choice of the model.

  1. Robust large-scale parallel nonlinear solvers for simulations.

    Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)


    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

  2. Elliptic Solvers for Adaptive Mesh Refinement Grids

    Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.


    We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.

  3. AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL

    Cercos-Pita, J. L.


    In this paper, AQUAgpusph, a new free Smoothed Particle Hydrodynamics (SPH) software accelerated with OpenCL, is described. The main differences and progress with respect to other existing alternatives are considered. These are the use of the Open Computing Language (OpenCL) framework instead of the Compute Unified Device Architecture (CUDA), the implementation of the most popular boundary conditions, the easy customization of the code to different problems, the extensibility with regard to Python scripts, and the runtime output which allows the tracking of simulations in real time, or a higher frequency in saving some results without a significant performance lost. These modifications are shown to improve the solver speed, the results quality, and allow for a wider areas of application. AQUAgpusph has been designed trying to provide researchers and engineers with a valuable tool to test and apply the SPH method. Three practical applications are discussed in detail. The evolution of a dam break is used to quantify and compare the computational performance and modeling accuracy with the most popular SPH Graphics Processing Unit (GPU) accelerated alternatives. The dynamics of a coupled system, a Tuned Liquid Damper (TLD), is discussed in order to show the integration capabilities of the solver with external dynamics. Finally, the sloshing flow inside a nuclear reactor is simulated in order to show the capabilities of the solver to treat 3-D problems with complex geometries and of industrial interest.

  4. An asynchronous solver for systems of ODEs linked by a directed tree structure

    Small, Scott J.; Jay, Laurent O.; Mantilla, Ricardo; Curtu, Rodica; Cunha, Luciana K.; Fonley, Morgan; Krajewski, Witold F.


    This paper documents our development and evaluation of a numerical solver for systems of sparsely linked ordinary differential equations in which the connectivity between equations is determined by a directed tree. These types of systems arise in distributed hydrological models. The numerical solver is based on dense output Runge-Kutta methods that allow for asynchronous integration. A partition of the system is used to distribute the workload among different processes, enabling a parallel implementation that capitalizes on a distributed memory system. Communication between processes is performed asynchronously. We illustrate the solver capabilities by integrating flow transport equations for a ˜17,000 km2 river basin subdivided into 305,000 sub-watersheds that are interconnected by the river network. Numerical experiments for a few models are performed and the runtimes and scalability on our parallel computer are presented. Efficient numerical integrators such as the one demonstrated here bring closer to reality the goal of implementing fully distributed real-time flood forecasting systems supported by physics based hydrological models and high-quality/high-resolution rainfall products.

  5. A comparison of SuperLU solvers on the intel MIC architecture

    Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.


    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.

  6. Multiscale Universal Interface: A Concurrent Framework for Coupling Heterogeneous Solvers

    Tang, Yu-Hang; Bian, Xin; Li, Zhen; Karniadakis, George E


    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 c...

  7. Integrating Problem Solvers from Analogous Markets in New Product Ideation

    Franke, Nikolaus; Poetz, Marion; Schreier, Martin


    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...... that including problem solvers from analogous markets versus the target market accounts for almost two-thirds of the well-known effect of involving lead users instead of average problem solvers. This effect is further amplified when the analogous distance between the markets increases, i.e., when searching...... 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...

  8. Hybrid Riemann Solvers for Large Systems of Conservation Laws

    Schmidtmann, Birte; Torrilhon, Manuel


    In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid computing the characteristic decomposition of the flux Jacobian. Instead, they require only an estimate of the globally fastest wave speeds in both directions. Thus, this family of solvers is particularly efficient for large systems of conservation laws, i.e. with many different propagation speeds, and when no explicit expression for the eigensystem is available. Even though only fastest wave speeds are needed as input values, the new family of Riemann solvers reproduces all waves with less dissipation than HLL, which has the same prerequisites, requiring only one additional flux evaluation.

  9. Parallel iterative solvers and preconditioners using approximate hierarchical methods

    Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)


    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.

  10. A Python interface to Diffpack-based classes and solvers

    Munthe-Kaas, Heidi Vikki


    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...

  11. An Interactive Chemical Equilibrium Solver for the Personal Computer

    Negus, Charles H.


    AN INTERACTIVE CHEMICAL EQUILIBRIUM SOLVER FOR THE PERSONAL COMPUTER Charles Hugh Negus Felix J. Pierce, Chairman Mechanical Engineering The Virginia Tech Equilibrium Chemistry (VTEC) code is a keyboard interactive, user friendly, chemical equilibrium solver for use on a personal computer. The code is particularly suitable for a teaching / learning environment. For a set of reactants at a defined thermodynamic state given by a user, the program will select all species...

  12. An Immersed Boundary Method for Complex Flow and Heat Transfer

    Paravento, F.; Pourquie, M.J.; Boersma, B.J.


    The need to predict flow and heat transfer problems requires a flexible and fast tool able to simulate complex geometries without increasing the complexity of the flow solver architecture. Here we use a finite volume code that uses a direct solver with pressure correction. A new immersed boundary me

  13. A Course in Transport Phenomena in Multicomponent, Multiphase, Reacting Systems.

    Carbonell, R. G.; Whitaker, S.


    This course concentrates on a rigorous development of the multicomponent transport equations, boundary conditions at phase interfaces, and volume-averaged transport equations for multiphase reacting systems. (BB)

  14. A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

    Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo


    The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

  15. A Comparison of Stiff ODE Solvers for Astrochemical Kinetics Problems

    Nejad, Lida A. M.


    The time dependent chemical rate equations arising from astrochemical kinetics problems are described by a system of stiff ordinary differential equations (ODEs). In this paper, using three astrochemical models of varying physical and computational complexity, and hence different degrees of stiffness, we present a comprehensive performance survey of a set of well-established ODE solver packages from the ODEPACK collection, namely LSODE, LSODES, VODE and VODPK. For completeness, we include results from the GEAR package in one of the test models. The results demonstrate that significant performance improvements can be obtained over GEAR which is still being used by many astrochemists by default. We show that a simple appropriate ordering of the species set results in a substantial improvement in the performance of the tested ODE solvers. The sparsity of the associated Jacobian matrix can be exploited and results using the sparse direct solver routine LSODES show an extensive reduction in CPU time without any loss in accuracy. We compare the performance and the computed abundances of one model with a 175 species set and a reduced set of 88 species, keeping all physical and chemical parameters identical with both sets.We found that the calculated abundances using two different size models agree quite well. However, with no extra computational effort and more reliable results, it is possible for the computation to be many times faster with the larger species set than the reduced set, depending on the use of solvers, the ordering and the chosen options. It is also shown that though a particular solver with certain chosen parameters may have severe difficulty or even fail to complete a run over the required integration time, another solver can easily complete the run with a wider range of control parameters and options. As a result of the superior performance of LSODES for the solution of astrochemical kinetics systems, we have tailor-made a sparse version of the VODE

  16. Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

    Ma Yanfeng; He Erming; Zeng Xianang; Li Junjie


    An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL) in a ‘‘semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the compu-tational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD) Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are signif-icant for these cases and the further data analysis confirms the validity and practicability of the cou-pled method.

  17. Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

    Ma Yanfeng


    Full Text Available An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.

  18. A Framework for the Modelling of Biphasic Reacting Systems

    Anantpinijwatna, Amata; Sin, Gürkan; O’Connell, John P.


    Biphasic reacting systems have a broad application range from organic reactions in pharmaceutical and agro-bio industries to CO 2 capture. However, mathematical modelling of biphasic reacting systems is a formidable challenge due to many phenomena underlying the process such as chemical equilibri...... systems: a PTC-based reaction system and pseudo-PTC system....

  19. Euler/Navier-Stokes Solvers Applied to Ducted Fan Configurations

    Keith, Theo G., Jr.; Srivastava, Rakesh


    Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.

  20. Albany/FELIX: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

    I. Kalashnikova


    Full Text Available This paper describes a new parallel, scalable and robust finite-element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and Template-Based Generic Programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using: (1 new test cases derived using the method of manufactured solutions, and (2 canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution is then studied on problems involving a realistic Greenland ice sheet geometry discretized using structured and unstructured meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

  1. Acceleration of the OpenFOAM-based MHD solver using graphics processing units

    He, Qingyun; Chen, Hongli, E-mail:; Feng, Jingchao


    Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.

  2. The novel high-performance 3-D MT inverse solver

    Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey


    We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.

  3. Viscous flow modelling using unstructured meshes for aeronautical applications

    Szmelter, J.; Pagano, A.

    The novel application of viscous coupling to unstructured meshes has been proposed and developed. The method allows fro viscous flows modelling and avoids the difficulty of generating highly stretched tetrahedral in 3D or triangular in 2D elements required for Navier-Stokes solvers. The time step allowed by the explicit euler solver is limited by the size of the "Euler" mesh, resulting in faster algorithms than standard explicit Navier-Stokes solvers.

  4. Numerical comparison of Riemann solvers for astrophysical hydrodynamics

    Klingenberg, Christian; Waagan, Knut


    The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.

  5. Constraint solvers: An empirical evaluation of design decisions

    Kotthoff, Lars


    This paper presents an evaluation of the design decisions made in four state-of-the-art constraint solvers; Choco, ECLiPSe, Gecode, and Minion. To assess the impact of design decisions, instances of the five problem classes n-Queens, Golomb Ruler, Magic Square, Social Golfers, and Balanced Incomplete Block Design are modelled and solved with each solver. The results of the experiments are not meant to give an indication of the performance of a solver, but rather investigate what influence the choice of algorithms and data structures has. The analysis of the impact of the design decisions focuses on the different ways of memory management, behaviour with increasing problem size, and specialised algorithms for specific types of variables. It also briefly considers other, less significant decisions.

  6. An adaptive fast multipole accelerated Poisson solver for complex geometries

    Askham, T.; Cerfon, A. J.


    We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient ;black box; fast solver.

  7. Dry deposition model for a microscale aerosol dispersion solver based on the moment method

    Šíp, Viktor


    A dry deposition model suitable for use in the moment method has been developed. Contributions from five main processes driving the deposition - Brownian diffusion, interception, impaction, turbulent impaction, and sedimentation - are included in the model. The deposition model was employed in the moment method solver implemented in the OpenFOAM framework. Applicability of the developed expression and the moment method solver was tested on two example problems of particle dispersion in the presence of a vegetation on small scales: a flow through a tree patch in 2D and a flow through a hedgerow in 3D. Comparison with the sectional method showed that the moment method using the developed deposition model is able to reproduce the shape of the particle size distribution well. The relative difference in terms of the third moment of the distribution was below 10\\% in both tested cases, and decreased away from the vegetation. Main source of this difference is a known overprediction of the impaction efficiency. When ...

  8. Decomposition During Search for Propagation-Based Constraint Solvers

    Mann, Martin; Will, Sebastian


    We describe decomposition during search (DDS), an integration of and/or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into independent partial problems, avoiding redundant work. The paper discusses how DDS interacts with key features that make propagation-based solvers successful: constraint propagation, especially for global constraints, and dynamic search heuristics. We have implemented DDS for the Gecode constraint programming library. Two applications, solution counting in graph coloring and protein structure prediction, exemplify the benefits of DDS in practice.

  9. LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators

    Gonzalez, Juan; Nunez, Rafael C, E-mail: [Accelogic, 1830 Main Street, Suite 204, Weston, FL (United States)


    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.

  10. Efficient use of iterative solvers in nested topology optimization

    Amir, Oded; Stolpe, Mathias; Sigmund, Ole


    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the analysis problem, generated by a Krylov...... subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence measures...

  11. An Easy Method To Accelerate An Iterative Algebraic Equation Solver

    Yao, Jin [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)


    This article proposes to add a simple term to an iterative algebraic equation solver with an order n convergence rate, and to raise the order of convergence to (2n - 1). In particular, a simple algebraic equation solver with the 5th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an low overhead cost of function evaluation that can be ignored as the size of the system increases.

  12. Numerical System Solver Developed for the National Cycle Program

    Binder, Michael P.


    As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

  13. Diamond tool machining of materials which react with diamond

    Lundin, Ralph L.; Stewart, Delbert D.; Evans, Christopher J.


    Apparatus for the diamond machining of materials which detrimentally react with diamond cutting tools in which the cutting tool and the workpiece are chilled to very low temperatures. This chilling halts or retards the chemical reaction between the workpiece and the diamond cutting tool so that wear rates of the diamond tool on previously detrimental materials are comparable with the diamond turning of materials which do not react with diamond.

  14. Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

    Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.


    Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have

  15. Multilevel techniques lead to accurate numerical upscaling and scalable robust solvers for reservoir simulation

    Christensen, Max la Cour; Villa, Umberto; Vassilevski, Panayot


    This paper demonstrates an application of element-based Algebraic Multigrid (AMGe) technique developed at LLNL (19) to the numerical upscaling and preconditioning of subsurface porous media flow problems. The upscaling results presented here are further extension of our recent work in 3. The AMGe...... be used both as an upscaling tool and as a robust and scalable solver. The methods employed in the present paper have provable O(N) scaling and are particularly well suited for modern multicore architectures, because the construction of the coarse spaces by solving many small local problems offers a high...... level of concurrency in the computations. Numerical experiments demonstrate the accuracy of using AMGe as an upscaling tool and comparisons are made to more traditional flow-based upscaling techniques. The efficient solution of both the original and upscaled problem is also addressed, and a specialized...

  16. of Transient Flows in Turbomachines

    Alexander Wiedermann


    Full Text Available This paper focuses on development and validation of a viscous solver for the computation of unsteady flows in turbomachinery blade rows and stages consisting of rotors and stators. The code has been evolved from steady-state single flow solvers developed by Wiedermann based on time-marching finite difference schemes. A two-equation eddy viscosity model is applied, and the wall boundary conditions are determined by the y+-distance of the first grid line away from the wall. For the solution of transient flow fields the original time-stepping algorithm is replaced by a time-accurate scheme.

  17. Parallel time domain solvers for electrically large transient scattering problems

    Liu, Yang


    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.

  18. Implementing parallel elliptic solver on a Beowulf cluster

    Marcin Paprzycki


    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.

  19. Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

    Mairing, Jackson Pasini


    Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

  20. Time-varying Riemann solvers for conservation laws on networks

    Garavello, Mauro; Piccoli, Benedetto

    We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.

  1. A new fast direct solver for the boundary element method

    Huang, S.; Liu, Y. J.


    A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.

  2. Implementing parallel elliptic solver on a Beowulf cluster

    Marcin Paprzycki; Svetozara Petrova; Julian Sanchez


    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.

  3. A vectorizable adaptive grid solver for PDEs in 3D

    Blom, J.G.; Verwer, J.G.


    This paper describes the application of an adaptive-grid finite-difference solver to some time-dependent three-dimensional systems of partial differential equations. The code is a 3D extension of the 2D code VLUGR2[3].

  4. Using a satisfiability solver to identify deterministic finite state automata

    Heule, M.J.H.; Verwer, S.


    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 p

  5. Parallel Solver for H(div) Problems Using Hybridization and AMG

    Lee, Chak S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)


    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.

  6. A Subluminal Relativistic Magnetohydrodynamics Scheme with ADER-WENO Predictor and Multidimensional Riemann Solver-Based Corrector

    Balsara, Dinshaw S


    The relativistic magnetohydrodynamics (RMHD) set of equations has recently seen increased use in astrophysical computations. Even so, RMHD codes remain fragile. The reconstruction can sometimes yield superluminal velocities in certain parts of the mesh. In this paper we present a reconstruction strategy that overcomes this problem by making a single conservative to primitive transformation per cell followed by higher order WENO reconstruction on a carefully chosen set of primitives that guarantee subluminal reconstruction of the flow variables. For temporal evolution via a predictor step we also present second, third and fourth order accurate ADER methods that keep the velocity subluminal during the predictor step. The RMHD system also requires the magnetic field to be evolved in a divergence-free fashion. In the treatment of classical numerical MHD the analogous issue has seen much recent progress with the advent of multidimensional Riemann solvers. By developing multidimensional Riemann solvers for RMHD, we...

  7. Reacting gas mixtures in the state-to-state approach: The chemical reaction rates

    Kustova, Elena V. [Department of Mathematics and Mechanics, Saint Petersburg State University, 198504 Universitetskiy pr., 28, Saint Petersburg (Russian Federation); Kremer, Gilberto M. [Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-980 Curitiba (Brazil)


    In this work chemically reacting mixtures of viscous flows are analyzed within the framework of Boltzmann equation. By applying a modified Chapman-Enskog method to the system of Boltzmann equations general expressions for the rates of chemical reactions and vibrational energy transitions are determined as functions of two thermodynamic forces: the velocity divergence and the affinity. As an application chemically reacting mixtures of N{sub 2} across a shock wave are studied, where the first lowest vibrational states are taken into account. Here we consider only the contributions from the first four single quantum vibrational-translational energy transitions. It is shown that the contribution to the chemical reaction rate related to the affinity is much larger than that of the velocity divergence.

  8. Reacting gas mixtures in the state-to-state approach: The chemical reaction rates

    Kustova, Elena V.; Kremer, Gilberto M.


    In this work chemically reacting mixtures of viscous flows are analyzed within the framework of Boltzmann equation. By applying a modified Chapman-Enskog method to the system of Boltzmann equations general expressions for the rates of chemical reactions and vibrational energy transitions are determined as functions of two thermodynamic forces: the velocity divergence and the affinity. As an application chemically reacting mixtures of N2 across a shock wave are studied, where the first lowest vibrational states are taken into account. Here we consider only the contributions from the first four single quantum vibrational-translational energy transitions. It is shown that the contribution to the chemical reaction rate related to the affinity is much larger than that of the velocity divergence.

  9. A High Performance QDWH-SVD Solver using Hardware Accelerators

    Sukkari, Dalal E.


    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.

  10. Advances in three-dimensional geoelectric forward solver techniques

    Blome, M.; Maurer, H. R.; Schmidt, K.


    Modern geoelectrical data acquisition systems allow large amounts of data to be collected in a short time. Inversions of such data sets require powerful forward solvers for predicting the electrical potentials. State-of-the-art solvers are typically based on finite elements. Recent developments in numerical mathematics led to direct matrix solvers that allow the equation systems arising from such finite element problems to be solved very efficiently. They are particularly useful for 3-D geoelectrical problems, where many electrodes are involved. Although modern direct matrix solvers include optimized memory saving strategies, their application to realistic, large-scale 3-D problems is still somewhat limited. Therefore, we present two novel techniques that allow the number of gridpoints to be reduced considerably, while maintaining a high solution accuracy. In the areas surrounding an electrode array we attach infinite elements that continue the electrical potentials to infinity. This does not only reduce the number of gridpoints, but also avoids the artificial Dirichlet or mixed boundary conditions that are well known to be the cause of numerical inaccuracies. Our second development concerns the singularity removal in the presence of significant surface topography. We employ a fast multipole boundary element method for computing the singular potentials. This renders unnecessary mesh refinements near the electrodes, which results in substantial savings of gridpoints of up to more than 50 per cent. By means of extensive numerical tests we demonstrate that combined application of infinite elements and singularity removal allows the number of gridpoints to be reduced by a factor of ~6-10 compared with traditional finite element methods. This will be key for applying finite elements and direct matrix solver techniques to realistic 3-D inversion problems.

  11. Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers

    Bjorner, Nikolaj


    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

  12. Migration of vectorized iterative solvers to distributed memory architectures

    Pommerell, C. [AT& T Bell Labs., Murray Hill, NJ (United States); Ruehl, R. [CSCS-ETH, Manno (Switzerland)


    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.

  13. A fast Laplace solver approach to pore scale permeability

    Arns, Christoph; Adler, Pierre


    The permeability of a porous medium can be derived by solving the Stokes equations in the pore space with no slip at the walls. The resulting velocity averaged over the pore volume yields the permeability KS by application of the Darcy law. The Stokes equations can be solved by a number of different techniques such as finite differences, finite volume, Lattice Boltzmann, but whatever the technique it remains a heavy task since there are four unknowns at each node (the three velocity components and the pressure) which necessitate the solution of four equations (the projection of Newton's law on each axis and mass conservation). By comparison, the Laplace equation is scalar with a single unknown at each node. The objective of this work is to replace the Stokes equations by an elliptical equation with a space dependent permeability. More precisely, the local permeability k is supposed to be proportional to (r-alpha)**2 where r is the distance of the voxel to the closest wall, and alpha a constant; k is zero in the solid phase. The elliptical equation is div(k gradp)=0. A macroscopic pressure gradient is assumed to be exerted on the medium and again the resulting velocity averaged over space yields a permeability K_L. In order to validate this method, systematic calculations have been performed. First, elementary shapes (plane channel, circular pipe, rectangular channels) were studied for which flow occurs along parallel lines in which case KL is the arithmetic average of the k's. KL was calculated for various discretizations of the pore space and various values of alpha. For alpha=0.5, the agreement with the exact analytical value of KS is excellent for the plane and rectangular channels while it is only approximate for circular pipes. Second, the permeability KL of channels with sinusoidal walls was calculated and compared with analytical results and numerical ones provided by a Lattice Boltzmann algorithm. Generally speaking, the discrepancy does not exceed 25% when

  14. Mechanism for Self-Reacted Friction Stir Welding

    Venable, Richard; Bucher, Joseph


    A mechanism has been designed to apply the loads (the stirring and the resection forces and torques) in self-reacted friction stir welding. This mechanism differs somewhat from mechanisms used in conventional friction stir welding, as described below. The tooling needed to apply the large reaction loads in conventional friction stir welding can be complex. Self-reacted friction stir welding has become popular in the solid-state welding community as a means of reducing the complexity of tooling and to reduce costs. The main problems inherent in self-reacted friction stir welding originate in the high stresses encountered by the pin-and-shoulder assembly that produces the weld. The design of the present mechanism solves the problems. The mechanism includes a redesigned pin-and-shoulder assembly. The welding torque is transmitted into the welding pin by a square pin that fits into a square bushing with set-screws. The opposite or back shoulder is held in place by a Woodruff key and high-strength nut on a threaded shaft. The Woodruff key reacts the torque, while the nut reacts the tensile load on the shaft.

  15. ASTROP2-LE: A Mistuned Aeroelastic Analysis System Based on a Two Dimensional Linearized Euler Solver

    Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral


    An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.

  16. Validation Process for LEWICE by Use of a Navier-Stokes Solver

    Wright, William B.; Porter, Christopher E.


    A research project is underway at NASA Glenn to produce computer software that can accurately predict ice growth under any meteorological conditions for any aircraft surface. This report will present results from the latest LEWICE release, version 3.5. This program differs from previous releases in its ability to model mixed phase and ice crystal conditions such as those encountered inside an engine. It also has expanded capability to use structured grids and a new capability to use results from unstructured grid flow solvers. A quantitative comparison of the results against a database of ice shapes that have been generated in the NASA Glenn Icing Research Tunnel (IRT) has also been performed. This paper will extend the comparison of ice shapes between LEWICE 3.5 and experimental data from a previous paper. Comparisons of lift and drag are made between experimentally collected data from experimentally obtained ice shapes and simulated (CFD) data on simulated (LEWICE) ice shapes. Comparisons are also made between experimentally collected and simulated performance data on select experimental ice shapes to ensure the CFD solver, FUN3D, is valid within the flight regime. The results show that the predicted results are within the accuracy limits of the experimental data for the majority of cases.

  17. Parallelization of pressure equation solver for incompressible N-S equations

    Ichihara, Kiyoshi; Yokokawa, Mitsuo; Kaburaki, Hideo


    A pressure equation solver in a code for 3-dimensional incompressible flow analysis has been parallelized by using red-black SOR method and PCG method on Fujitsu VPP500, a vector parallel computer with distributed memory. For the comparison of scalability, the solver using the red-black SOR method has been also parallelized on the Intel Paragon, a scalar parallel computer with a distributed memory. The scalability of the red-black SOR method on both VPP500 and Paragon was lost, when number of processor elements was increased. The reason of non-scalability on both systems is increasing communication time between processor elements. In addition, the parallelization by DO-loop division makes the vectorizing efficiency lower on VPP500. For an effective implementation on VPP500, a large scale problem which holds very long vectorized DO-loops in the parallel program should be solved. PCG method with red-black SOR method applied to incomplete LU factorization (red-black PCG) has more iteration steps than normal PCG method with forward and backward substitution, in spite of same number of the floating point operations in a DO-loop of incomplete LU factorization. The parallelized red-black PCG method has less merits than the parallelized red-black SOR method when the computational region has fewer grids, because the low vectorization efficiency is obtained in red-black PCG method. (author).

  18. Atmospheric circulation of tidally-locked exoplanets: a suite of benchmark tests for dynamical solvers

    Heng, Kevin; Phillipps, Peter J


    The complexity of atmospheric modelling and its inherent non-linearity, together with the limited amount of data of exoplanets available, motivate model intercomparisons and benchmark tests. In the geophysical community, the Held-Suarez test is a standard benchmark for comparing dynamical core simulations of the Earth's atmosphere with different solvers, based on statistically-averaged flow quantities. In the present study, we perform analogues of the Held-Suarez test for tidally-locked exoplanets with the GFDL-Princeton Flexible Modeling System (FMS) by subjecting both the spectral and finite difference dynamical cores to a suite of tests, including the standard benchmark for Earth, a hypothetical tidally-locked Earth, a "shallow" hot Jupiter model and a "deep" model of HD 209458b. We find qualitative and quantitative agreement between the solvers for the Earth, tidally-locked Earth and shallow hot Jupiter benchmarks, but the agreement is less than satisfactory for the deep model of HD 209458b. Further inves...

  19. REACT: Resettable Hold Down and Release Actuator for Space Applications

    Nava, Nestor; Collado, Marcelo; Cabás, Ramiro


    A new HDRA based on SMA technology, called REACT, has been designed for development of loads and appendixes in space applications. This design involves a rod supported by spheres that block its axial movement during a preload application. The rod shape allows misalignment and blocks the rotation around axial axis for a proper installation of the device. Because of the high preload requirements for this type of actuators, finite element analysis (FEA) has been developed in order to check the structure resistance. The results of the FEA have constrained the REACT design, in terms of dimensions, materials, and shape of the mechanical parts. A complete test campaign for qualification of REACT is proposed. Several qualification models are intended to be built for testing in parallel. Therefore, it is a way to demonstrate margins which allows getting some statistics.

  20. A solution algorithm for fluid-particle flows across all flow regimes

    Kong, Bo; Fox, Rodney O.


    Many fluid-particle flows occurring in nature and in technological applications exhibit large variations in the local particle volume fraction. For example, in circulating fluidized beds there are regions where the particles are close-packed as well as very dilute regions where particle-particle collisions are rare. Thus, in order to simulate such fluid-particle systems, it is necessary to design a flow solver that can accurately treat all flow regimes occurring simultaneously in the same flow domain. In this work, a solution algorithm is proposed for this purpose. The algorithm is based on splitting the free-transport flux solver dynamically and locally in the flow. In close-packed to moderately dense regions, a hydrodynamic solver is employed, while in dilute to very dilute regions a kinetic-based finite-volume solver is used in conjunction with quadrature-based moment methods. To illustrate the accuracy and robustness of the proposed solution algorithm, it is implemented in OpenFOAM for particle velocity moments up to second order, and applied to simulate gravity-driven, gas-particle flows exhibiting cluster-induced turbulence. By varying the average particle volume fraction in the flow domain, it is demonstrated that the flow solver can handle seamlessly all flow regimes present in fluid-particle flows.

  1. An exact solver for the DCJ median problem.

    Zhang, Meng; Arndt, William; Tang, Jijun


    The "double-cut-and-join" (DCJ) model of genome rearrangement proposed by Yancopoulos et al. uses the single DCJ operation to account for all genome rearrangement events. Given three signed permutations, the DCJ median problem is to find a fourth permutation that minimizes the sum of the pairwise DCJ distances between it and the three others. In this paper, we present a branch-and-bound method that provides accurate solution to the multichromosomal DCJ median problems. We conduct extensive simulations and the results show that the DCJ median solver performs better than other median solvers for most of the test cases. These experiments also suggest that DCJ model is more suitable for real datasets where both reversals and transpositions occur.

  2. On improving linear solver performance: a block variant of GMRES

    Baker, A H; Dennis, J M; Jessup, E R


    The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.

  3. LDRD report : parallel repartitioning for optimal solver performance.

    Heaphy, Robert; Devine, Karen Dragon; Preis, Robert (University of Paderborn, Paderborn, Germany); Hendrickson, Bruce Alan; Heroux, Michael Allen; Boman, Erik Gunnar


    We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.

  4. Parallel Auxiliary Space AMG Solver for $H(div)$ Problems

    Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)


    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.

  5. HLL Riemann Solvers and Alfven Waves in Black Hole Magnetospheres

    Punsly, Brian; Kim, Jinho; Garain, Sudip


    In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. However, numerical simulations of black hole magnetospheres are often based on 1-D HLL Riemann solvers that readily dissipate Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, it is unclear how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. The HLL Riemann solver is also notorious for producing large recurring...

  6. Scalable Out-of-Core Solvers on Xeon Phi Cluster

    D' Azevedo, Ed F [ORNL; Chan, Ki Shing [Chinese University of Hong Kong (CUHK); Su, Shiquan [Center for Computational Materials Science; Wong, Kwai [ORNL


    This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.

  7. Benchmarking ICRF Full-wave Solvers for ITER

    R. V. Budny, L. Berry, R. Bilato, P. Bonoli, M. Brambilla, R. J. Dumont, A. Fukuyama, R. Harvey, E. F. Jaeger, K. Indireshkumar, E. Lerche, D. McCune, C. K. Phillips, V. Vdovin, J. Wright, and members of the ITPA-IOS


    Abstract 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.

  8. Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries

    Phillip, B.


    Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.

  9. Brittle Solvers: Lessons and insights into effective solvers for visco-plasticity in geodynamics

    Spiegelman, M. W.; May, D.; Wilson, C. R.


    Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear solvers. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to

  10. Parallel Nonnegative Least Squares Solvers for Model Order Reduction


    not for the PQN method. For the latter method the size of the active set is controlled to promote sparse solutions. This is described in Section 3.2.1...or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington...21005-5066 primary author’s email: <>. Parallel nonnegative least squares (NNLS) solvers are developed specifically for

  11. Surviving Solver Sensitivity: An ASP Practitioner’s Guide

    Silverthorn, Bryan; Lierler, Yuliya; Schneider, Marius


    Answer set programming (ASP) is a declarative programming formalism that allows a practitioner to specify a problem without describing an algorithm for solving it. In ASP, the tools for processing problem specifications are called answer set solvers. Because specified problems are often NP complete, these systems often require significant computational effort to succeed. Furthermore, they offer different heuristics, expose numerous parameters, and their running time is sensitive to the config...

  12. Direct linear programming solver in C for structural applications

    Damkilde, L.; Hoyer, O.; Krenk, S.


    An optimization problem can be characterized by an object-function, which is maximized, and restrictions, which limit the variation of the variables. A subclass of optimization is Linear Programming (LP), where both the object-function and the restrictions are linear functions of the variables. The traditional solution methods for LP problems are based on the simplex method, and it is customary to allow only non-negative variables. Compared to other optimization routines the LP solvers are more robust and the optimum is reached in a finite number of steps and is not sensitive to the starting point. For structural applications many optimization problems can be linearized and solved by LP routines. However, the structural variables are not always non-negative, and this requires a reformation, where a variable x is substituted by the difference of two non-negative variables, x(sup + ) and x(sup - ). The transformation causes a doubling of the number of variables, and in a computer implementation the memory allocation doubles and for a typical problem the execution time at least doubles. This paper describes a LP solver written in C, which can handle a combination of non-negative variables and unlimited variables. The LP solver also allows restart, and this may reduce the computational costs if the solution to a similar LP problem is known a priori. The algorithm is based on the simplex method, and differs only in the logical choices. Application of the new LP solver will at the same time give both a more direct problem formulation and a more efficient program.

  13. Resolving Neighbourhood Relations in a Parallel Fluid Dynamic Solver

    Frisch, Jerome


    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.

  14. A chemical reaction network solver for the astrophysics code NIRVANA

    Ziegler, U.


    Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes

  15. A contribution to the great Riemann solver debate

    Quirk, James J.


    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.



    Based on constructing programmed constraint and constraint perturbation equation, a kinematics and dynamics numerical simulation model is established for virtual mechanism, in which the difference scheme guarantee precision in simulation procedure and its numerical solutions satisfy programmed manifold stability. A crank-piston mechanism in a car engine, a steering mechanism and a suspension mechanism are simulated in a virtual environment, then comparing the simulation results with those obtained in ADAMS under the same circumstances proved the solver valid.

  17. Modeling and design of reacting systems with phase transfer catalysis

    Piccolo, Chiara; Hodges, George; Piccione, Patrick M.;


    , some of the design issues related to improved reaction operation are analyzed. Since the solubility of the different forms of the PTC in the organic solvent affects ultimately the catalyst partition coefficients, therefore, the organic solvent plays an important role in the design of PTC-based reacting...

  18. Termite Proteins Cross-React with Cockroach Allergens

    Shrimp are among a group of 8 foods that commonly cause food allergy, and shrimp allergens have been demonstrated to cross-react with arthropod proteins, such as those from cockroaches. Edible insects are beginning to be popularized as an alternate source of protein and have a high nutrition value....

  19. Moment estimation for chemically reacting systems by extended Kalman filtering

    Ruess, J; Milias-Argeitis, A; Summers, S; Lygeros, J


    In stochastic models of chemically reacting systems that contain bimolecular reactions, the dynamics of the moments of order up to n of the species populations do not form a closed system, in the sense that their time-derivatives depend on moments of order n + 1. To close the dynamics, the moments o

  20. Direct solvers performance on h-adapted grids

    Paszynski, Maciej


    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.


    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)


    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.

  2. QED multi-dimensional vacuum polarization finite-difference solver

    Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo


    The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

  3. NITSOL: A Newton iterative solver for nonlinear systems

    Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)


    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.

  4. Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

    Pavarino, L.F.


    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.

  5. A Discontinuous Galerkin Chimera Overset Solver

    Galbraith, Marshall Christopher

    This work summarizes the development of an accurate, efficient, and flexible Computational Fluid Dynamics computer code that is an improvement relative to the state of the art. The improved accuracy and efficiency is obtained by using a high-order discontinuous Galerkin (DG) discretization scheme. In order to maximize the computational efficiency, quadrature-free integration and numerical integration optimized as matrix-vector multiplications is employed and implemented through a pre-processor (PyDG). Using the PyDG pre-processor, a C++ polynomial library has been developed that uses overloaded operators to design an efficient Domain Specific Language (DSL) that allows expressions involving polynomials to be written as if they are scalars. The DSL, which makes the syntax of computer code legible and intuitive, promotes maintainability of the software and simplifies the development of additional capabilities. The flexibility of the code is achieved by combining the DG scheme with the Chimera overset method. The Chimera overset method produces solutions on a set of overlapping grids that communicate through an exchange of data on grid boundaries (known as artificial boundaries). Finite volume and finite difference discretizations use fringe points, which are layers of points on the artificial boundaries, to maintain the interior stencil on artificial boundaries. The fringe points receive solution values interpolated from overset grids. Proper interpolation requires fringe points to be contained in overset grids. Insufficient overlap must be corrected by modifying the grid system. The Chimera scheme can also exclude regions of grids that lie outside the computational domain; a process commonly known as hole cutting. The Chimera overset method has traditionally enabled the use of high-order finite difference and finite volume approaches such as WENO and compact differencing schemes, which require structured meshes, for modeling fluid flow associated with complex

  6. Application of a hybrid kinetic-continuum solver to the near wall modelling

    Rovenskaya, O.; Croce, G.


    A hybrid method dynamically coupling the direct numerical solution of the S-model kinetic equation and Navier-Stokes equations is applied to a numerical simulation of the flow through the channel of a finite length due to arbitrarily pressure ratios and for a wide range of Knudsen number. The decomposition of the physical domain into kinetic and hydrodynamic sub-domains is updated at each time step. The solution is advanced in time simultaneously in both kinetic and hydrodynamic domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy and mass through the interface. Solver efficiency is increased via MPI (Message Passing Interface) parallelization. Accuracy and reliability of the method, for different decomposition criteria, are assessed via comparison with a pure kinetic solution.

  7. Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver (Journal Version)

    Livne, Oren E


    Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the symmetric linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. It is robust and requires no fine tuning. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and a novel energy correction of the coarse-level systems. This results ...

  8. Three-dimensional turbine blade design using a Navier-Stokes solver and Artificial Neural Network

    Pierret, S.; Braembussche, R.A. van den [Von Karman Institute, Rhode-Saint-Genese (Belgium)


    Improving turbine efficiency by applying non-radial stacking and three-dimensional design techniques has received considerable attention in the recent years. A big source of losses is the spanwise non-uniformity of the next stage inlet flow angle resulting form the non-uniformity of the outlet flow angle of the preceding blade row. This non-uniformity can be reduced by adjusting the 2D sections along the span and/or by leaning the blades. The present method describes the design of a 3D blade geometry built by a radial stacking of several 2D blade sections which are provided by a 2D design system. A 3D Navier-Stokes solver is used to check the blade performance and to update the requirements imposed for the next design of the 2D blade sections. The 2D sections are designed using an Artificial Neural Network (ANN). The latter one constructs an approximate model (response surface) using a database containing the 2D Navier-Stokes solutions obtained from previous designs. It is used for the optimisation of the 2D blade geometry by means of Simulated Annealing (SA). The optimum 2D geometry is then verified by a 2D Navier-Stokes solver. This procedure results in a considerable speed-up of the design process by reducing both the interventions of the operator and the computational effort. It also allows the design of more efficient blades, satisfying both the aerodynamic and mechanical constraints. The method has been used to design different types of turbine blades of which one example will be presented. (Author)

  9. An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR

    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)


    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 L2 norm.

  10. Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities

    Paszyńska, Anna


    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.

  11. Direct Numerical Simulation of a Compressible Reacting Boundary Layer using a Temporal Slow Growth Homogenization

    Topalian, Victor; Oliver, Todd; Ulerich, Rhys; Moser, Robert


    A DNS of a compressible, reacting boundary layer flow at Reθ ~ 430 was performed using a temporal slow-growth homogenization, for a multispecies flow model of air at supersonic regime. The overall scenario parameters are related to those of the flow over an ablating surface of a space capsule upon Earth's atmospheric re-entry. The simulation algorithm features Fourier spatial discretization in the streamwise and spanwise directions, B-splines in the wall normal direction, and is marched semi-implicitly in time using the SMR91 scheme. Flow statistics will be presented for relevant flow quantities, in particular those related with RANS modeling. Since analogous slow growth computations can be performed using RANS to predict the flow mean profiles, the use of data gathered from this type of simulation as a vehicle for the calibration and uncertainty quantification of RANS models will be discussed. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].

  12. Experimental investigation of a reacting transverse jet in a high pressure oscillating vitiated crossflow

    Fugger, Christopher A.

    Staged combustion is one design approach in a gas turbine engine to reduce pollutant emission levels. In axially staged combustion, portions of the air and fuel are injected downstream of a lean premixed low NOx primary combustion zone. The gas residence time at elevated temperatures is decreased resulting in lower thermal NOx, and the reduced oxygen and high temperature vitiated primary zone flow further help to reduce pollutant emissions and quickly complete combustion. One implementation of axially staged combustion is transverse fuel jet injection. An important consideration for staged combustion systems, though, is how the primary and secondary combustion zones can couple through the acoustic resonances of the chamber. These couplings can lead to additional source terms that pump energy into the resonant acoustic field and help sustain the high-amplitude combustor pressure oscillations. An understanding of these couplings is important so that it may be possible to design a secondary combustion system that provides inherent damping to the combustor system. To systematically characterize the coupling of a reacting jet in unsteady crossflow in detail, the effects of an an unsteady pressure flowfield and an unsteady velocity flowfield are separately investigated. An optically accessible resonant combustion chamber was designed and built as part of this work to generate a standing wave unsteady vitiated crossflow at a chamber pressure of 0.9 MPa. The location of transverse jet injection corresponds to one of two locations, where one location is the pressure node and the other location the pressure anti-node of the resonant chamber acoustic mode. The injection location is optically accessible, and the dynamic interactions between the transverse jet flow and the 1st and 2nd axial combustor modes are measured using 10 kHz OH-PLIF and 2D PIV. This document analyzes five test cases: two non-reacting jets and three reacting jets. All cases correspond to jet injection

  13. The international river interface cooperative: Public domain flow and morphodynamics software for education and applications

    Nelson, Jonathan M.; Shimizu, Yasuyuki; Abe, Takaaki; Asahi, Kazutake; Gamou, Mineyuki; Inoue, Takuya; Iwasaki, Toshiki; Kakinuma, Takaharu; Kawamura, Satomi; Kimura, Ichiro; Kyuka, Tomoko; McDonald, Richard R.; Nabi, Mohamed; Nakatsugawa, Makoto; Simões, Francisco R.; Takebayashi, Hiroshi; Watanabe, Yasunori


    This paper describes a new, public-domain interface for modeling flow, sediment transport and morphodynamics in rivers and other geophysical flows. The interface is named after the International River Interface Cooperative (iRIC), the group that constructed the interface and many of the current solvers included in iRIC. The interface is entirely free to any user and currently houses thirteen models ranging from simple one-dimensional models through three-dimensional large-eddy simulation models. Solvers are only loosely coupled to the interface so it is straightforward to modify existing solvers or to introduce other solvers into the system. Six of the most widely-used solvers are described in detail including example calculations to serve as an aid for users choosing what approach might be most appropriate for their own applications. The example calculations range from practical computations of bed evolution in natural rivers to highly detailed predictions of the development of small-scale bedforms on an initially flat bed. The remaining solvers are also briefly described. Although the focus of most solvers is coupled flow and morphodynamics, several of the solvers are also specifically aimed at providing flood inundation predictions over large spatial domains. Potential users can download the application, solvers, manuals, and educational materials including detailed tutorials at The iRIC development group encourages scientists and engineers to use the tool and to consider adding their own methods to the iRIC suite of tools.

  14. The international river interface cooperative: Public domain flow and morphodynamics software for education and applications

    Nelson, Jonathan M.; Shimizu, Yasuyuki; Abe, Takaaki; Asahi, Kazutake; Gamou, Mineyuki; Inoue, Takuya; Iwasaki, Toshiki; Kakinuma, Takaharu; Kawamura, Satomi; Kimura, Ichiro; Kyuka, Tomoko; McDonald, Richard R.; Nabi, Mohamed; Nakatsugawa, Makoto; Simoes, Francisco J.; Takebayashi, Hiroshi; Watanabe, Yasunori


    This paper describes a new, public-domain interface for modeling flow, sediment transport and morphodynamics in rivers and other geophysical flows. The interface is named after the International River Interface Cooperative (iRIC), the group that constructed the interface and many of the current solvers included in iRIC. The interface is entirely free to any user and currently houses thirteen models ranging from simple one-dimensional models through three-dimensional large-eddy simulation models. Solvers are only loosely coupled to the interface so it is straightforward to modify existing solvers or to introduce other solvers into the system. Six of the most widely-used solvers are described in detail including example calculations to serve as an aid for users choosing what approach might be most appropriate for their own applications. The example calculations range from practical computations of bed evolution in natural rivers to highly detailed predictions of the development of small-scale bedforms on an initially flat bed. The remaining solvers are also briefly described. Although the focus of most solvers is coupled flow and morphodynamics, several of the solvers are also specifically aimed at providing flood inundation predictions over large spatial domains. Potential users can download the application, solvers, manuals, and educational materials including detailed tutorials at The iRIC development group encourages scientists and engineers to use the tool and to consider adding their own methods to the iRIC suite of tools.

  15. Viscous-flow Calculations of Submarine Maneuvering Hydrodynamic Coefficients and Flow Field based on Same Grid Topology

    Liushuai CAO; Jun ZHU; Guanghui ZENG


    .... In a collaborative exercise, the authors performed calculations on the bare hull DRAPA SUBOFF submarine to investigate the capability of viscous-flow solvers to predict the forces and moments as well...

  16. Experimental thermodynamics experimental thermodynamics of non-reacting fluids

    Neindre, B Le


    Experimental Thermodynamics, Volume II: Experimental Thermodynamics of Non-reacting Fluids focuses on experimental methods and procedures in the study of thermophysical properties of fluids. The selection first offers information on methods used in measuring thermodynamic properties and tests, including physical quantities and symbols for physical quantities, thermodynamic definitions, and definition of activities and related quantities. The text also describes reference materials for thermometric fixed points, temperature measurement under pressures, and pressure measurements. The publicatio

  17. Improved numerical methods for turbulent viscous recirculating flows

    Turan, A.; Vandoormaal, J. P.


    The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

  18. Wind-US Unstructured Flow Solutions for a Transonic Diffuser

    Mohler, Stanley R., Jr.


    The Wind-US Computational Fluid Dynamics flow solver computed flow solutions for a transonic diffusing duct. The calculations used an unstructured (hexahedral) grid. The Spalart-Allmaras turbulence model was used. Static pressures along the upper and lower wall agreed well with experiment, as did velocity profiles. The effect of the smoothing input parameters on convergence and solution accuracy was investigated. The meaning and proper use of these parameters are discussed for the benefit of Wind-US users. Finally, the unstructured solver is compared to the structured solver in terms of run times and solution accuracy.

  19. An Immersed Boundary - Adaptive Mesh Refinement solver (IB-AMR) for high fidelity fully resolved wind turbine simulations

    Angelidis, Dionysios; Sotiropoulos, Fotis


    The geometrical details of wind turbines determine the structure of the turbulence in the near and far wake and should be taken in account when performing high fidelity calculations. Multi-resolution simulations coupled with an immersed boundary method constitutes a powerful framework for high-fidelity calculations past wind farms located over complex terrains. We develop a 3D Immersed-Boundary Adaptive Mesh Refinement flow solver (IB-AMR) which enables turbine-resolving LES of wind turbines. The idea of using a hybrid staggered/non-staggered grid layout adopted in the Curvilinear Immersed Boundary Method (CURVIB) has been successfully incorporated on unstructured meshes and the fractional step method has been employed. The overall performance and robustness of the second order accurate, parallel, unstructured solver is evaluated by comparing the numerical simulations against conforming grid calculations and experimental measurements of laminar and turbulent flows over complex geometries. We also present turbine-resolving multi-scale LES considering all the details affecting the induced flow field; including the geometry of the tower, the nacelle and especially the rotor blades of a wind tunnel scale turbine. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the Sandia National Laboratories.

  20. A Reacting-Shrinking Core Model for Pyrolysis and Combustion of a Single Biomass Particle

    Gordon, Alfredo L.; Avila, Claudio R.; Garcia, Ximena A. (Dept. of Chemical Engineering, Univ. of Concepcion (Chile)). e-mail:


    Consecutive heating and pyrolysis of the solid due to incident heat flow represented by a shrinking reacting core approximation and combustion, described by a shrinking unreacting core description, allow modeling the combustion of a cylindrical biomass particle. A bi-dimensional approach (radial and axial) describes mass and heat balances and first order kinetics characterizes the reaction rates. A finite differences algorithm numerically solved the model. Results showed good agreement with available experimental data. The parameter analysis for the pyrolysis step shows high sensibility to the kinetic constants, the incident heat flow, the initial moisture and particle size. Parameters with a significant effect on combustion are the concentration and effective diffusivity of the oxidizing agent in the atmosphere around the reaction surface

  1. Using Solver Interfaced Virtual Reality in PEACER Design Process

    Lee, Hyong Won; Nam, Won Chang; Jeong, Seung Ho; Hwang, Il Soon; Shin, Jong Gye; Kim, Chang Hyo [Seoul National University, Seoul (Korea, Republic of)


    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

  2. User documentation for KINSOL, a nonlinear solver for sequential and parallel computers

    Taylor, A. G., LLNL


    KINSOL is a general purpose nonlinear system solver callable from either C or Fortran programs It is based on NKSOL [3], but is written in ANSI-standard C rather than Fortran77 Its most notable feature is that it uses Krylov Inexact Newton techniques in the system`s approximate solution, thus sharing significant modules previously written within CASC at LLNL to support CVODE[6, 7]/PVODE[9, 5] It also requires almost no matrix storage for solving the Newton equations as compared to direct methods The name KINSOL is derived from those techniques Krylov Inexact Newton SOLver The package was arranged so that selecting one of two forms of a single module in the compilation process will allow the entire package to be created in either sequential (serial) or parallel form The parallel version of KINSOL uses MPI (Message-Passing Interface) [8] and an appropriately revised version of the vector module NVECTOR, as mentioned above, to achieve parallelism and portability KINSOL in parallel form is intended for the SPMD (Single Program Multiple Data) model with distributed memory, in which all vectors are identically distributed across processors In particular, the vector module NVECTOR is designed to help the user assign a contiguous segment of a given vector to each of the processors for parallel computation Several primitives were added to NVECTOR as originally written for PVODE to implement KINSOL KINSOL has been run on a Cray-T3D, an eight- processor DEC ALPHA and a cluster of workstations It is currently being used in a simulation of tokamak edge plasmas and in groundwater two-phase flow studies at LLNL The remainder of this paper is organized as follows Section 2 sets the mathematical notation and summarizes the basic methods Section 3 summarizes the organization of the KINSOL solver, while Section 4 summarizes its usage Section 5 describes a preconditioner module, Section 6 describes a set of Fortran/C interfaces, Section 7 describes an example problem, and Section 8

  3. A fast and automatic full-potential finite volume solver on Cartesian grids for unconventional configurations

    Fanxi LYU


    Full Text Available To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design, a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper. Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algorithms. The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual (GMRES algorithm. During computation, solution-based mesh adaptation is also applied so as to capture flow features more accurately. An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead. According to the characteristics of the Cartesian grids, the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces, which can significantly improve the solution converging speed. The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing, a DLR-F4 wing-body, and an unconventional figuration of a blended wing body (BWB. The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation, and the results suggest its capacity in application for aircraft conceptual design.

  4. M2Di: Concise and efficient MATLAB 2-D Stokes solvers using the Finite Difference Method

    Räss, Ludovic; Duretz, Thibault; Podladchikov, Yury Y.; Schmalholz, Stefan M.


    Recent development of many multiphysics modeling tools reflects the currently growing interest for studying coupled processes in Earth Sciences. The core of such tools should rely on fast and robust mechanical solvers. Here we provide M2Di, a set of routines for 2-D linear and power law incompressible viscous flow based on Finite Difference discretizations. The 2-D codes are written in a concise vectorized MATLAB fashion and can achieve a time to solution of 22 s for linear viscous flow on 10002 grid points using a standard personal computer. We provide application examples spanning from finely resolved crystal-melt dynamics, deformation of heterogeneous power law viscous fluids to instantaneous models of mantle flow in cylindrical coordinates. The routines are validated against analytical solution for linear viscous flow with highly variable viscosity and compared against analytical and numerical solutions of power law viscous folding and necking. In the power law case, both Picard and Newton iterations schemes are implemented. For linear Stokes flow and Picard linearization, the discretization results in symmetric positive-definite matrix operators on Cartesian grids with either regular or variable grid spacing allowing for an optimized solving procedure. For Newton linearization, the matrix operator is no longer symmetric and an adequate solving procedure is provided. The reported performance of linear and power law Stokes flow is finally analyzed in terms of wall time. All MATLAB codes are provided and can readily be used for educational as well as research purposes. The M2Di routines are available from Bitbucket and the University of Lausanne Scientific Computing Group website, and are also supplementary material to this article.

  5. Reformulation of the Fourier-Bessel steady state mode solver

    Gauthier, Robert C.


    The Fourier-Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.

  6. A Parallel Algebraic Multigrid Solver on Graphics Processing Units

    Haase, Gundolf


    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.

  7. A Simple Quantum Integro-Differential Solver (SQuIDS)

    Delgado, Carlos Alberto Arguelles; Weaver, Christopher N


    Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.

  8. Fast Multipole-Based Elliptic PDE Solver and Preconditioner

    Ibeid, Huda


    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

  9. Preconditioned CG-solvers and finite element grids

    Bauer, R.; Selberherr, S. [Technical Univ. of Vienna (Austria)


    To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.

  10. Conjugate gradient solvers on Intel Xeon Phi and NVIDIA GPUs

    Kaczmarek, O; Steinbrecher, P; Wagner, M


    Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of the Fermion Matrix. This part is therefore frequently optimized for various HPC architectures. Here we compare the performance of the Intel Xeon Phi to current Kepler-based NVIDIA Tesla GPUs running a conjugate gradient solver. By exposing more parallelism to the accelerator through inverting multiple vectors at the same time, we obtain a performance greater than 300 GFlop/s on both architectures. This more than doubles the performance of the inversions. We also give a short overview of the Knights Corner architecture, discuss some details of the implementation and the effort required to obtain the achieved performance.

  11. Modelo de selección de cartera con Solver

    P. Fogués Zornoza


    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.

  12. On the relationship between ODE solvers and iterative solvers for linear equations

    Lorber, A.; Joubert, W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)


    The connection between the solution of linear systems of equations by both iterative methods and explicit time stepping techniques is investigated. Based on the similarities, a suite of Runge-Kutta time integration schemes with extended stability domains are developed using Chebyshev iteration polynomials. These Runge-Kutta schemes are applied to linear and non-linear systems arising from the numerical solution of PDE`s containing either physical or artificial transient terms. Specifically, the solutions of model linear convection and convection-diffusion equations are presented, as well as the solution of a representative non-linear Navier-Stokes fluid flow problem. Included are results of parallel computations.

  13. Application of alternating decision trees in selecting sparse linear solvers

    Bhowmick, Sanjukta


    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.

  14. Riemann solvers and Alfven waves in black hole magnetospheres

    Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip


    In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.

  15. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    Copeland, D. M.


    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.

  16. ReACT Methodology Proof of Concept Final Report

    Bri Rolston; Sarah Freeman


    The Department of Energy’s Office of Electricity Delivery and Energy Reliability (DOE-OE) funded INL Researchers to evaluate a novel process for assessing and mitigating cyber security risks. The proof of concept level of the method was tested in an industry environment. This case study, plus additional case studies will support the further development of the method into a tool to assist industry in securing their critical networks. This report provides an understanding of the process developed in the Response Analysis and Characterization Tool (ReACT) project. This report concludes with lessons learned and a roadmap for final development of these tools for use by industry.

  17. Final Report 1996. STP.30074. Simulation of industrial flow processes; Sluttrapport 1996. STP.30074. Simulering av industrielle stroemningsprosesser

    Teigland, R.; Hallanger, A.


    CMR has for many years been developing simulation programs for industrial processes. This report summarizes the final development of MUSIC (MUltifluid SImulation Code). The principle topics in this development are: Multiphase flow, Linear equation solvers based on Krylov subspace methods, Multiblock linear solver and coupling to the iteration strategy of SIMPLE, Lagrange simulator, Multigrid methods, Movable grids, Parallel linear solvers in MUSIC. The new numerical algorithms implemented are discussed, with an emphasis on the work done in 1996. 24 refs.

  18. Effect of reacted acidic monomer with calcium on bonding performance.

    Fujita, K; Ma, S; Aida, M; Maeda, T; Ikemi, T; Hirata, M; Nishiyama, N


    We determined the number of reacted and unreacted 10-methacryloyloxydecyl dihydrogen phosphate (10-MDP) molecules with calcium during the demineralization process of hydroxyapatite or dentin by 10-MDP-based one-step (Clearfil Tri-S Bond, TS) or two-step self-etch adhesive (Clearfil SE Bond Primer, SE). We then examined the effects of the number of reacted and/or unreacted 10-MDP molecules on the initial bond strength and bond durability of the resultant adhesive layer. The null hypotheses were that (1) the etching efficacy of tooth apatite by 10-MDP used in TS was the same as that in SE, and (2) the unreacted 10-MDP polymer included within the adhesive layer does not affect bond durability. Addition of hydroxyapatite or dentin to the TS and SE resulted in decreases in the NMR peak intensities for 10-MDP. The peak intensity for 10-MDP showed a greater reduction in SE than in TS, consistent with the observation that SE provided significantly higher initial mean bond strengths than TS. Further, the unreacted 10-MDP polymer within the adhesive layer did not decrease the mean bond strength, despite the application of 20,000x thermo-cycling.

  19. Sticky Tunes: How Do People React to Involuntary Musical Imagery?

    Williamson, Victoria J.; Liikkanen, Lassi A.; Jakubowski, Kelly; Stewart, Lauren


    The vast majority of people experience involuntary musical imagery (INMI) or ‘earworms’; perceptions of spontaneous, repetitive musical sound in the absence of an external source. The majority of INMI episodes are not bothersome, while some cause disruption ranging from distraction to anxiety and distress. To date, little is known about how the majority of people react to INMI, in particular whether evaluation of the experience impacts on chosen response behaviours or if attempts at controlling INMI are successful or not. The present study classified 1046 reports of how people react to INMI episodes. Two laboratories in Finland and the UK conducted an identical qualitative analysis protocol on reports of INMI reactions and derived visual descriptive models of the outcomes using grounded theory techniques. Combined analysis carried out across the two studies confirmed that many INMI episodes were considered neutral or pleasant, with passive acceptance and enjoyment being among the most popular response behaviours. A significant number of people, however, reported on attempts to cope with unwanted INMI. The most popular and effective behaviours in response to INMI were seeking out the tune in question, and musical or verbal distraction. The outcomes of this study contribute to our understanding of the aetiology of INMI, in particular within the framework of memory theory, and present testable hypotheses for future research on successful INMI coping strategies. PMID:24497938

  20. Sticky tunes: how do people react to involuntary musical imagery?

    Victoria J Williamson

    Full Text Available The vast majority of people experience involuntary musical imagery (INMI or 'earworms'; perceptions of spontaneous, repetitive musical sound in the absence of an external source. The majority of INMI episodes are not bothersome, while some cause disruption ranging from distraction to anxiety and distress. To date, little is known about how the majority of people react to INMI, in particular whether evaluation of the experience impacts on chosen response behaviours or if attempts at controlling INMI are successful or not. The present study classified 1046 reports of how people react to INMI episodes. Two laboratories in Finland and the UK conducted an identical qualitative analysis protocol on reports of INMI reactions and derived visual descriptive models of the outcomes using grounded theory techniques. Combined analysis carried out across the two studies confirmed that many INMI episodes were considered neutral or pleasant, with passive acceptance and enjoyment being among the most popular response behaviours. A significant number of people, however, reported on attempts to cope with unwanted INMI. The most popular and effective behaviours in response to INMI were seeking out the tune in question, and musical or verbal distraction. The outcomes of this study contribute to our understanding of the aetiology of INMI, in particular within the framework of memory theory, and present testable hypotheses for future research on successful INMI coping strategies.

  1. A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems

    Dumbser, Michael, E-mail: [Laboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, I-38123 Trento (Italy); Balsara, Dinshaw S., E-mail: [Physics Department, University of Notre Dame du Lac, 225 Nieuwland Science Hall, Notre Dame, IN 46556 (United States)


    In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearly degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non

  2. Numerical Simulations of the Single-mode, Reacting Richtmyer-Meshkov Instability Using Detailed Chemistry

    Attal, Nitesh; Ramaprabhu, Praveen


    The interaction of a shock wave with a chemically reacting front is of importance to the design of supersonic combustors and scramjets where mixing from the Richtmyer-Meshkov Instability (RMI) could be tapped to increase combustion efficiency. We will describe results of shock-driven, reacting RMI of a sinusoidally perturbed, single-mode interface separating Hydrogen (fuel) and Oxygen at 300 K and 1625 K respectively. The non-premixed interface was accelerated by a Mach 1.2 shock traversing from the light (H2) to heavy (O2) fluid (Atwood number = 0.5) in a numerical shock tube of aspect ratio 12. The 2D simulations were performed using the compressible flow code FLASH, with modifications to handle detailed chemistry and temperature-dependent material properties. The initial thickness of the material interface was systematically varied to study the effect of the diffusion thickness on the flame and instability dynamics. Product formation and heat release as a result of chemical reactions were described according to the 9-species, 19-steps detailed reaction mechanism.

  3. Phase-field lattice Boltzmann modeling of boiling using a sharp-interface energy solver

    Mohammadi-Shad, Mahmood; Lee, Taehun


    The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.

  4. Oscillation-Free Methods for Modeling Fluid-Porous Interfaces Using Segregated Solvers on Unstructured Grids

    Stanic, Milos; Nordlund, Markus; Kuczaj, Arkadiusz; Frederix, Edoardo; Geurts, Bernard


    Porous media flows can be found in a large number of fields ranging from engineering to medical applications. A volume-averaged approach to simulating porous media is often used because of its practicality and computational efficiency. Derivation of the volume-averaged porous flow equations introduces additional porous resistance terms to the momentum equation. When discretized these porous resistance terms create a body force discontinuity at the porous-fluid interface, which may lead to spurious oscillations if not accounted for properly. A variety of numerical techniques has been proposed to solve this problem, but few of them have concentrated on collocated grids and segregated solvers, which have wide applications in academia and industry. In this work we discuss the source of the spurious oscillations, quantify their amplitude and apply interface treatments methods that successfully remove the oscillations. The interface treatment methods are tested in a variety of realistic scenarios, including the porous plug and Beaver-Joseph test cases and show excellent results, minimizing or entirely removing the spurious oscillations at the porous-fluid interface. This research was financially supported by Philip Morris Products S.A.

  5. Analysis of reacting flowfields in low-thrust rocket engines and plumes

    Weiss, Jonathan Mitchell

    levels of predicted quantities suggest the method should prove valuable for predicting parametric trends for design studies. In addition, issues such as numerical stability, robustness and computational efficiency are addressed. These include the evaluation of a numerically compatible two-equation turbulence model and the implementation of a time-derivative preconditioning method for convergence enhancement of low Mach number, chemically reacting flows.

  6. Parallel Sparse Linear System and Eigenvalue Problem Solvers: From Multicore to Petascale Computing


    problems that achieve high performance on a single multicore node and clusters of many multicore nodes. Further, we demonstrate both the superior ...the superior robustness and parallel scalability of our solvers compared to other publicly available parallel solvers for these two fundamental...LU‐ and algebraic multigrid‐preconditioned Krylov subspace methods. This has been demonstrated in previous annual reports of this

  7. Parallel Implementation of a Semidefinite Programming Solver based on CSDP in a distributed memory cluster

    Ivanov, I.D.; de Klerk, E.


    In this paper we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface (MPI), and the Sc

  8. Motivation, Challenge, and Opportunity of Successful Solvers on an Innovation Platform

    Hossain, Mokter


    The objective of this study is to identify motivations, challenges, and opportunities of successful solvers participating in virtual teams of innovation contests (ICs) organized by an innovation intermediary. Based on 82 interviews of successful solvers, this study provides novel insights into ICs...

  9. Parallel Implementation of a Semidefinite Programming Solver based on CSDP in a distributed memory cluster

    Ivanov, I.D.; de Klerk, E.


    In this paper we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface (MPI), and the Sc

  10. A Comparative Study on Different Parallel Solvers for Nonlinear Analysis of Complex Structures

    Lei Zhang


    Full Text Available The parallelization of 2D/3D software SAPTIS is discussed for nonlinear analysis of complex structures. A comparative study is made on different parallel solvers. The numerical models are presented, including hydration models, water cooling models, modulus models, creep model, and autogenous deformation models. A finite element simulation is made for the whole process of excavation and pouring of dams using these models. The numerical results show a good agreement with the measured ones. To achieve a better computing efficiency, four parallel solvers utilizing parallelization techniques are employed: (1 a parallel preconditioned conjugate gradient (PCG solver based on OpenMP, (2 a parallel preconditioned Krylov subspace solver based on MPI, (3 a parallel sparse equation solver based on OpenMP, and (4 a parallel GPU equation solver. The parallel solvers run either in a shared memory environment OpenMP or in a distributed memory environment MPI. A comparative study on these parallel solvers is made, and the results show that the parallelization makes SAPTIS more efficient, powerful, and adaptable.

  11. An implementation of a parallel MOL solver on the Intel gamma parallel computer

    Lawkins, W.F.; Payne, J.S.


    A implicit parallel method-of-lines solver that has been implemented on the MIMD Intel Gamma prototype supercomputer is discussed. The strategy for implementation is to execute the ODE solver sequentially and to do the numerical linear algebra in parallel. Performance studies for this implementation are presented.

  12. A Newton-Krylov solver for fast spin-up of online ocean tracers

    Lindsay, Keith


    We present a Newton-Krylov based solver to efficiently spin up tracers in an online ocean model. We demonstrate that the solver converges, that tracer simulations initialized with the solution from the solver have small drift, and that the solver takes orders of magnitude less computational time than the brute force spin-up approach. To demonstrate the application of the solver, we use it to efficiently spin up the tracer ideal age with respect to the circulation from different time intervals in a long physics run. We then evaluate how the spun-up ideal age tracer depends on the duration of the physics run, i.e., on how equilibrated the circulation is.

  13. General second order complete active space self-consistent-field solver for large-scale systems

    Sun, Qiming


    One challenge of the complete active space self-consistent field (CASSCF) program is to solve the transition metal complexes which are typically medium or large-size molecular systems with large active space. We present an AO-driven second order CASSCF solver to efficiently handle systems which have a large number of AO functions and many active orbitals. This solver allows user to replace the active space Full CI solver with any multiconfigurational solver without breaking the quadratic convergence feature. We demonstrate the capability of the CASSCF solver with the study of Fe(ii)-porphine ground state using DMRG-CASSCF method for 22 electrons in 27 active orbitals and 3000 basis functions.

  14. Verification and validation of a parallel 3D direct simulation Monte Carlo solver for atmospheric entry applications

    Nizenkov, Paul; Noeding, Peter; Konopka, Martin; Fasoulas, Stefanos


    The in-house direct simulation Monte Carlo solver PICLas, which enables parallel, three-dimensional simulations of rarefied gas flows, is verified and validated. Theoretical aspects of the method and the employed schemes are briefly discussed. Considered cases include simple reservoir simulations and complex re-entry geometries, which were selected from literature and simulated with PICLas. First, the chemistry module is verified using simple numerical and analytical solutions. Second, simulation results of the rarefied gas flow around a 70° blunted-cone, the REX Free-Flyer as well as multiple points of the re-entry trajectory of the Orion capsule are presented in terms of drag and heat flux. A comparison to experimental measurements as well as other numerical results shows an excellent agreement across the different simulation cases. An outlook on future code development and applications is given.

  15. Progress in developing Poisson-Boltzmann equation solvers

    Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil


    This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185

  16. Progress in developing Poisson-Boltzmann equation solvers.

    Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil


    This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

  17. A General Symbolic PDE Solver Generator: Beyond Explicit Schemes

    K. Sheshadri


    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.

  18. SolveDB: Integrating Optimization Problem Solvers Into SQL Databases

    Siksnys, Laurynas; Pedersen, Torben Bach


    Many real-world decision problems involve solving optimization problems based on data in an SQL database. Traditionally, solving such problems requires combining a DBMS with optimization software packages for each required class of problems (e.g. linear and constraint programming) -- leading...... to workflows that are cumbersome, complex, inefficient, and error-prone. In this paper, we present SolveDB - a DBMS for optimization applications. SolveDB supports solvers for different problem classes and offers seamless data management and optimization problem solving in a pure SQL-based setting. This allows...... for much simpler and more effective solutions of database-based optimization problems. SolveDB is based on the 3-level ANSI/SPARC architecture and allows formulating, solving, and analysing solutions of optimization problems using a single so-called solve query. SolveDB provides (1) an SQL-based syntax...

  19. Accurate derivative evaluation for any Grad–Shafranov solver

    Ricketson, L.F. [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States); Cerfon, A.J., E-mail: [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States); Rachh, M. [Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States); Freidberg, J.P. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)


    We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad–Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.

  20. Fast Multipole-Based Preconditioner for Sparse Iterative Solvers

    Ibeid, Huda


    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.

  1. Reflection-free finite volume Maxwell's solver for adaptive grids

    Elkina, Nina


    We present a non-staggered method for the Maxwell equations in adaptively refined grids. The code is based on finite volume central scheme that preserves in a discrete form both divergence-free property of magnetic field and the Gauss law. High spatial accuracy is achieved with help of non-oscillatory extrema preserving piece-wise or piece-wise-quadratic reconstructions. The semi-discrete equations are solved by implicit-explicit Runge-Kutta method. The new adaptive grid Maxwell's solver is examined based on several 1d examples, including the an propagation of a Gaussian pulse through vacuum and partially ionised gas. Two-dimensional extension is tested with a Gaussian pulse incident on dielectric disc. Additionally, we focus on testing computational accuracy and efficiency.

  2. Visualising magnetic fields numerical equation solvers in action

    Beeteson, John Stuart


    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

  3. Preconditioned fully implicit PDE solvers for monument conservation

    Semplice, Matteo


    Mathematical models for the description, in a quantitative way, of the damages induced on the monuments by the action of specific pollutants are often systems of nonlinear, possibly degenerate, parabolic equations. Although some the asymptotic properties of the solutions are known, for a short window of time, one needs a numerical approximation scheme in order to have a quantitative forecast at any time of interest. In this paper a fully implicit numerical method is proposed, analyzed and numerically tested for parabolic equations of porous media type and on a systems of two PDEs that models the sulfation of marble in monuments. Due to the nonlinear nature of the underlying mathematical model, the use of a fixed point scheme is required and every step implies the solution of large, locally structured, linear systems. A special effort is devoted to the spectral analysis of the relevant matrices and to the design of appropriate iterative or multi-iterative solvers, with special attention to preconditioned Krylo...

  4. Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS

    Harrison, Robert; Thornton, William


    We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.

  5. Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver

    Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P


    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 wavefront 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 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 numeric...

  6. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    Copeland, Dylan


    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.

  7. Extending the QUDA Library with the eigCG Solver

    Strelchenko, Alexei [Fermilab; Stathopoulos, Andreas [William-Mary Coll.


    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

  8. Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

    Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)


    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.

  9. Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

    Raman, Venkatramanan

    A novel computational scheme is formulated for simulating turbulent reactive flows in complex geometries with detailed chemical kinetics. A Probability Density Function (PDF) based method that handles the scalar transport equation is coupled with an existing Finite Volume (FV) Reynolds-Averaged Navier-Stokes (RANS) flow solver. The PDF formulation leads to closed chemical source terms and facilitates the use of detailed chemical mechanisms without approximations. The particle-based PDF scheme is modified to handle complex geometries and grid structures. Grid-independent particle evolution schemes that scale linearly with the problem size are implemented in the Monte-Carlo PDF solver. A novel algorithm, in situ adaptive tabulation (ISAT) is employed to ensure tractability of complex chemistry involving a multitude of species. Several non-reacting test cases are performed to ascertain the efficiency and accuracy of the method. Simulation results from a turbulent jet-diffusion flame case are compared against experimental data. The effect of micromixing model, turbulence model and reaction scheme on flame predictions are discussed extensively. Finally, the method is used to analyze the Dow Chlorination Reactor. Detailed kinetics involving 37 species and 158 reactions as well as a reduced form with 16 species and 21 reactions are used. The effect of inlet configuration on reactor behavior and product distribution is analyzed. Plant-scale reactors exhibit quenching phenomena that cannot be reproduced by conventional simulation methods. The FV-PDF method predicts quenching accurately and provides insight into the dynamics of the reactor near extinction. The accuracy of the fractional time-stepping technique in discussed in the context of apparent multiple-steady states observed in a non-premixed feed configuration of the chlorination reactor.

  10. REAC/TS Radiation Accident Registry: An Overview

    Doran M. Christensen, DO, REAC/TS Associate Director and Staff Physician Becky Murdock, REAC/TS Registry and Health Physics Technician


    Over the past four years, REAC/TS has presented a number of case reports from its Radiation Accident Registry. Victims of radiological or nuclear incidents must meet certain dose criteria for an incident to be categorized as an “accident” and be included in the registry. Although the greatest numbers of “accidents” in the United States that have been entered into the registry involve radiation devices, the greater percentage of serious accidents have involved sealed sources of one kind or another. But if one looks at the kinds of accident scenarios that have resulted in extreme consequence, i.e., death, the greater share of deaths has occurred in medical settings.

  11. Reacting chemistry at the air-water interface

    Murakami, Tomoyuki; Morgan, Thomas; Huwel, Lutz; Graham, William


    Plasma interaction with gas-liquid interfaces is becoming increasingly important in biological applications, chemical analysis and medicine. It introduces electrons, new ionic species and reactive species and contributes to chemical and electrical self-organization at the interface. To provide insight into the associated physics and chemistry at work in the evolution of the plasma in the air-water interface (AWI), a time-dependent one-dimensional modelling has been developed. The numerical simulation is used to solve the kinetic equations and help identify the important reaction mechanisms and describe the phenomena associated with hundreds of reacting pathways in gas-phase and liquid-phase AWI chemistry. This work was partly supported by JSPS KAKENHI Grant Number 16K04998.

  12. Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier-Stokes equations on GPU

    Bauer, Petr; Klement, Vladimír; Oberhuber, Tomáš; Žabka, Vítězslav


    We present a complete GPU implementation of a geometric multigrid solver for the numerical solution of the Navier-Stokes equations for incompressible flow. The approximate solution is constructed on a two-dimensional unstructured triangular mesh. The problem is discretized by means of the mixed finite element method with semi-implicit timestepping. The linear saddle-point problem arising from the scheme is solved by the geometric multigrid method with a Vanka-type smoother. The parallel solver is based on the red-black coloring of the mesh triangles. We achieved a speed-up of 11 compared to a parallel (4 threads) code based on OpenMP and 19 compared to a sequential code.

  13. Towards faster solution of large power flow problems

    Idema, R.; Papaefthymiou, G.; Lahaye, D.J.P.; Vuik, C.; Van der Sluis, L.


    Current and future developments in the power system industry demand fast power flow solvers for larger power flow problems. The established methods are no longer viable for such problems, as they are not scalable in the problem size. In this paper, the use of Newton-Krylov power flow methods is prop


    A Mettler-Toledo ReactIR system has been used for in-line, real-time monitoring of the product stream from a spinning tube-in-tube reactor (STT®, Kreido Laboratories, Camarillo California). This combination of a process intensified continuous-flow reactor and an in-situ analytic...

  15. Nonlinear dynamics and intermittency in a turbulent reacting wake with density ratio as bifurcation parameter

    Suresha, Suhas; Sujith, R. I.; Emerson, Benjamin; Lieuwen, Tim


    The flame or flow behavior of a turbulent reacting wake is known to be fundamentally different at high and low values of flame density ratio (ρu/ρb ), as the flow transitions from globally stable to unstable. This paper analyzes the nonlinear dynamics present in a bluff-body stabilized flame, and identifies the transition characteristics in the wake as ρu/ρb is varied over a Reynolds number (based on the bluff-body lip velocity) range of 1000-3300. Recurrence quantification analysis (RQA) of the experimentally obtained time series of the flame edge fluctuations reveals that the time series is highly aperiodic at high values of ρu/ρb and transitions to increasingly correlated or nearly periodic behavior at low values. From the RQA of the transverse velocity time series, we observe that periodicity in the flame oscillations are related to periodicity in the flow. Therefore, we hypothesize that this transition from aperiodic to nearly periodic behavior in the flame edge time series is a manifestation of the transition in the flow from globally stable, convective instability to global instability as ρu/ρb decreases. The recurrence analysis further reveals that the transition in periodicity is not a sudden shift; rather it occurs through an intermittent regime present at low and intermediate ρu/ρb . During intermittency, the flow behavior switches between aperiodic oscillations, reminiscent of a globally stable, convective instability, and periodic oscillations, reminiscent of a global instability. Analysis of the distribution of the lengths of the periodic regions in the intermittent time series and the first return map indicate the presence of type-II intermittency.

  16. Reliability-based aeroelastic optimization of a composite aircraft wing via fluid-structure interaction of high fidelity solvers

    Nikbay, M.; Fakkusoglu, N.; Kuru, M. N.


    We consider reliability based aeroelastic optimization of a AGARD 445.6 composite aircraft wing with stochastic parameters. Both commercial engineering software and an in-house reliability analysis code are employed in this high-fidelity computational framework. Finite volume based flow solver Fluent is used to solve 3D Euler equations, while Gambit is the fluid domain mesh generator and Catia-V5-R16 is used as a parametric 3D solid modeler. Abaqus, a structural finite element solver, is used to compute the structural response of the aeroelastic system. Mesh based parallel code coupling interface MPCCI-3.0.6 is used to exchange the pressure and displacement information between Fluent and Abaqus to perform a loosely coupled fluid-structure interaction by employing a staggered algorithm. To compute the probability of failure for the probabilistic constraints, one of the well known MPP (Most Probable Point) based reliability analysis methods, FORM (First Order Reliability Method) is implemented in Matlab. This in-house developed Matlab code is embedded in the multidisciplinary optimization workflow which is driven by Modefrontier. Modefrontier 4.1, is used for its gradient based optimization algorithm called NBI-NLPQLP which is based on sequential quadratic programming method. A pareto optimal solution for the stochastic aeroelastic optimization is obtained for a specified reliability index and results are compared with the results of deterministic aeroelastic optimization.

  17. The impact of improved sparse linear solvers on industrial engineering applications

    Heroux, M. [Cray Research, Inc., Eagan, MN (United States); Baddourah, M.; Poole, E.L.; Yang, Chao Wu


    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.

  18. A parallel direct solver for the self-adaptive hp Finite Element Method

    Paszyński, Maciej R.


    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.

  19. A multi-dimensional finite volume cell-centered direct ALE solver for hydrodynamics

    Clair, G.; Ghidaglia, J.-M.; Perlat, J.-P.


    In this paper we describe a second order multi-dimensional scheme, belonging to the class of direct Arbitrary Lagrangian-Eulerian (ALE) methods, for the solution of non-linear hyperbolic systems of conservation law. The scheme is constructed upon a cell-centered explicit Lagrangian solver completed with an edge-based upwinded formulation of the numerical fluxes, computed from the MUSCL-Hancock method, to obtain a full ALE formulation. Numerical fluxes depend on nodal grid velocities which are either set or computed to avoid most of the mesh problems typically encountered in purely Lagrangian simulations. In order to assess the robustness of the scheme, most results proposed in this paper have been obtained by computing the grid velocities as a fraction of the Lagrangian nodal velocities, the ratio being set before running the test case. The last part of the paper describes preliminary results about the triple point test case run in the ALE framework by computing the grid velocities with the fully adaptive Large Eddy Limitation (L.E.L.) method proposed in [1]. Such a method automatically computes the grid velocities at each node defining the mesh from the local characteristics of the flow. We eventually discuss the advantages and the drawback of the coupling.

  20. RANS-VOF Solver for Solitary Wave Run-up on A Circular Cylinder

    曹洪建; 万德成


    Simulation of solitary wave run-up on a vertical circular cylinder is carried out in a viscous numerical wave tank developed based on the open source codes OpenFOAM. An incompressible two-phase flow solver naoe-FOAM-SJTU is used to solve the Reynolds-Averaged Navier–Stokes (RANS) equations with the SST k-wturbulence model. The PISO algorithm is utilized for the pressure-velocity coupling. The air-water interface is captured via Volume of Fluid (VOF) technique. The present numerical model is validated by simulating the solitary wave run-up and reflected against a vertical wall, and solitary wave run-up on a vertical circular cylinder. Comparisons between numerical results and available experimental data show satisfactory agreement. Furthermore, simulations are carried out to study the solitary wave run-up on the cylinder with different incident wave height H and different cylinder radius a. The relationships of the wave run-up height with the incident wave height H, cylinder radius a are analyzed. The evolutions of the scattering free surface and vortex shedding are also presented to give a better understanding of the process of nonlinear wave-cylinder interaction.