Grid Generation Techniques Utilizing the Volume Grid Manipulator

Science.gov (United States)

Alter, Stephen J.

1998-01-01

This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.

A finite volume method for cylindrical heat conduction problems based on local analytical solution

KAUST Repository

Li, Wang

2012-10-01

A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.

A finite volume method for cylindrical heat conduction problems based on local analytical solution

KAUST Repository

Li, Wang; Yu, Bo; Wang, Xinran; Wang, Peng; Sun, Shuyu

2012-01-01

A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.

Optimal variable-grid finite-difference modeling for porous media

International Nuclear Information System (INIS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-01-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)

Test Functions for Three-Dimensional Control-Volume Mixed Finite-Element Methods on Irregular Grids

National Research Council Canada - National Science Library

Naff, R. L; Russell, T. F; Wilson, J. D

2000-01-01

.... For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error...

A spatial discretization of the MHD equations based on the finite volume - spectral method

International Nuclear Information System (INIS)

Miyoshi, Takahiro

2000-05-01

Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

Energy Technology Data Exchange (ETDEWEB)

Jayakumar, J S; Kumar, Inder [Bhabha Atomic Research Center, Mumbai (India); Eswaran, V, E-mail: jsjayan@gmail.com, E-mail: inderk@barc.gov.in, E-mail: eswar@iitk.ac.in [Indian Institute of Technology, Kanpur (India)

2010-12-15

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-{omega}. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

Science.gov (United States)

Jayakumar, J. S.; Kumar, Inder; Eswaran, V.

2010-12-01

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

International Nuclear Information System (INIS)

Jayakumar, J S; Kumar, Inder; Eswaran, V

2010-01-01

Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

Science.gov (United States)

Barall, Michael

2009-01-01

We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

Finite Volumes for Complex Applications VII

CERN Document Server

Ohlberger, Mario; Rohde, Christian

2014-01-01

The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative propert...

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

KAUST Repository

Chu, Chunlei

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.

Energy stable and high-order-accurate finite difference methods on staggered grids

Science.gov (United States)

O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan

2017-10-01

For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

Flow simulation of a Pelton bucket using finite volume particle method

International Nuclear Information System (INIS)

Vessaz, C; Jahanbakhsh, E; Avellan, F

2014-01-01

The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets

Modeling seismic wave propagation using staggered-grid mimetic finite differences

Directory of Open Access Journals (Sweden)

Freysimar Solano-Feo

2017-04-01

Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.

Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids

Energy Technology Data Exchange (ETDEWEB)

Meese, Ernst Arne

1998-07-01

Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.

Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael

2017-10-01

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

Three-body unitarity in the finite volume

Energy Technology Data Exchange (ETDEWEB)

Mai, M. [The George Washington University, Washington, DC (United States); Doering, M. [The George Washington University, Washington, DC (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

2017-12-15

The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic 3 → 3 amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated. (orig.)

SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

KAUST Repository

Gao, Longfei

2018-02-16

We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

GRIZ: Visualization of finite element analysis results on unstructured grids

International Nuclear Information System (INIS)

Dovey, D.; Loomis, M.D.

1994-01-01

GRIZ is a general-purpose post-processing application that supports interactive visualization of finite element analysis results on three-dimensional unstructured grids. GRIZ includes direct-to-videodisc animation capabilities and is being used as a production tool for creating engineering animations

Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2012-07-01

Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...

Chiral crossover transition in a finite volume

Science.gov (United States)

Shi, Chao; Jia, Wenbao; Sun, An; Zhang, Liping; Zong, Hongshi

2018-02-01

Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature {T}{{c}} of the crossover, showing a significant decrease in {T}{{c}} as L decreases below 3 fm. Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment & Technology in Huazhong University of Science & Technology (DMETKF2015015)

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

KAUST Repository

Wheeler, Mary F.

2011-01-01

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.

Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids

Energy Technology Data Exchange (ETDEWEB)

Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory

2012-07-19

A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

International Nuclear Information System (INIS)

Coelho, Pedro J.

2014-01-01

Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

8th conference on Finite Volumes for Complex Applications

CERN Document Server

Omnes, Pascal

2017-01-01

This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including m...

Finite volume model for two-dimensional shallow environmental flow

Science.gov (United States)

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Finite volume form factors in the presence of integrable defects

International Nuclear Information System (INIS)

Bajnok, Z.; Buccheri, F.; Hollo, L.; Konczer, J.; Takacs, G.

2014-01-01

We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee–Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee–Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found

Adaptive mesh refinement for a finite volume method for flow and transport of radionuclides in heterogeneous porous media

International Nuclear Information System (INIS)

Amaziane, Brahim; Bourgeois, Marc; El Fatini, Mohamed

2014-01-01

In this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Surete Nucleaire). The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow. (authors)

Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver

Science.gov (United States)

Kestener, Pierre

2017-10-01

RamsesGPU is a reimplementation of RAMSES (ascl:1011.007) which drops the adaptive mesh refinement (AMR) features to optimize 3D uniform grid algorithms for modern graphics processor units (GPU) to provide an efficient software package for astrophysics applications that do not need AMR features but do require a very large number of integration time steps. RamsesGPU provides an very efficient C++/CUDA/MPI software implementation of a second order MUSCL-Handcock finite volume fluid solver for compressible hydrodynamics as a magnetohydrodynamics solver based on the constraint transport technique. Other useful modules includes static gravity, dissipative terms (viscosity, resistivity), and forcing source term for turbulence studies, and special care was taken to enhance parallel input/output performance by using state-of-the-art libraries such as HDF5 and parallel-netcdf.

FINITE VOLUME METHOD FOR SOLVING THREE-DIMENSIONAL ELECTRIC FIELD DISTRIBUTION

Directory of Open Access Journals (Sweden)

Paţiuc V.I.

2011-04-01

Full Text Available The paper examines a new approach to finite volume method which is used to calculate the electric field spatially homogeneous three-dimensional environment. It is formulated the problem Dirihle with building of the computational grid on base of space partition, which is known as Delone triangulation with the use of Voronoi cells. It is proposed numerical algorithm for calculating the potential and electric field strength in the space formed by a cylinder placed in the air. It is developed algorithm and software which were for the case, when the potential on the inner surface of the cylinder has been assigned and on the outer surface and the bottom of cylinder it was assigned zero potential. There are presented results of calculations of distribution in the potential space and electric field strength.

Finite difference techniques for nonlinear hyperbolic conservation laws

International Nuclear Information System (INIS)

Sanders, R.

1985-01-01

The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references

A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

Science.gov (United States)

Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen

2017-06-01

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

Science.gov (United States)

Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe

2009-08-01

In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.

Development of a high-order finite volume method with multiblock partition techniques

Directory of Open Access Journals (Sweden)

E. M. Lemos

2012-03-01

Full Text Available This work deals with a new numerical methodology to solve the Navier-Stokes equations based on a finite volume method applied to structured meshes with co-located grids. High-order schemes used to approximate advective, diffusive and non-linear terms, connected with multiblock partition techniques, are the main contributions of this paper. Combination of these two techniques resulted in a computer code that involves high accuracy due the high-order schemes and great flexibility to generate locally refined meshes based on the multiblock approach. This computer code has been able to obtain results with higher or equal accuracy in comparison with results obtained using classical procedures, with considerably less computational effort.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced

Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects

CERN Document Server

Alkan, Erdogan; Elsherbeni, Atef

2013-01-01

This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid

Wind turbine aerodynamics using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations...

Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids

Science.gov (United States)

Housman, Jeffrey A.; Kiris, Cetin

2016-01-01

Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.

A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

Directory of Open Access Journals (Sweden)

Hassan Badreddine

2017-01-01

Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.

Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

Science.gov (United States)

Raju, R. Srinivasa; Ramesh, K.

2018-05-01

The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

Hydrothermal analysis in engineering using control volume finite element method

CERN Document Server

Sheikholeslami, Mohsen

2015-01-01

Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),

New 2D adaptive mesh refinement algorithm based on conservative finite-differences with staggered grid

Science.gov (United States)

Gerya, T.; Duretz, T.; May, D. A.

2012-04-01

We present new 2D adaptive mesh refinement (AMR) algorithm based on stress-conservative finite-differences formulated for non-uniform rectangular staggered grid. The refinement approach is based on a repetitive cell splitting organized via a quad-tree construction (every parent cell is split into 4 daughter cells of equal size). Irrespective of the level of resolution every cell has 5 staggered nodes (2 horizontal velocities, 2 vertical velocities and 1 pressure) for which respective governing equations, boundary conditions and interpolation equations are formulated. The connectivity of the grid is achieved via cross-indexing of grid cells and basic nodal points located in their corners: four corner nodes are indexed for every cell and up to 4 surrounding cells are indexed for every node. The accuracy of the approach depends critically on the formulation of the stencil used at the "hanging" velocity nodes located at the boundaries between different levels of resolution. Most accurate results are obtained for the scheme based on the volume flux balance across the resolution boundary combined with stress-based interpolation of velocity orthogonal to the boundary. We tested this new approach with a number of 2D variable viscosity analytical solutions. Our tests demonstrate that the adaptive staggered grid formulation has convergence properties similar to those obtained in case of a standard, non-adaptive staggered grid formulation. This convergence is also achieved when resolution boundary crosses sharp viscosity contrast interfaces. The convergence rates measured are found to be insensitive to scenarios when the transition in grid resolution crosses sharp viscosity contrast interfaces. We compared various grid refinement strategies based on distribution of different field variables such as viscosity, density and velocity. According to these tests the refinement allows for significant (0.5-1 order of magnitude) increase in the computational accuracy at the same

Dense QCD in a Finite Volume

OpenAIRE

Yamamoto, Naoki; Kanazawa, Takuya

2009-01-01

We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap $\\Delta$. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the $Z(2)_...

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

Science.gov (United States)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

Wind turbine rotor-tower interaction using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are pres...

Final Report for DOE grant DE-FG02-07ER64432 "New Grid and Discretization Technologies for Ocean and Ice Simulations"

Energy Technology Data Exchange (ETDEWEB)

Gunzburger, Max

2013-03-12

The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

International Nuclear Information System (INIS)

Mirza, Anwar M.; Iqbal, Shaukat; Rahman, Faizur

2007-01-01

A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K + variational principle for slab geometry. The program has a core K + module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10 2 has been achieved using the new approach in some cases

A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

Energy Technology Data Exchange (ETDEWEB)

Mirza, Anwar M. [Department of Computer Science, National University of Computer and Emerging Sciences, NUCES-FAST, A.K. Brohi Road, H-11, Islamabad (Pakistan)], E-mail: anwar.m.mirza@gmail.com; Iqbal, Shaukat [Faculty of Computer Science and Engineering, Ghulam Ishaq Khan (GIK) Institute of Engineering Science and Technology, Topi-23460, Swabi (Pakistan)], E-mail: shaukat@giki.edu.pk; Rahman, Faizur [Department of Physics, Allama Iqbal Open University, H-8 Islamabad (Pakistan)

2007-07-15

A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K{sup +} variational principle for slab geometry. The program has a core K{sup +} module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10{sup 2} has been achieved using the new approach in some cases.

Development and analysis of finite volume methods

International Nuclear Information System (INIS)

Omnes, P.

2010-05-01

This document is a synthesis of a set of works concerning the development and the analysis of finite volume methods used for the numerical approximation of partial differential equations (PDEs) stemming from physics. In the first part, the document deals with co-localized Godunov type schemes for the Maxwell and wave equations, with a study on the loss of precision of this scheme at low Mach number. In the second part, discrete differential operators are built on fairly general, in particular very distorted or nonconforming, bidimensional meshes. These operators are used to approach the solutions of PDEs modelling diffusion, electro and magneto-statics and electromagnetism by the discrete duality finite volume method (DDFV) on staggered meshes. The third part presents the numerical analysis and some a priori as well as a posteriori error estimations for the discretization of the Laplace equation by the DDFV scheme. The last part is devoted to the order of convergence in the L2 norm of the finite volume approximation of the solution of the Laplace equation in one dimension and on meshes with orthogonality properties in two dimensions. Necessary and sufficient conditions, relatively to the mesh geometry and to the regularity of the data, are provided that ensure the second-order convergence of the method. (author)

A parallel finite-volume finite-element method for transient compressible turbulent flows with heat transfer

International Nuclear Information System (INIS)

Masoud Ziaei-Rad

2010-01-01

In this paper, a two-dimensional numerical scheme is presented for the simulation of turbulent, viscous, transient compressible flows in the simultaneously developing hydraulic and thermal boundary layer region. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. This combination together with a new method applied for the boundary conditions allows for accurate computation of the variables in the entrance region and for a wide range of flow fields from subsonic to transonic. The Roe-Riemann solver is used for the convective terms, whereas the standard Galerkin technique is applied for the viscous terms. A modified κ-ε model with a two-layer equation for the near-wall region combined with a compressibility correction is used to predict the turbulent viscosity. Parallel processing is also employed to divide the computational domain among the different processors to reduce the computational time. The method is applied to some test cases in order to verify the numerical accuracy. The results show significant differences between incompressible and compressible flows in the friction coefficient, Nusselt number, shear stress and the ratio of the compressible turbulent viscosity to the molecular viscosity along the developing region. A transient flow generated after an accidental rupture in a pipeline was also studied as a test case. The results show that the present numerical scheme is stable, accurate and efficient enough to solve the problem of transient wall-bounded flow.

A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis

KAUST Repository

Jagad, P. I.

2018-04-12

A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell-Centered Colocated Variables. Part I: Discretization, International Journal of Heat and Mass Transfer, vol. 48 (6), 1117-1127, 2005) is extended to include the solid-body stress analysis. The transport terms for a cell-face are evaluated in a structured grid-like manner. The Cartesian gradients at the center of each cell-face are evaluated using the coordinate transformation relations. The accuracy of the procedure is demonstrated by solving several benchmark problems involving different boundary conditions, source terms, and types of loading.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

International Nuclear Information System (INIS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.

2017-01-01

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

Energy Technology Data Exchange (ETDEWEB)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

2017-04-01

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.

A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

Science.gov (United States)

Bui, Trong T.

1999-01-01

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

Dynamic visual cryptography on deformable finite element grids

Science.gov (United States)

Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.

2017-07-01

Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

Science.gov (United States)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

Science.gov (United States)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

KAUST Repository

Wheeler, Mary F.; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since

Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD

Science.gov (United States)

Lujan, M.; Alexandru, A.; Freeman, W.; Lee, F. X.

2016-10-01

We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild, and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is αK0 phys=0.356 (74 )(46 )×10-4 fm3 . In contrast, for neutron, the electric polarizability depends strongly on the volume. After removing the finite volume corrections, our neutron polarizability results are in good agreement with chiral perturbation theory. For the connected part of the neutral pion polarizability, the negative trend persists, and it is not due to finite volume effects but likely sea quark charging effects.

Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

Science.gov (United States)

Lai, Changliang; Wang, Junbiao; Liu, Chuang

2014-10-01

Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.

Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

International Nuclear Information System (INIS)

Botchorishvili, Ramaz; Pironneau, Olivier

2003-01-01

We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

Science.gov (United States)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Finite element analysis of optimized H shape spring in a nuclear fuel spacer grid by using contact definition

International Nuclear Information System (INIS)

Kim, Jae-Yong; Yoon, Kyung-Ho

2007-01-01

The primary role of the grid springs in spacer grid is to hold the fuel rods in an appropriate position using friction force and to prevent the fuel rods dropping during reactor operation. The spring force decreases as the fuel burn-up increases since the spring stiffness is degraded due to the high temperature and the irradiation effect in the reactor core. So this phenomenon has to be considered when the initial spring force of grid spring is designed. To check whether the spring have suitable spring force, the characterization test of spring is conducted. In this paper, finite element analysis using contact definition is established for prediction the spring stiffness without test. The test and analysis results are compared to check the availability of finite element model for investing the spring characteristics in assembly condition. (author)

A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

KAUST Repository

Saad, Bilal Mohammed; Saad, Mazen Naufal B M

2014-01-01

We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

KAUST Repository

Saad, Bilal Mohammed

2014-06-28

We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

6th international symposium on finite volumes for complex applications

CERN Document Server

Halama, Jan; Herbin, Raphaèle; Hubert, Florence; Fort, Jaroslav; FVCA 6; Finite Volumes for Complex Applications VI : Problems and perspectives

2011-01-01

Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematical or numerical difficulties, such as true error analysis and adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/diffusion equations and sources. To overcome existing problems and to find solution methods for future applications requires many efforts and always new developments. The goal of The International Symposium on Finite Volumes for Complex Applica

Finite-volume effects due to spatially non-local operators arXiv

CERN Document Server

Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.

Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\\pi (L- \\xi)} $, where $m_\\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \\xi|^n$ that can lead to enhanced volume effects. These ...

A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids

Energy Technology Data Exchange (ETDEWEB)

Bungartz, H.J. [Technische Universitaet Muenchen (Germany)

1996-12-31

In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.

Multi-phase Volume Segmentation with Tetrahedral Mesh

DEFF Research Database (Denmark)

Nguyen Trung, Tuan; Dahl, Vedrana Andersen; Bærentzen, Jakob Andreas

Volume segmentation is efficient for reconstructing material structure, which is important for several analyses, e.g. simulation with finite element method, measurement of quantitative information like surface area, surface curvature, volume, etc. We are concerned about the representations of the 3......D volumes, which can be categorized into two groups: fixed voxel grids [1] and unstructured meshes [2]. Among these two representations, the voxel grids are more popular since manipulating a fixed grid is easier than an unstructured mesh, but they are less efficient for quantitative measurements....... In many cases, the voxel grids are converted to explicit meshes, however the conversion may reduce the accuracy of the segmentations, and the effort for meshing is also not trivial. On the other side, methods using unstructured meshes have difficulty in handling topology changes. To reduce the complexity...

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

Science.gov (United States)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results

International Nuclear Information System (INIS)

Emonot, P.

1992-01-01

In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

Energy Technology Data Exchange (ETDEWEB)

Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)

2016-06-08

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.

Finite volume QCD at fixed topological charge

OpenAIRE

Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya

2007-01-01

In finite volume the partition function of QCD with a given $\\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of...

An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu

2010-07-01

An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)

Solving hyperbolic equations with finite volume methods

CERN Document Server

Vázquez-Cendón, M Elena

2015-01-01

Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software withi...

Dense QCD in a Finite Volume

International Nuclear Information System (INIS)

Yamamoto, Naoki; Kanazawa, Takuya

2009-01-01

We study the properties of QCD at high baryon density in a finite volume where color superconductivity occurs. We derive exact sum rules for complex eigenvalues of the Dirac operator at a finite chemical potential, and show that the Dirac spectrum is directly related to the color superconducting gap Δ. Also, we find a characteristic signature of color superconductivity: an X-shaped spectrum of partition function zeros in the complex quark mass plane near the origin, reflecting the Z(2) L xZ(2) R symmetry of the diquark pairing. Our results are universal in the domain Δ -1 π -1 where L is the linear size of the system and m π is the pion mass at high density.

Finite-volume cumulant expansion in QCD-colorless plasma

Energy Technology Data Exchange (ETDEWEB)

Ladrem, M. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Physics Department, Algiers (Algeria); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ahmed, M.A.A. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Taiz University in Turba, Physics Department, Taiz (Yemen); Alfull, Z.Z. [Taibah University, Physics Department, Faculty of Science, Al-Madinah, Al-Munawwarah (Saudi Arabia); Cherif, S. [ENS-Vieux Kouba (Bachir El-Ibrahimi), Laboratoire de Physique et de Mathematiques Appliquees (LPMA), Algiers (Algeria); Ghardaia University, Sciences and Technologies Department, Ghardaia (Algeria)

2015-09-15

Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point T{sub 0}(V) of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the L{sub mn}-method. The first six cumulants C{sub 1,2,3,4,5,6} with the corresponding under-normalized ratios (skewness Σ, kurtosis κ, pentosis Π{sub ±}, and hexosis H{sub 1,2,3}) and three unnormalized combinations of them, (O = σ{sup 2}κΣ{sup -1},U = σ{sup -2}Σ{sup -1},N = σ{sup 2}κ) are calculated and studied as functions of (T, V). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed.Anumerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value T{sub 0}(V) agrees with that expected T{sub 0}{sup N}(V) from the order parameter and the thermal susceptibility χ{sub T} (T, V), according to the standard procedure of localization to within about 2%. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable. (orig.)

Biquartic Finite Volume Element Metho d Based on Lobatto-Guass Structure

Institute of Scientific and Technical Information of China (English)

Gao Yan-ni; Chen Yan-li

2015-01-01

In this paper, a biquartic finite volume element method based on Lobatto-Guass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimates but also some super-convergent properties are available and could be proved for this method. The numer-ical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method.

Confining dyon gas with finite-volume effects under control

Energy Technology Data Exchange (ETDEWEB)

Bruckmann, Falk [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Dinter, Simon [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ilgenfritz, Ernst-Michael [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Maier, Benjamin; Mueller-Preussker, Michael [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Wagner, Marc [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik

2011-11-15

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature Tfinite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles. (orig.)

Confining dyon gas with finite-volume effects under control

International Nuclear Information System (INIS)

Bruckmann, Falk; Maier, Benjamin; Mueller-Preussker, Michael; Wagner, Marc; Frankfurt Univ.

2011-11-01

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T c , we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles. (orig.)

Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

Energy Technology Data Exchange (ETDEWEB)

Chen, Li; He, Ya-Ling [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Kang, Qinjun [Computational Earth Science Group (EES-16), Los Alamos National Laboratory, Los Alamos, NM (United States); Tao, Wen-Quan, E-mail: wqtao@mail.xjtu.edu.cn [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2013-12-15

A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of which obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.

Grid Generating Automatically Method of Finite Element Analysis for Rotator Structure%旋转体结构有限元网格自动划分法

Institute of Scientific and Technical Information of China (English)

许贤泽

2000-01-01

The finite element analysis is applied to structure and freedom-system analysis. Its grid generating method is important to the finite element modeling,which generates the grid automatically by the sectional division method and gets the finite element grid model, thus accomplishing the pre-work of the finite element analysis.%用有限元法对进行结构和自由度体系进行分析，其网格的生成是建立有限元模型的重要技术，利用分块分割法对网格自动划分，从而形成有限元网格模型，完成有限元分析的前处理。

Lattice study of finite volume effect in HVP for muon g-2

Directory of Open Access Journals (Sweden)

Izubuchi Taku

2018-01-01

Full Text Available We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp,in lattice QCD by comparison with two different volumes, L4 = (5.44 and (8.14 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a−1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

Lattice study of finite volume effect in HVP for muon g-2

Science.gov (United States)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

International Nuclear Information System (INIS)

Meyers, M.D.; Huang, C.-K.; Zeng, Y.; Yi, S.A.; Albright, B.J.

2015-01-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

Science.gov (United States)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

Adaptive moving grid methods for two-phase flow in porous media

KAUST Repository

Dong, Hao

2014-08-01

In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media. © 2013 Elsevier B.V. All rights reserved.

On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

KAUST Repository

Gao, Longfei; Ketcheson, David I.; Keyes, David E.

2017-01-01

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application

Development op finite volume methods for fluid dynamics

International Nuclear Information System (INIS)

Delcourte, S.

2007-09-01

We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)

Development of a hip joint model for finite volume simulations.

Science.gov (United States)

Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A

2014-01-01

This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM.

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

Science.gov (United States)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.

2017-01-01

. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

An enhanced matrix-free edge-based finite volume approach to model structures

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2010-01-01

Full Text Available application to a number of test-cases. As will be demonstrated, the finite volume approach exhibits distinct advantages over the Q4 finite element formulation. This provides an alternative approach to the analysis of solid mechanics and allows...

An enhanced finite volume method to model 2D linear elastic structures

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2014-04-01

Full Text Available . Suliman) Preprint submitted to Applied Mathematical Modelling July 22, 2013 Keywords: finite volume, finite element, locking, error analysis 1. Introduction Since the 1960s, the finite element method has mainly been used for modelling the mechanics... formulation provides higher accuracy 2 for displacement solutions. It is well known that the linear finite element formulation suffers from sensitivity to element aspect ratio or shear locking when subjected to bend- ing [16]. Fallah [8] and Wheel [6] present...

Well balanced finite volume methods for nearly hydrostatic flows

International Nuclear Information System (INIS)

Botta, N.; Klein, R.; Langenberg, S.; Luetzenkirchen, S.

2004-01-01

In numerical approximations of nearly hydrostatic flows, a proper representation of the dominant hydrostatic balance is of crucial importance: unbalanced truncation errors can induce unacceptable spurious motions, e.g., in dynamical cores of models for numerical weather prediction (NWP) in particular near steep topography. In this paper we develop a new strategy for the construction of discretizations that are 'well-balanced' with respect to dominant hydrostatics. The classical idea of formulating the momentum balance in terms of deviations of pressure from a balanced background distribution is realized here through local, time dependent hydrostatic reconstructions. Balanced discretizations of the pressure gradient and of the gravitation source term are achieved through a 'discrete Archimedes' buoyancy principle'. This strategy is applied to extend an explicit standard finite volume Godunov-type scheme for compressible flows with minimal modifications. The resulting method has the following features: (i) It inherits its conservation properties from the underlying base scheme. (ii) It is exactly balanced, even on curvilinear grids, for a large class of near-hydrostatic flows. (iii) It solves the full compressible flow equations without reference to a background state that is defined for an entire vertical column of air. (iv) It is robust with respect to details of the implementation, such as the choice of slope limiting functions, or the particularities of boundary condition discretizations

Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry

DEFF Research Database (Denmark)

Volakis, John L.; Sertel, Kubilay; Jørgensen, Erik

2004-01-01

n this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons of volume integral equation formulations with the finite element-boundary integral method are given in terms of accu...... of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications....

Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

International Nuclear Information System (INIS)

Xi Li-Ying; Chen Huan-Ming; Zheng Fu; Gao Hua; Tong Yang; Ma Zhi

2015-01-01

Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg–Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems. (paper)

Treating network junctions in finite volume solution of transient gas flow models

Science.gov (United States)

Bermúdez, Alfredo; López, Xián; Vázquez-Cendón, M. Elena

2017-09-01

A finite volume scheme for the numerical solution of a non-isothermal non-adiabatic compressible flow model for gas transportation networks on non-flat topography is introduced. Unlike standard Euler equations, the model takes into account wall friction, variable height and heat transfer between the pipe and the environment which are source terms. The case of one single pipe was considered in a previous reference by the authors, [8], where a finite volume method with upwind discretization of the flux and source terms has been proposed in order to get a well-balanced scheme. The main goal of the present paper is to go a step further by considering a network of pipes. The main issue is the treatment of junctions for which container-like 2D finite volumes are introduced. The couplings between pipes (1D) and containers (2D) are carefully described and the conservation properties are analyzed. Numerical tests including real gas networks are solved showing the performance of the proposed methodology.

An efficicient data structure for three-dimensional vertex based finite volume method

Science.gov (United States)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Simulation of pore pressure accumulation under cyclic loading using Finite Volume Method

DEFF Research Database (Denmark)

Tang, Tian; Hededal, Ole

2014-01-01

This paper presents a finite volume implementation of a porous, nonlinear soil model capable of simulating pore pressure accumulation under cyclic loading. The mathematical formulations are based on modified Biot’s coupled theory by substituting the original elastic constitutive model...... with an advanced elastoplastic model suitable for describing monotonic as well as cyclic loading conditions. The finite volume method is applied to discretize these formulations. The resulting set of coupled nonlinear algebraic equations are then solved by a ’segregated’ solution procedure. An efficient return...

Hidden charm molecules in a finite volume

International Nuclear Information System (INIS)

Albaladejo, M.; Hidalgo-Duque, C.; Nieves, J.; Oset, E.

2014-01-01

In the present paper we address the interaction of charmed mesons in hidden charm channels in a finite box. We use the interaction from a recent model based on heavy quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and several methods for the analysis of these levels ("inverse problem") are investigated. (author)

Dual-mixed finite elements for the three-field Stokes model as a finite volume method on staggered grids

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2017-01-01

In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated

A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

Science.gov (United States)

Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

2018-04-01

In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

Finite element analysis of the contact between fuel rod and spacer grid

Energy Technology Data Exchange (ETDEWEB)

Kim, Hyung Kyu; Kim, Young Koon; Kang, Heung Seok; Yoon, Kyung Ho; Song, Kee Nam [Korea Atomic Energy Research Institute, Taejon (Korea)

1999-01-01

For the research on the fretting failure problem of nuclear fuel, the contact length and normal stress field are evaluated for the contact between fuel rod and spacer grid by using the Finite Element Method (FEM). An assumption of semi-infiniteness is necessary for applying the Contact Mechanics which is based on the classical theory of elasticity to the present problem. For the contact problem of fuel fretting, the contact mechanical solutions could be utilized well with sufficient accuracy if the contact bodies (i.e., the cladding tube and the spacer grid) can be assumed as semi-infinite bodies. To this end, the contact length evaluated by FEM is discussed together with the relevant research which concerned the effect of dimension for the validity of the assumption of semi-infiniteness. Normal stress profile on the contact is also studied through comparing the theoretical and the FE results. For the analysis of contact problem by FEM, ANSYS code (Version 5.3) is utilized and the geometry is chosen to be the Hertzian (cylinder-to-cylinder), the strip-to-cylinder and the fuel rod/spacer grid contact (strip-to-tube). Present research will be utilized for accessing the fuel fretting problem by FEM together with the theoretical (i.e., contact mechanical) analysis which has been published as KAERI/TR-1113/98. (author). 15 refs., 44 figs., 4 tabs.

Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

Science.gov (United States)

Schwing, Alan Michael

For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

Science.gov (United States)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Twisted finite-volume corrections to K{sub l3} decays with partially-quenched and rooted-staggered quarks

Energy Technology Data Exchange (ETDEWEB)

Bernard, Claude [Department of Physics, Washington University,One Brookings Drive, Saint Louis (United States); Bijnens, Johan [Department of Astronomy and Theoretical Physics, Lund University,Sölvegatan 14A, SE 223-62 Lund (Sweden); Gámiz, Elvira [CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada,Campus de Fuente Nueva, E-18002 Granada (Spain); Relefors, Johan [Department of Astronomy and Theoretical Physics, Lund University,Sölvegatan 14A, SE 223-62 Lund (Sweden)

2017-03-23

The determination of |V{sub us}| from kaon semileptonic decays requires the value of the form factor f{sub +}(q{sup 2}=0) which can be calculated precisely on the lattice. We provide the one-loop partially quenched chiral perturbation theory expressions both with and without including the effects of staggered quarks for all form factors at finite volume and with partially twisted boundary conditions for both the vector current and scalar density matrix elements at all q{sup 2}. We point out that at finite volume there are more form factors than just f{sub +} and f{sub −} for the vector current matrix element but that the Ward identity is fully satisfied. The size of the finite-volume corrections at present lattice sizes is small. This will help improve the lattice determination of f{sub +}(q{sup 2}=0) since the finite-volume error is the dominant error source for some calculations. The size of the finite-volume corrections may be estimated on a single lattice ensemble by comparing results for various twist choices.

Comparison of different precondtioners for nonsymmtric finite volume element methods

Energy Technology Data Exchange (ETDEWEB)

Mishev, I.D.

1996-12-31

We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.

Finite Volume Effect of Baryons in Strange Hadronic Matter

Institute of Scientific and Technical Information of China (English)

SUN Bao-Xi; LI Lei; NING Ping-Zhi; ZHAO En-Guang

2001-01-01

The finite volume effect of baryons in strange hadronic matter (SHM) is studied within the framework of relativistic mean-field theory. As this effect is concerned, the saturation density of SHM turns lower, and the binding energy per baryon decreases. Its influence to the compression modulus of SHM is also discussed.

A computationally efficient 3D finite-volume scheme for violent liquid–gas sloshing

CSIR Research Space (South Africa)

Oxtoby, Oliver F

2015-10-01

Full Text Available We describe a semi-implicit volume-of-fluid free-surface-modelling methodology for flow problems involving violent free-surface motion. For efficient computation, a hybrid-unstructured edge-based vertex-centred finite volume discretisation...

Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

International Nuclear Information System (INIS)

Hof, Bas van’t; Veldman, Arthur E.P.

2012-01-01

The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Extrusion Process by Finite Volume Method Using OpenFoam Software

International Nuclear Information System (INIS)

Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose; Ivankovic, Alojz

2011-01-01

The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.

A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

KAUST Repository

Paszyński, Maciej R.

2013-04-01

This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

KAUST Repository

Paszyński, Maciej R.; Calo, Victor M.; Pardo, David

2013-01-01

This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

Finite volume at two-loops in chiral perturbation theory

International Nuclear Information System (INIS)

Bijnens, Johan; Rössler, Thomas

2015-01-01

We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.

A Monte Carlo method and finite volume method coupled optical simulation method for parabolic trough solar collectors

International Nuclear Information System (INIS)

Liang, Hongbo; Fan, Man; You, Shijun; Zheng, Wandong; Zhang, Huan; Ye, Tianzhen; Zheng, Xuejing

2017-01-01

Highlights: •Four optical models for parabolic trough solar collectors were compared in detail. •Characteristics of Monte Carlo Method and Finite Volume Method were discussed. •A novel method was presented combining advantages of different models. •The method was suited to optical analysis of collectors with different geometries. •A new kind of cavity receiver was simulated depending on the novel method. -- Abstract: The PTC (parabolic trough solar collector) is widely used for space heating, heat-driven refrigeration, solar power, etc. The concentrated solar radiation is the only energy source for a PTC, thus its optical performance significantly affects the collector efficiency. In this study, four different optical models were constructed, validated and compared in detail. On this basis, a novel coupled method was presented by combining advantages of these models, which was suited to carry out a mass of optical simulations of collectors with different geometrical parameters rapidly and accurately. Based on these simulation results, the optimal configuration of a collector with highest efficiency can be determined. Thus, this method was useful for collector optimization and design. In the four models, MCM (Monte Carlo Method) and FVM (Finite Volume Method) were used to initialize photons distribution, as well as CPEM (Change Photon Energy Method) and MCM were adopted to describe the process of reflecting, transmitting and absorbing. For simulating reflection, transmission and absorption, CPEM was more efficient than MCM, so it was utilized in the coupled method. For photons distribution initialization, FVM saved running time and computation effort, whereas it needed suitable grid configuration. MCM only required a total number of rays for simulation, whereas it needed higher computing cost and its results fluctuated in multiple runs. In the novel coupled method, the grid configuration for FVM was optimized according to the “true values” from MCM of

A non-perturbative analysis in finite volume gauge theory

International Nuclear Information System (INIS)

Koller, J.; State Univ. of New York, Stony Brook; Van Baal, P.; State Univ. of New York, Stony Brook

1988-01-01

We discuss SU(2) gauge theory on a three-torus using a finite volume expansion. Our discovery of natural coordinates allows us to obtain continuum results in a region where Monte Carlo data are also available. The obtained results agree well with the perturbative and semiclassical analysis for small volumes, and there is fair agreement with the Monte Carlo results in intermediate volumes. The simple picture which emerges for the approximate low energy dynamics is that of three interacting particles enclosed in a sphere, with zero total 'angular momentum'. The validity of an adiabatic approximation is investigated. The fundamentally new understanding gained, is that non-perturbative dynamics can be incorporated by imposing boundary conditions which arise through the nontrivial topology of configuration space. (orig.)

A numerical formulation using unstructured grids for modeling two-phase flows in porous media considering heterogeneities and capillarity effects

International Nuclear Information System (INIS)

Hurtado, F.S.V.; Maliska, C.R.

2005-01-01

This paper briefly describes a two-dimensional numerical formulation using unstructured grids, developed for simulating two-phase immiscible displacements in porous media. The Element-based Finite Volume Method (EbFVM) is used for discretizing the model differential equations. (authors)

A numerical formulation using unstructured grids for modeling two-phase flows in porous media considering heterogeneities and capillarity effects

Energy Technology Data Exchange (ETDEWEB)

Hurtado, F.S.V.; Maliska, C.R. [Santa Catarina Federal Univ., Computational Fluid Dynamics Lab., Mechanical Engineering Dept., Florianopolis, SC (Brazil)

2005-07-01

This paper briefly describes a two-dimensional numerical formulation using unstructured grids, developed for simulating two-phase immiscible displacements in porous media. The Element-based Finite Volume Method (EbFVM) is used for discretizing the model differential equations. (authors)

A lattice Boltzmann coupled to finite volumes method for solving phase change problems

Directory of Open Access Journals (Sweden)

El Ganaoui Mohammed

2009-01-01

Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.

Adaptive solution of the multigroup diffusion equation on irregular structured grids using a conforming finite element method formulation

International Nuclear Information System (INIS)

Ragusa, J. C.

2004-01-01

In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)

Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

International Nuclear Information System (INIS)

Knudsen, W.C.

1992-01-01

The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gases consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor

Hybrid finite-volume/transported PDF method for the simulation of turbulent reactive flows

Science.gov (United States)

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.

Finite-volume simulation of the flow around a sailing boat with unsteady motion; Hiteijo undo wo okonau hansotei no yuten taisekiho ni yoru simulation

Energy Technology Data Exchange (ETDEWEB)

Akimoto, H. [Tottori University, Tottori (Japan). Faculty of Engineering

1997-06-01

A new simulation code WISDAM-7 is developed to simulate performance of a sailing boat moving three-dimensionally on a free surface. It adequately predicts forces acting on each element, such as hull, sail, keel and rudder, and use them as the inputs to solve equations of hull motion of 6 freedoms. Its major features are the grid system fit for both free and hull surfaces, generation of discrete space by the finite-volume method, handling of the velocity vectors directly as those in the Descartes system, velocity and pressure placed at the cell center, use of the moving grid system for free and object surfaces, and use of equations of hull motion of 6 freedoms. It is confirmed by comparing simulated motion of an IACC class yacht with the observed surface pressure distributions in the test tank that the new method satisfies the basic requirements for simulation of sailing boat motion and expands the applicable range of CFD to general motion conditions. 8 refs., 18 figs.

Precise determination of universal finite volume observables in the Gross-Neveu model

Energy Technology Data Exchange (ETDEWEB)

Korzec, T.

2007-01-26

The Gross-Neveu model is a quantum field theory in two space time dimensions that shares many features with quantum chromo dynamics. In this thesis the continuum model and its discretized versions are reviewed and a finite volume renormalization scheme is introduced and tested. Calculations in the limit of infinitely many fermion flavors as well as perturbative computations are carried out. In extensive Monte-Carlo simulations of the one flavor and the four flavor lattice models with Wilson fermions a set of universal finite volume observables is calculated to a high precision. In the one flavor model which is equivalent to the massless Thirring model the continuum extrapolated Monte-Carlo results are confronted with an exact solution of the model. (orig.)

Precise determination of universal finite volume observables in the Gross-Neveu model

International Nuclear Information System (INIS)

Korzec, T.

2007-01-01

The Gross-Neveu model is a quantum field theory in two space time dimensions that shares many features with quantum chromo dynamics. In this thesis the continuum model and its discretized versions are reviewed and a finite volume renormalization scheme is introduced and tested. Calculations in the limit of infinitely many fermion flavors as well as perturbative computations are carried out. In extensive Monte-Carlo simulations of the one flavor and the four flavor lattice models with Wilson fermions a set of universal finite volume observables is calculated to a high precision. In the one flavor model which is equivalent to the massless Thirring model the continuum extrapolated Monte-Carlo results are confronted with an exact solution of the model. (orig.)

A point-value enhanced finite volume method based on approximate delta functions

Science.gov (United States)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

Science.gov (United States)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Maxwell's equations in axisymmetrical geometry: coupling H(curl) finite element in volume and H(div) finite element in surface. The numerical code FuMel

International Nuclear Information System (INIS)

Cambon, S.; Lacoste, P.

2011-01-01

We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)

Comparative study of finite element method, isogeometric analysis, and finite volume method in elastic wave propagation of stress discontinuities

Czech Academy of Sciences Publication Activity Database

Berezovski, A.; Kolman, Radek; Blažek, Jiří; Kopačka, Ján; Gabriel, Dušan; Plešek, Jiří

2014-01-01

Roč. 19, č. 12 (2014) ISSN 1435-4934. [European Conference on Non-Destructive Testing (ECNDT 2014) /11./. Praha, 06.10.2014-10.10.2014] R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315 Institutional support: RVO:61388998 Keywords : elastic wave propagation * finite element method * isogeometric analysis * finite volume method * stress discontinuities * spurious oscillations Subject RIV: JR - Other Machinery http://www.ndt.net/events/ECNDT2014/app/content/Paper/25_Berezovski_Rev1.pdf

Hadronic electroweak processes in a finite volume

Energy Technology Data Exchange (ETDEWEB)

Agadjanov, Andria

2017-11-07

In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject, we formulate a framework for the extraction of the ΔNγ{sup *} as well as the B→K{sup *} transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the

Hadronic electroweak processes in a finite volume

International Nuclear Information System (INIS)

Agadjanov, Andria

2017-01-01

In the present thesis, we study a number of hadronic electroweak processes in a finite volume. Our work is motivated by the ongoing and future lattice simulations of the strong interaction theory called quantum chromodynamics. According to the available computational resources, the numerical calculations are necessarily performed on lattices with a finite spatial extension. The first part of the thesis is based on the finite volume formalism which is a standard method to investigate the processes with the final state interactions, and in particular, the elastic hadron resonances, on the lattice. Throughout the work, we systematically apply the non-relativistic effective field theory. The great merit of this approach is that it encodes the low-energy dynamics directly in terms of the effective range expansion parameters. After a brief introduction into the subject, we formulate a framework for the extraction of the ΔNγ * as well as the B→K * transition form factors from lattice data. Both processes are of substantial phenomenological interest, including the search for physics beyond the Standard Model. Moreover, we provide a proper field-theoretical definition of the resonance matrix elements, and advocate it in comparison to the one based on the infinitely narrow width approximation. In the second part we consider certain aspects of the doubly virtual nucleon Compton scattering. The main objective of the work is to answer the question whether there is, in the Regge language, a so-called fixed pole in the process. To answer this question, the unknown subtraction function, which enters one of the dispersion relations for the invariant amplitudes, has to be determined. The external field method provides a feasible approach to tackle this problem on the lattice. Considering the nucleon in a periodic magnetic field, we derive a simple relation for the ground state energy shift up to a second order in the field strength. The obtained result encodes the value of the

Large parallel volumes of finite and compact sets in d-dimensional Euclidean space

DEFF Research Database (Denmark)

Kampf, Jürgen; Kiderlen, Markus

The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric...

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

Science.gov (United States)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

Directory of Open Access Journals (Sweden)

K. Yapici

2013-12-01

Full Text Available In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies.

A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

International Nuclear Information System (INIS)

Banks, J.W.; Hittinger, J.A.

2010-01-01

Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections

International Nuclear Information System (INIS)

Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.

2011-01-01

This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)

A Monotone, Higher-Order Accurate, Fixed-Grid Finite-Volume Method for Advection Problems with Moving Boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2008-01-01

textabstractIn this paper, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is

On fully multidimensional and high order non oscillatory finite volume methods, I

International Nuclear Information System (INIS)

Lafon, F.

1992-11-01

A fully multidimensional flux formulation for solving nonlinear conservation laws of hyperbolic type is introduced to perform calculations on unstructured grids made of triangular or quadrangular cells. Fluxes are computed across dual median cells with a multidimensional 2D Riemann Solver (R2D Solver) whose intermediate states depend on either a three (on triangle R2DT solver) of four (on quadrangle, R2DQ solver) state solutions prescribed on the three or four sides of a gravity cell. Approximate Riemann solutions are computed via a linearization process of Roe's type involving multidimensional effects. Moreover, a monotonous scheme using stencil and central Lax-Friedrichs corrections on sonic curves are built in. Finally, high order accurate ENO-like (Essentially Non Oscillatory) reconstructions using plane and higher degree polynomial limitations are defined in the set up of finite element Lagrange spaces P k and Q k for k≥0, on triangles and quadrangles, respectively. Numerical experiments involving both linear and nonlinear conservation laws to be solved on unstructured grids indicate the ability of our techniques when dealing with strong multidimensional effects. An application to Euler's equations for the Mach three step problem illustrates the robustness and usefulness of our techniques using triangular and quadrangular grids. (Author). 33 refs., 13 figs

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

International Nuclear Information System (INIS)

Tan, Sirui; Huang, Lianjie

2014-01-01

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion

Development and application of a parallel finite volume method for flow simulation on unstructured grids with local refinement; Entwicklung und Anwendung eines parallelen Finite-Volumen-Verfahrens zur Stroemungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung

Energy Technology Data Exchange (ETDEWEB)

Seidl, V.

1997-11-01

A finite vomume method for calculation of steady and unsteady flow on unstructured grids is parallelized by local spatial and time decomposition. In the first case, a parallel variant of the conjugated gradient method with multiple local preconditioning is formulated and analyzed. The method is tested for simple applications (e.g. flow around a cylinder). The second part of the publication describes a direct numerical simulation of turbulent flow around a sphere at a Reynolds number of 5000 (based on flow velocity and sphere diameter). Current and Reynolds-averaged flow fields are discussed. Particular emphasis is placed on coordinate-independent representation of the anisotropy ratios of the Reynolds tensor and dissipation tensor. (orig.) [Deutsch] Ein Finite-Volumen-Verfahren fuer die Berechnung stationaerer und instationaerer Stroemungen auf unstrukturierten Netzen wird durch Gebietszerlegung im Raum und Zeit parallelisiert. Fuer die raeumliche Zerlegung wird eine parallele Variante der konjugierten Gradienten Methode mit mehrfacher, lokaler Vorkonditionierung formuliert und analysiert. Anhand einfacher Anwendungsbeispiele (Zylinderumstroemung, deckelgetriebene Nischenstroemung) wird das entwickelte Gesamtverfahren getestet und seine Effizienz bestimmt. Der zweite Teil der Arbeit beschreibt eine direkte numerische Simulation der turbulenten Kugelumstroemung bei einer Reynolds-Zahl von 5 000 (basierend auf Anstroemgeschwindigkeit und Kugeldurchmesser). In der Ergebnisauswertung werden augenblickliche und Reynolds-gemittelte Stroemungsfelder diskutiert und besonderer Wert auf eine koordinatenunabhaengige Darstellung der Anisotropieverhaeltnisse des Reynolds-Tensors und des Dissipationstensors gelegt. (orig.)

Multichannel 1 → 2 transition amplitudes in a finite volume

Energy Technology Data Exchange (ETDEWEB)

Briceno, Raul A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Hansen, Maxwell T. [Univ. of Washington, Seattle, WA (United States); Walker-Loud, Andre [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States)

2015-02-03

We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B⁰ → K*l⁺l⁻) or meson photo production (e.g., πγ* → ππ). We observe that, while the spectrum solely depends upon the on-shell scattering amplitude, the correlation functions also depend upon off-shell amplitudes. The main result of this work is a non-perturbative generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular-momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including two processes mentioned above as well as examples where the final state is an admixture of two open channels.

MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

KAUST Repository

Iliev, Oleg

2014-01-01

This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid with a sophisticated finite volume method, namely MPFA O-method, is used to discretize the system of equations. Numerical results for two examples are presented, namely, channel flow and flow in a ring with a rolled porous medium. © Springer International Publishing Switzerland 2014.

Evaluation of a new welding process used to joint grids thimbles properly in 16 x 16 fuel assemblies, using the finite element method

Energy Technology Data Exchange (ETDEWEB)

Schettino, Carlos Frederico Mattos, E-mail: DPNcarlosschettino@inb.gov.b [Industrias Nucleares do Brasil S.A. (DPN/INB), Resende, RJ (Brazil). Diretoria de Producao Nuclear; Silva, Marcio Adriano Coelho da, E-mail: marcio.adriano@inb.gov.b [Industrias Nucleares do Brasil S.A. (GEACON/INB), Resende, RJ (Brazil). Gerencia de Analise Tecnica do Combustivel

2011-07-01

The present work aims to evaluate structurally the new welding process used to join the grids to the guide thimbles properly in 16 x 16 fuel assemblies. This new process is an increase of the number of welding points, 4 to 8, between grids and guide thimbles, giving more stiffness to the whole structure. A finite element model of the fuel assembly design was generated in the program ANSYS 12.1. To build this model were used elements BEAM-4 and several spring type elements. The analysis covered specific loads and displacements, simulating the boundaries conditions found during small deflection acting on the entire structure. The method used to development this analysis was the simulation of a finite element model performing a fuel assembly with four weld points on each grid cell containing the guide thimbles, and then the results of it was compare with another model, with eight weld points on each grid cell containing the guide thimbles. The behavior of the structure under the acting displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the new grid to guide thimble welding process improve the dimensional stability when submitted to loads and displacements required on the fuel assembly design. The performed analysis provided INB to get more information of extreme importance, for the continuity of the development of new process of manufacturing and to improve the design of the current fuel assemblies used in reactors. (author)

Evaluation of a new welding process used to joint grids thimbles properly in 16 x 16 fuel assemblies, using the finite element method

International Nuclear Information System (INIS)

Schettino, Carlos Frederico Mattos; Silva, Marcio Adriano Coelho da

2011-01-01

The present work aims to evaluate structurally the new welding process used to join the grids to the guide thimbles properly in 16 x 16 fuel assemblies. This new process is an increase of the number of welding points, 4 to 8, between grids and guide thimbles, giving more stiffness to the whole structure. A finite element model of the fuel assembly design was generated in the program ANSYS 12.1. To build this model were used elements BEAM-4 and several spring type elements. The analysis covered specific loads and displacements, simulating the boundaries conditions found during small deflection acting on the entire structure. The method used to development this analysis was the simulation of a finite element model performing a fuel assembly with four weld points on each grid cell containing the guide thimbles, and then the results of it was compare with another model, with eight weld points on each grid cell containing the guide thimbles. The behavior of the structure under the acting displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the new grid to guide thimble welding process improve the dimensional stability when submitted to loads and displacements required on the fuel assembly design. The performed analysis provided INB to get more information of extreme importance, for the continuity of the development of new process of manufacturing and to improve the design of the current fuel assemblies used in reactors. (author)

The low-energy effective theory of QCD at small quark masses in a finite volume

Energy Technology Data Exchange (ETDEWEB)

Lehner, Christoph

2010-01-15

At low energies the theory of quantum chromodynamics (QCD) can be described effectively in terms of the lightest particles of the theory, the pions. This approximation is valid for temperatures well below the mass difference of the pions to the next heavier particles. We study the low-energy effective theory at very small quark masses in a finite volume V. The corresponding perturbative expansion in 1/{radical}(V) is called {epsilon} expansion. At each order of this expansion a finite number of low-energy constants completely determine the effective theory. These low-energy constants are of great phenomenological importance. In the leading order of the {epsilon} expansion, called {epsilon} regime, the theory becomes zero-dimensional and is therefore described by random matrix theory (RMT). The dimensionless quantities of RMT are mapped to dimensionful quantities of the low-energy effective theory using the leading-order lowenergy constants {sigma} and F. In this way {sigma} and F can be obtained from lattice QCD simulations in the '' regime by a fit to RMT predictions. For typical volumes of state-of-the-art lattice QCD simulations, finite-volume corrections to the RMT prediction cannot be neglected. These corrections can be calculated in higher orders of the {epsilon} expansion. We calculate the finite-volume corrections to {sigma} and F at next-to-next-to-leading order in the {epsilon} expansion. We also discuss non-universal modifications of the theory due to the finite volume. These results are then applied to lattice QCD simulations, and we extract {sigma} and F from eigenvalue correlation functions of the Dirac operator. As a side result, we provide a proof of equivalence between the parametrization of the partially quenched low-energy effective theory without singlet particle and that of the super-Riemannian manifold used earlier in the literature. Furthermore, we calculate a special version of the massless sunset diagram at finite volume without

Infinite volume of noncommutative black hole wrapped by finite surface

Energy Technology Data Exchange (ETDEWEB)

Zhang, Baocheng, E-mail: zhangbc.zhang@yahoo.com [School of Mathematics and Physics, China University of Geosciences, Wuhan 430074 (China); You, Li, E-mail: lyou@mail.tsinghua.edu.cn [State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084 (China)

2017-02-10

The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein–Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.

A Parallel Multiblock Structured Grid Method with Automated Interblocked Unstructured Grids for Chemically Reacting Flows

Science.gov (United States)

Spiegel, Seth Christian

An automated method for using unstructured grids to patch non- C0 interfaces between structured blocks has been developed in conjunction with a finite-volume method for solving chemically reacting flows on unstructured grids. Although the standalone unstructured solver, FVFLO-NCSU, is capable of resolving flows for high-speed aeropropulsion devices with complex geometries, unstructured-mesh algorithms are inherently inefficient when compared to their structured counterparts. However, the advantages of structured algorithms in developing a flow solution in a timely manner can be negated by the amount of time required to develop a mesh for complex geometries. The global domain can be split up into numerous smaller blocks during the grid-generation process to alleviate some of the difficulties in creating these complex meshes. An even greater abatement can be found by allowing the nodes on abutting block interfaces to be nonmatching or non-C 0 continuous. One code capable of solving chemically reacting flows on these multiblock grids is VULCAN, which uses a nonconservative approach for patching non-C0 block interfaces. The developed automated unstructured-grid patching algorithm has been installed within VULCAN to provide it the capability of a fully conservative approach for patching non-C0 block interfaces. Additionally, the FVFLO-NCSU solver algorithms have been deeply intertwined with the VULCAN source code to solve chemically reacting flows on these unstructured patches. Finally, the CGNS software library was added to the VULCAN postprocessor so structured and unstructured data can be stored in a single compact file. This final upgrade to VULCAN has been successfully installed and verified using test cases with particular interest towards those involving grids with non- C0 block interfaces.

Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method

OpenAIRE

Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N.

2016-01-01

We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely det...

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

Science.gov (United States)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Analyses of the Collapse Behavior of a Spacer Grid

International Nuclear Information System (INIS)

Jang, Myung-Geun; Na, Geum Ju; Jag, Yeon-Hui; Kim, Hee Cheol; Kim, Jong-Bong; Kim, Jaeyoug

2016-01-01

In order to investigate the protection capability of a spacer grid assembly for impact load, a hammer impact test has been carried out. The crush strength is measured in the hammer impact test. Song et al. carried out the experiment and finite element analysis for the hammer impact test for various weld line depth. Park et al. designed the spacer grid shape to get required crush strength via finite element analysis. Song et al. also optimized the spacer grid shape to maximize the crush strength, and carried out the finite element analysis for the hammer impact test considering the weld properties. Kim et al. carried out finite element analysis for various guide tube hole shape and compared the crush shape and crush strength. In this study, the effect of shape defect on the crush behavior in the hammer impact test is investigated. The spacer grid cannot be exactly the square. Therefore a lateral displacement (imperfection) is imposed to square spacer grid and then hammer impact is carried out. The effect of the lateral imperfection on the crush strength is investigated. The effect of the shape defect on the crushing behavior in the hammer impact test is investigated by finite element analysis. It is shown that the collapse become severe as the lateral imperfection displacement increases, especially when the imperfection is greater than or equal to 0.7 mm

Charged hadrons in local finite-volume QED+QCD with C* boundary conditions

CERN Document Server

Lucini, Biagio; Ramos, Alberto; Tantalo, Nazario

2016-01-01

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charg...

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

Science.gov (United States)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients

Science.gov (United States)

Batty, Christopher

2017-02-01

This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L∞ norm.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

Science.gov (United States)

Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

2018-06-01

In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

A mixed Fourier–Galerkin–finite-volume method to solve the fluid dynamics equations in cylindrical geometries

International Nuclear Information System (INIS)

Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M

2012-01-01

We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)

A finite integration method for conformal, structured-grid, electromagnetic simulation

International Nuclear Information System (INIS)

Cooke, S.J.; Shtokhamer, R.; Mondelli, A.A.; Levush, B.

2006-01-01

We describe a numerical scheme for solving Maxwell's equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwell's equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwell's equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faraday's law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Ampere's law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwell's equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295-319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi-Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401-425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi

Angular finite volume method for solving the multigroup transport equation with piecewise average scattering cross sections

Energy Technology Data Exchange (ETDEWEB)

Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)

2011-07-01

This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)

Development op finite volume methods for fluid dynamics; Developpement de methodes de volumes finis pour la mecanique des fluides

Energy Technology Data Exchange (ETDEWEB)

Delcourte, S

2007-09-15

We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)

A finite volume study for pressure waves propagation in a straight section of pipeline with caviation

Directory of Open Access Journals (Sweden)

C Silva

2016-09-01

Full Text Available The main objective of this research was to study the pressure waves propagation generated by a sudden closure of a valve in a straight pipe. The physical model consisted of a head tank that can be pressurized with air, and a copper pipe with a fast-closing ball valve on the downstream end of the line. The cavitation and fluid-structure interaction phenomena were integrated analytically into the one-dimensional continuity and momentum equations, by assuming that the fluid density and the flow area vary with pressure. These equations were solved through a high resolution finite volume method, in combination with others numerical methods such as Taylor series expansion, Newton method, Simpson's Rule and quadratic interpolation. Due to the complexity of the solution procedure, a computational code in FORTRAN 95 language was developed in order to obtain numerical solutions. Several discretizations of the computational grid were achieved to assess their impact on the solution. The model was validated with experimental data and analytic results obtained by other researchers. Several pressure values, in different points of pipe, were compared, and an excellent agreement was found for both cases.

3D Staggered-Grid Finite-Difference Simulation of Acoustic Waves in Turbulent Moving Media

Science.gov (United States)

Symons, N. P.; Aldridge, D. F.; Marlin, D.; Wilson, D. K.; Sullivan, P.; Ostashev, V.

2003-12-01

Acoustic wave propagation in a three-dimensional heterogeneous moving atmosphere is accurately simulated with a numerical algorithm recently developed under the DOD Common High Performance Computing Software Support Initiative (CHSSI). Sound waves within such a dynamic environment are mathematically described by a set of four, coupled, first-order partial differential equations governing small-amplitude fluctuations in pressure and particle velocity. The system is rigorously derived from fundamental principles of continuum mechanics, ideal-fluid constitutive relations, and reasonable assumptions that the ambient atmospheric motion is adiabatic and divergence-free. An explicit, time-domain, finite-difference (FD) numerical scheme is used to solve the system for both pressure and particle velocity wavefields. The atmosphere is characterized by 3D gridded models of sound speed, mass density, and the three components of the wind velocity vector. Dependent variables are stored on staggered spatial and temporal grids, and centered FD operators possess 2nd-order and 4th-order space/time accuracy. Accurate sound wave simulation is achieved provided grid intervals are chosen appropriately. The gridding must be fine enough to reduce numerical dispersion artifacts to an acceptable level and maintain stability. The algorithm is designed to execute on parallel computational platforms by utilizing a spatial domain-decomposition strategy. Currently, the algorithm has been validated on four different computational platforms, and parallel scalability of approximately 85% has been demonstrated. Comparisons with analytic solutions for uniform and vertically stratified wind models indicate that the FD algorithm generates accurate results with either a vanishing pressure or vanishing vertical-particle velocity boundary condition. Simulations are performed using a kinematic turbulence wind profile developed with the quasi-wavelet method. In addition, preliminary results are presented

SU(N) multi-Skyrmions at finite volume

Energy Technology Data Exchange (ETDEWEB)

Canfora, Fabrizio [Centro de Estudios Cientificos (CECS), Casilla, Valdivia (Chile); Di Mauro, Marco; Naddeo, Adele [Universita di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Fisciano, SA (Italy); Kurkov, Maxim A. [Universita di Napoli Federico II, Dipartimento di Matematica e Applicazioni ' ' R. Caccioppoli' ' , Napoli (Italy)

2015-09-15

We study multi-soliton solutions of the fourdimensional SU(N) Skyrme model by combining the hedgehog ansatz for SU(N) based on the harmonic maps of S{sup 2} into CP{sup N-1} and a geometrical trick which allows to analyze explicitly finite-volume effects without breaking the relevant symmetries of the ansatz. The geometric set-up allows to introduce a parameter which is related to the ft Hooft coupling of a suitable large N limit, in which N → ∞ and the curvature of the background metric approaches zero, in such a way that their product is constant. The relevance of such a parameter to the physics of the system is pointed out. In particular, we discuss how the discrete symmetries of the configurations depend on it. (orig.)

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

International Nuclear Information System (INIS)

Bijnens, Johan; Rössler, Thomas

2015-01-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

Energy Technology Data Exchange (ETDEWEB)

Bijnens, Johan; Rössler, Thomas [Department of Astronomy and Theoretical Physics, Lund University,Sölvegatan 14A, SE 223-62 Lund (Sweden)

2015-11-16

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.

Exact finite volume expectation values of local operators in excited states

Energy Technology Data Exchange (ETDEWEB)

Pozsgay, B. [MTA-BME “Momentum” Statistical Field Theory Research Group,Budafoki út 8, 1111 Budapest (Hungary); Szécsényi, I.M. [Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE (United Kingdom); Institute of Theoretical Physics, Eötvös Loránd University,Pázmány Péter sétány 1/A, 1117 Budapest (Hungary); Takács, G. [MTA-BME “Momentum” Statistical Field Theory Research Group,Budafoki út 8, 1111 Budapest (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics,Budafoki út 8, 1111 Budapest (Hungary)

2015-04-07

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Exact finite volume expectation values of local operators in excited states

International Nuclear Information System (INIS)

Pozsgay, B.; Szécsényi, I.M.; Takács, G.

2015-01-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

Science.gov (United States)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

Wheeler, Mary Fanett

2012-02-03

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.

A NEW THREE-DIMENSIONAL SOLAR WIND MODEL IN SPHERICAL COORDINATES WITH A SIX-COMPONENT GRID

Energy Technology Data Exchange (ETDEWEB)

Feng, Xueshang; Zhang, Man; Zhou, Yufen, E-mail: fengx@spaceweather.ac.cn [SIGMA Weather Group, State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China)

2014-09-01

In this paper, we introduce a new three-dimensional magnetohydrodynamics numerical model to simulate the steady state ambient solar wind from the solar surface to 215 R {sub s} or beyond, and the model adopts a splitting finite-volume scheme based on a six-component grid system in spherical coordinates. By splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, a finite volume method can be used for the fluid part and a constrained-transport method able to maintain the divergence-free constraint on the magnetic field can be used for the magnetic induction part. This new second-order model in space and time is validated when modeling the large-scale structure of the solar wind. The numerical results for Carrington rotation 2064 show its ability to produce structured solar wind in agreement with observations.

Volume-of-fluid algorithm on a non-orthogonal grid

International Nuclear Information System (INIS)

Jang, W.; Lien, F.S.; Ji, H.

2005-01-01

In the present study, a novel VOF method on a non-orthogonal grid is proposed and tested for several benchmark problems, including a simple translation test, a reversed single vortex flow and a shearing flow, with the objective to demonstrate the feasibility and accuracy of the present approach. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved. The sensitivity of various methods to the L 1 error in evaluating the interface normal and volume flux at each face of a non-orthogonal cell is examined. Time integration methods based on the operator-splitting approach in curvilinear coordinates, including the explicit-implicit (EX-IM) and explicit-explicit (EX-EX) combinations, are tested. (author)

A finite volume procedure for fluid flow, heat transfer and solid-body stress analysis

KAUST Repository

Jagad, P. I.; Puranik, B. P.; Date, A. W.

2018-01-01

A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell

Monte Carlo Finite Volume Element Methods for the Convection-Diffusion Equation with a Random Diffusion Coefficient

Directory of Open Access Journals (Sweden)

Qian Zhang

2014-01-01

Full Text Available The paper presents a framework for the construction of Monte Carlo finite volume element method (MCFVEM for the convection-diffusion equation with a random diffusion coefficient, which is described as a random field. We first approximate the continuous stochastic field by a finite number of random variables via the Karhunen-Loève expansion and transform the initial stochastic problem into a deterministic one with a parameter in high dimensions. Then we generate independent identically distributed approximations of the solution by sampling the coefficient of the equation and employing finite volume element variational formulation. Finally the Monte Carlo (MC method is used to compute corresponding sample averages. Statistic error is estimated analytically and experimentally. A quasi-Monte Carlo (QMC technique with Sobol sequences is also used to accelerate convergence, and experiments indicate that it can improve the efficiency of the Monte Carlo method.

Wavefront-ray grid FDTD algorithm

OpenAIRE

ÇİYDEM, MEHMET

2016-01-01

A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Num...

Axial coupling constant of the nucleon for two flavours of dynamical quarks in finite and infinite volume

International Nuclear Information System (INIS)

Khan, A.A.; Goeckeler, M.; Haegler, P.

2006-03-01

We present data for the axial coupling constant g A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point. (Orig.)

Axial coupling constant of the nucleon for two flavours of dynamical quarks in finite and infinite volume

Energy Technology Data Exchange (ETDEWEB)

Khan, A.A.; Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Haegler, P. [Technische Univ. Muenchen (DE). Physik-Department, Theoretische Physik] (and others)

2006-03-15

We present data for the axial coupling constant g{sub A} of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g{sub A} based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavours. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point. (Orig.)

Finite volume gauge theory partition functions in three dimensions

International Nuclear Information System (INIS)

Szabo, Richard J.

2005-01-01

We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the ε-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous considerations based on random matrix theory. They are used to describe the microscopic spectral correlation functions and smallest eigenvalue distributions of the QCD 3 Dirac operator, as well as the corresponding massive spectral sum rules

Exact finite volume expectation values of \\overline{Ψ}Ψ in the massive Thirring model from light-cone lattice correlators

Science.gov (United States)

Hegedűs, Árpád

2018-03-01

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

Energy Technology Data Exchange (ETDEWEB)

Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

1996-12-31

An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids

Science.gov (United States)

Wang, Feiyan; Morten, Jan Petter; Spitzer, Klaus

2018-05-01

In this paper, we present a recently developed anisotropic 3-D inversion framework for interpreting controlled-source electromagnetic (CSEM) data in the frequency domain. The framework integrates a high-order finite-element forward operator and a Gauss-Newton inversion algorithm. Conductivity constraints are applied using a parameter transformation. We discretize the continuous forward and inverse problems on unstructured grids for a flexible treatment of arbitrarily complex geometries. Moreover, an unstructured mesh is more desirable in comparison to a single rectilinear mesh for multisource problems because local grid refinement will not significantly influence the mesh density outside the region of interest. The non-uniform spatial discretization facilitates parametrization of the inversion domain at a suitable scale. For a rapid simulation of multisource EM data, we opt to use a parallel direct solver. We further accelerate the inversion process by decomposing the entire data set into subsets with respect to frequencies (and transmitters if memory requirement is affordable). The computational tasks associated with each data subset are distributed to different processes and run in parallel. We validate the scheme using a synthetic marine CSEM model with rough bathymetry, and finally, apply it to an industrial-size 3-D data set from the Troll field oil province in the North Sea acquired in 2008 to examine its robustness and practical applicability.

On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

KAUST Repository

Gao, Longfei

2017-10-26

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

Science.gov (United States)

Gao, Longfei; Ketcheson, David; Keyes, David

2018-02-01

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

Science.gov (United States)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

Science.gov (United States)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Finite-volume and partial quenching effects in the magnetic polarizability of the neutron

Science.gov (United States)

Hall, J. M. M.; Leinweber, D. B.; Young, R. D.

2014-03-01

There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modeling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behavior of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, βn=1.93(11)stat(11)sys×10-4 fm3, which is in agreement with current experimental results.

Interactive volume visualization of general polyhedral grids

KAUST Repository

Muigg, Philipp; Hadwiger, Markus; Doleisch, Helmut; Grö ller, Eduard M.

2011-01-01

This paper presents a novel framework for visualizing volumetric data specified on complex polyhedral grids, without the need to perform any kind of a priori tetrahedralization. These grids are composed of polyhedra that often are non

Finite spatial volume approach to finite temperature field theory

International Nuclear Information System (INIS)

Weiss, Nathan

1981-01-01

A relativistic quantum field theory at finite temperature T=β -1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned. (auth)

Simplicity of state and overlap structure in finite-volume realistic spin glasses

International Nuclear Information System (INIS)

Newman, C.M.; Stein, D.L.

1998-01-01

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of δ functions at ±q EA . This rules out the nonstandard mean-field picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean-field picture, argues against the possibility of even limited versions of mean-field ordering in realistic spin glasses. If broken spin-flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet-scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes. copyright 1998 The American Physical Society

Topology optimization using the finite volume method

DEFF Research Database (Denmark)

in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix K and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression c = u^\\T \\tilde{K}u $, where \\tilde{K} is different from K...... the well known Reuss lower bound. [1] Bendsøe, M.P.; Sigmund, O. 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, H. K.; W. Malalasekera 1995: An introduction to Computational Fluid Dynamics: the Finite Volume Method. London: Longman...

Finite spatial-volume effect for π-N sigma term in lattice QCD

International Nuclear Information System (INIS)

Fukushima, M.; Chiba, S.; Tanigawa, T.

2003-01-01

We report on a finite spatial-volume effect for the pion-nucleon sigma term σ πN for quenched Wilson fermion on 8 3 x 20 and 16 3 x 20 lattices at β = 5.7 with the spatial lattice size of La∼1.12fm and La∼2.24fm, respectively. It is found that the spatial size dependence of the connected part of σ πN con is significant small. We observed the magnitude of finite size effect for the disconnected part of σ πN dis is much larger than for to connected one and an almost drastic decrease of σ πN dis amounting to 50% between La∼2.24fm to the smaller lattice size of La∼1.12fm. (author)

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

Science.gov (United States)

Johansen, Hans; Colella, Phillip

1998-11-01

We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations.

Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems

Czech Academy of Sciences Publication Activity Database

Marcinkowski, L.; Rahman, T.; Loneland, A.; Valdman, Jan

2016-01-01

Roč. 56, č. 3 (2016), s. 967-993 ISSN 0006-3835 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:67985556 Keywords : Domain decomposition * Additive Schwarz method * Finite volume element * GMRES Subject RIV: BA - General Mathematics Impact factor: 1.670, year: 2016 http://library.utia.cas.cz/separaty/2015/MTR/valdman-0447835.pdf

Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

Science.gov (United States)

Zhang, L.; Zhao, J. M.; Liu, L. H.; Wang, S. Y.

2012-09-01

The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.

Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

International Nuclear Information System (INIS)

Zhang, L.; Zhao, J.M.; Liu, L.H.; Wang, S.Y.

2012-01-01

The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.

High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms

International Nuclear Information System (INIS)

Xing Yulong; Shu Chiwang

2006-01-01

Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions

An Eulerian-Lagrangian finite-element method for modeling crack growth in creeping materials

International Nuclear Information System (INIS)

Lee Hae Sung.

1991-01-01

This study is concerned with the development of finite-element-solution methods for analysis of quasi-static, ductile crack growth in history-dependent materials. The mixed Eulerian-Langrangian description (ELD) kinematic model is shown to have several desirable properties for modeling inelastic crack growth. Accordingly, a variational statement based on the ELD for history-dependent materials is developed, and a new moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method is applied to the analysis of transient, quasi-static, mode-III crack growth in creeping materials. A generalized Petrov-Galerkin method (GPG) is developed that simultaneously stabilizes the statement to admit L 2 basis functions for the nonlinear strain field. Quasi-static, model-III crack growth in creeping materials under small-scale-yielding (SSY) conditions is considered. The GPG/ELD moving-grid finite-element formulation is used to model a transient crack-growth problem. The GPG/ELD results compare favorably with previously-published numerical results and the asymptotic solutions

Fracture criterion for brittle materials based on statistical cells of finite volume

International Nuclear Information System (INIS)

Cords, H.; Kleist, G.; Zimmermann, R.

1986-06-01

An analytical consideration of the Weibull Statistical Analysis of brittle materials established the necessity of including one additional material constant for a more comprehensive description of the failure behaviour. The Weibull analysis is restricted to infinitesimal volume elements in consequence of the differential calculus applied. It was found that infinitesimally small elements are in conflict with the basic statistical assumption and that the differential calculus is not needed in fact since nowadays most of the stress analyses are based on finite element calculations, and these are most suitable for a subsequent statistical analysis of strength. The size of a finite statistical cell has been introduced as the third material parameter. It should represent the minimum volume containing all statistical features of the material such as distribution of pores, flaws and grains. The new approach also contains a unique treatment of failure under multiaxial stresses. The quantity responsible for failure under multiaxial stresses is introduced as a modified strain energy. Sixteen different tensile specimens including CT-specimens have been investigated experimentally and analyzed with the probabilistic fracture criterion. As a result it can be stated that the failure rates of all types of specimens made from three different grades of graphite are predictable. The accuracy of the prediction is one standard deviation. (orig.) [de

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

Science.gov (United States)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

Science.gov (United States)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

A-Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Problems Coupled Through a Boundary with Non-Matching Grids

Science.gov (United States)

2013-08-01

both MFE and GFV, are often similar in size. As a gross measure of the effect of geometric projection and of the use of quadrature, we also report the...interest MFE ∑(e,ψ) or GFV ∑(e,ψ). Tables 1 and 2 show this using coarse and fine forward solutions. Table 1. The forward problem with solution (4.1) is run...adjoint data components ψu and ψp are constant everywhere and ψξ = 0. adj. grid MFE ∑(e,ψ) ∑MFEi ratio GFV ∑(e,ψ) ∑GFV i ratio 20x20 : 32x32 1.96E−3

Integrating GRID tools to build a computing resource broker: activities of DataGrid WP1

International Nuclear Information System (INIS)

Anglano, C.; Barale, S.; Gaido, L.; Guarise, A.; Lusso, S.; Werbrouck, A.

2001-01-01

Resources on a computational Grid are geographically distributed, heterogeneous in nature, owned by different individuals or organizations with their own scheduling policies, have different access cost models with dynamically varying loads and availability conditions. This makes traditional approaches to workload management, load balancing and scheduling inappropriate. The first work package (WP1) of the EU-funded DataGrid project is addressing the issue of optimizing the distribution of jobs onto Grid resources based on a knowledge of the status and characteristics of these resources that is necessarily out-of-date (collected in a finite amount of time at a very loosely coupled site). The authors describe the DataGrid approach in integrating existing software components (from Condor, Globus, etc.) to build a Grid Resource Broker, and the early efforts to define a workable scheduling strategy

Cosmos++: relativistic magnetohydrodynamics on unstructured grids with local adaptive refinement

International Nuclear Information System (INIS)

Salmonson, Jay D; Anninos, Peter; Fragile, P Chris; Camarda, Karen

2007-01-01

A code and methodology are introduced for solving the fully general relativistic magnetohydrodynamic (GRMHD) equations using time-explicit, finite-volume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. It provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threaded oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. Some recent studies will be summarized

Numerical modelling in building thermo-aeraulics: from CFD modelling to an hybrid finite volume / zonal approach; Modelisation numerique de la thermoaeraulique du batiment: des modeles CFD a une approche hybride volumes finis / zonale

Energy Technology Data Exchange (ETDEWEB)

Bellivier, A.

2004-05-15

For 3D modelling of thermo-aeraulics in building using field codes, it is necessary to reduce the computing time in order to model increasingly larger volumes. The solution suggested in this study is to couple two modelling: a zonal approach and a CFD approach. The first part of the work that was carried out is the setting of a simplified CFD modelling. We propose rules for use of coarse grids, a constant effective viscosity law and adapted coefficients for heat exchange in the framework of building thermo-aeraulics. The second part of this work concerns the creation of fluid Macro-Elements and their coupling with a calculation of CFD finite volume type. Depending on the boundary conditions of the problem, a local description of the driving flow is proposed via the installation and use of semi-empirical evolution laws. The Macro-Elements is then inserted in CFD computation: the values of velocity calculated by the evolution laws are imposed on the CFD cells corresponding to the Macro-Element. We use these two approaches on five cases representative of thermo-aeraulics in buildings. The results are compared with experimental data and with traditional RANS simulations. We highlight the significant gain of time that our approach allows while preserving a good quality of numerical results. (author)

Finite size scaling and lattice gauge theory

International Nuclear Information System (INIS)

Berg, B.A.

1986-01-01

Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs

Uncertainty modelling and analysis of volume calculations based on a regular grid digital elevation model (DEM)

Science.gov (United States)

Li, Chang; Wang, Qing; Shi, Wenzhong; Zhao, Sisi

2018-05-01

The accuracy of earthwork calculations that compute terrain volume is critical to digital terrain analysis (DTA). The uncertainties in volume calculations (VCs) based on a DEM are primarily related to three factors: 1) model error (ME), which is caused by an adopted algorithm for a VC model, 2) discrete error (DE), which is usually caused by DEM resolution and terrain complexity, and 3) propagation error (PE), which is caused by the variables' error. Based on these factors, the uncertainty modelling and analysis of VCs based on a regular grid DEM are investigated in this paper. Especially, how to quantify the uncertainty of VCs is proposed by a confidence interval based on truncation error (TE). In the experiments, the trapezoidal double rule (TDR) and Simpson's double rule (SDR) were used to calculate volume, where the TE is the major ME, and six simulated regular grid DEMs with different terrain complexity and resolution (i.e. DE) were generated by a Gauss synthetic surface to easily obtain the theoretical true value and eliminate the interference of data errors. For PE, Monte-Carlo simulation techniques and spatial autocorrelation were used to represent DEM uncertainty. This study can enrich uncertainty modelling and analysis-related theories of geographic information science.

Numerical investigation of finite-volume effects for the HVP

Science.gov (United States)

Boyle, Peter; Gülpers, Vera; Harrison, James; Jüttner, Andreas; Portelli, Antonin; Sachrajda, Christopher

2018-03-01

It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

Finite-volume Atmospheric Model of the IAP/LASG (FAMIL)

Science.gov (United States)

Bao, Q.

2015-12-01

The Finite-volume Atmospheric Model of the IAP/LASG (FAMIL) is introduced in this work. FAMIL have the flexible horizontal and vertical resolutions up to 25km and 1Pa respectively, which currently running on the "Tianhe 1A&2" supercomputers. FAMIL is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL, this talk describes the simulated characteristics of energy and water balances, precipitation, Asian Summer Monsoon and stratospheric circulation, and compares them with observational/reanalysis data. Finally, the model biases as well as possible solutions are discussed.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

Science.gov (United States)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Modelling of Evaporator in Waste Heat Recovery System using Finite Volume Method and Fuzzy Technique

Directory of Open Access Journals (Sweden)

Jahedul Islam Chowdhury

2015-12-01

Full Text Available The evaporator is an important component in the Organic Rankine Cycle (ORC-based Waste Heat Recovery (WHR system since the effective heat transfer of this device reflects on the efficiency of the system. When the WHR system operates under supercritical conditions, the heat transfer mechanism in the evaporator is unpredictable due to the change of thermo-physical properties of the fluid with temperature. Although the conventional finite volume model can successfully capture those changes in the evaporator of the WHR process, the computation time for this method is high. To reduce the computation time, this paper develops a new fuzzy based evaporator model and compares its performance with the finite volume method. The results show that the fuzzy technique can be applied to predict the output of the supercritical evaporator in the waste heat recovery system and can significantly reduce the required computation time. The proposed model, therefore, has the potential to be used in real time control applications.

Concomitant GRID boost for Gamma Knife radiosurgery

International Nuclear Information System (INIS)

Ma Lijun; Kwok, Young; Chin, Lawrence S.; Simard, J. Marc; Regine, William F.

2005-01-01

We developed an integrated GRID boost technique for Gamma Knife radiosurgery. The technique generates an array of high dose spots within the target volume via a grid of 4-mm shots. These high dose areas were placed over a conventional Gamma Knife plan where a peripheral dose covers the full target volume. The beam weights of the 4-mm shots were optimized iteratively to maximize the integral dose inside the target volume. To investigate the target volume coverage and the dose to the adjacent normal brain tissue for the technique, we compared the GRID boosted treatment plans with conventional Gamma Knife treatment plans using physical and biological indices such as dose-volume histogram (DVH), DVH-derived indices, equivalent uniform dose (EUD), tumor control probabilities (TCP), and normal tissue complication probabilities (NTCP). We found significant increase in the target volume indices such as mean dose (5%-34%; average 14%), TCP (4%-45%; average 21%), and EUD (2%-22%; average 11%) for the GRID boost technique. No significant change in the peripheral dose coverage for the target volume was found per RTOG protocol. In addition, the EUD and the NTCP for the normal brain adjacent to the target (i.e., the near region) were decreased for the GRID boost technique. In conclusion, we demonstrated a new technique for Gamma Knife radiosurgery that can escalate the dose to the target while sparing the adjacent normal brain tissue

Global Time Tomography of Finite Frequency Waves with Optimized Tetrahedral Grids.

Science.gov (United States)

Montelli, R.; Montelli, R.; Nolet, G.; Dahlen, F. A.; Masters, G.; Hung, S.

2001-12-01

Besides true velocity heterogeneities, tomographic images reflect the effect of data errors, model parametrization, linearization, uncertainties involved with the solution of the forward problem and the greatly inadequate sampling of the earth by seismic rays. These influences cannot be easily separated and often produce artefacts in the final image with amplitudes comparable to those of the velocity heterogeneities. In practice, the tomographer uses some form of damping of the ill-resolved aspects of the model to get a unique solution and reduce the influence of the errors. However damping is not fully adequate, and may reveal a strong influence of the ray path coverage in tomographic images. If some cells are ill determinated regularization techniques may lead to heterogeneity because these cells are damped towards zero. Thus we want a uniform resolution of the parameters in our model. This can be obtained by using an irregular grid with variable length scales. We have introduced an irregular parametrization of the velocity structure by using a Delaunay triangulation. Extensively work on error analysis of tomographic images together with mesh optimization has shown that both resolution and ray density can provide the critical informations needed to re-design grids. However, criteria based on resolution are preferred in the presence of narrow ray beams coming from the same direction. This can be understood if we realise that resolution is not only determined by the number of rays crossing a region, but also by their azimutal coverage. We shall discuss various strategies for grid optimization. In general the computation of the travel times is restricted to ray theory, the infinite frequency approximation of the elastodynamic equation of motion. This simplifies the mathematic and is therefore widely applied in seismic tomography. But ray theory does not account for scattering, wavefront healing and other diffraction effects that render the traveltime of a finite

An overset grid approach to linear wave-structure interaction

DEFF Research Database (Denmark)

Read, Robert; Bingham, Harry B.

2012-01-01

A finite-difference based approach to wave-structure interaction is reported that employs the overset approach to grid generation. A two-dimensional code that utilizes the Overture C++ library has been developed to solve the linear radiation problem for a floating body of arbitrary form. This sof......A finite-difference based approach to wave-structure interaction is reported that employs the overset approach to grid generation. A two-dimensional code that utilizes the Overture C++ library has been developed to solve the linear radiation problem for a floating body of arbitrary form...

Assessment of the Unstructured Grid Software TetrUSS for Drag Prediction of the DLR-F4 Configuration

Science.gov (United States)

Pirzadeh, Shahyar Z.; Frink, Neal T.

2002-01-01

An application of the NASA unstructured grid software system TetrUSS is presented for the prediction of aerodynamic drag on a transport configuration. The paper briefly describes the underlying methodology and summarizes the results obtained on the DLR-F4 transport configuration recently presented in the first AIAA computational fluid dynamics (CFD) Drag Prediction Workshop. TetrUSS is a suite of loosely coupled unstructured grid CFD codes developed at the NASA Langley Research Center. The meshing approach is based on the advancing-front and the advancing-layers procedures. The flow solver employs a cell-centered, finite volume scheme for solving the Reynolds Averaged Navier-Stokes equations on tetrahedral grids. For the present computations, flow in the viscous sublayer has been modeled with an analytical wall function. The emphasis of the paper is placed on the practicality of the methodology for accurately predicting aerodynamic drag data.

A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

Energy Technology Data Exchange (ETDEWEB)

Garrick, Daniel P. [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States); Owkes, Mark [Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States); Regele, Jonathan D., E-mail: jregele@iastate.edu [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)

2017-06-15

Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

Optimal moving grids for time-dependent partial differential equations

Science.gov (United States)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

New finite volume methods for approximating partial differential equations on arbitrary meshes

International Nuclear Information System (INIS)

Hermeline, F.

2008-12-01

This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)

Hybrid finite difference/finite element immersed boundary method.

Science.gov (United States)

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

Grid sensitivity capability for large scale structures

Science.gov (United States)

Nagendra, Gopal K.; Wallerstein, David V.

1989-01-01

The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

Science.gov (United States)

Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

2017-11-01

Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

Numerical investigation of finite-volume effects for the HVP

Directory of Open Access Journals (Sweden)

Boyle Peter

2018-01-01

Full Text Available It is important to correct for finite-volume (FV effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP. For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan

2012-01-01

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite

A SUB-GRID VOLUME-OF-FLUIDS (VOF) MODEL FOR MIXING IN RESOLVED SCALE AND IN UNRESOLVED SCALE COMPUTATIONS

International Nuclear Information System (INIS)

Vold, Erik L.; Scannapieco, Tony J.

2007-01-01

A sub-grid mix model based on a volume-of-fluids (VOF) representation is described for computational simulations of the transient mixing between reactive fluids, in which the atomically mixed components enter into the reactivity. The multi-fluid model allows each fluid species to have independent values for density, energy, pressure and temperature, as well as independent velocities and volume fractions. Fluid volume fractions are further divided into mix components to represent their 'mixedness' for more accurate prediction of reactivity. Time dependent conversion from unmixed volume fractions (denoted cf) to atomically mixed (af) fluids by diffusive processes is represented in resolved scale simulations with the volume fractions (cf, af mix). In unresolved scale simulations, the transition to atomically mixed materials begins with a conversion from unmixed material to a sub-grid volume fraction (pf). This fraction represents the unresolved small scales in the fluids, heterogeneously mixed by turbulent or multi-phase mixing processes, and this fraction then proceeds in a second step to the atomically mixed fraction by diffusion (cf, pf, af mix). Species velocities are evaluated with a species drift flux, ρ i u di = ρ i (u i -u), used to describe the fluid mixing sources in several closure options. A simple example of mixing fluids during 'interfacial deceleration mixing with a small amount of diffusion illustrates the generation of atomically mixed fluids in two cases, for resolved scale simulations and for unresolved scale simulations. Application to reactive mixing, including Inertial Confinement Fusion (ICF), is planned for future work.

3D Finite Volume Modeling of ENDE Using Electromagnetic T-Formulation

Directory of Open Access Journals (Sweden)

Yue Li

2012-01-01

Full Text Available An improved method which can analyze the eddy current density in conductor materials using finite volume method is proposed on the basis of Maxwell equations and T-formulation. The algorithm is applied to solve 3D electromagnetic nondestructive evaluation (E’NDE benchmark problems. The computing code is applied to study an Inconel 600 work piece with holes or cracks. The impedance change due to the presence of the crack is evaluated and compared with the experimental data of benchmark problems No. 1 and No. 2. The results show a good agreement between both calculated and measured data.

A finite volume method for density driven flows in porous media

Directory of Open Access Journals (Sweden)

Hilhorst Danielle

2013-01-01

Full Text Available In this paper, we apply a semi-implicit finite volume method for the numerical simulation of density driven flows in porous media; this amounts to solving a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We compute the solutions for two specific problems: a problem involving a rotating interface between salt and fresh water and the classical but difficult Henry’s problem. All solutions are compared to results obtained by running FEflow, a commercial software package for the simulation of groundwater flow, mass and heat transfer in porous media.

A control volume based finite difference method for solving the equilibrium equations in terms of displacements

DEFF Research Database (Denmark)

Hattel, Jesper; Hansen, Preben

1995-01-01

This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....

Staggered-grid finite-difference acoustic modeling with the Time-Domain Atmospheric Acoustic Propagation Suite (TDAAPS).

Energy Technology Data Exchange (ETDEWEB)

Aldridge, David Franklin; Collier, Sandra L. (U.S. Army Research Laboratory); Marlin, David H. (U.S. Army Research Laboratory); Ostashev, Vladimir E. (NOAA/Environmental Technology Laboratory); Symons, Neill Phillip; Wilson, D. Keith (U.S. Army Cold Regions Research Engineering Lab.)

2005-05-01

This document is intended to serve as a users guide for the time-domain atmospheric acoustic propagation suite (TDAAPS) program developed as part of the Department of Defense High-Performance Modernization Office (HPCMP) Common High-Performance Computing Scalable Software Initiative (CHSSI). TDAAPS performs staggered-grid finite-difference modeling of the acoustic velocity-pressure system with the incorporation of spatially inhomogeneous winds. Wherever practical the control structure of the codes are written in C++ using an object oriented design. Sections of code where a large number of calculations are required are written in C or F77 in order to enable better compiler optimization of these sections. The TDAAPS program conforms to a UNIX style calling interface. Most of the actions of the codes are controlled by adding flags to the invoking command line. This document presents a large number of examples and provides new users with the necessary background to perform acoustic modeling with TDAAPS.

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

Science.gov (United States)

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly

Conservative and bounded volume-of-fluid advection on unstructured grids

Science.gov (United States)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a

Multi-channel 1-to-2 transition amplitudes in a finite volume

Energy Technology Data Exchange (ETDEWEB)

Briceno, Raul [JLAB; Hansen, Maxwell [Helmholtz Institute Mainz; Walker-Loud, Andre P [W& M. JLAB

2015-04-01

We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar out-state. Our result, which is valid for energies below higher-particle inelastic thresholds, generalizes the Lellouch-Luscher formula in two ways: we allow the external current to inject arbitrary momentum into the system and we allow for the final state to be composed an arbitrary number of strongly coupled two-particle states with arbitrary partial waves (including partial-wave mixing induced by the volume). We also illustrate how our general result can be applied to some key examples, such as heavy meson decays and meson photo production. Finally, we point out complications that arise involving unstable resonance states, such as B to K*+l+l when staggered or mixed-action/partially-quenched calculations are performed.

Chimera Grid Tools

Science.gov (United States)

Chan, William M.; Rogers, Stuart E.; Nash, Steven M.; Buning, Pieter G.; Meakin, Robert

2005-01-01

Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.

Characterization of resonances using finite size effects

International Nuclear Information System (INIS)

Pozsgay, B.; Takacs, G.

2006-01-01

We develop methods to extract resonance widths from finite volume spectra of (1+1)-dimensional quantum field theories. Our two methods are based on Luscher's description of finite size corrections, and are dubbed the Breit-Wigner and the improved ''mini-Hamiltonian'' method, respectively. We establish a consistent framework for the finite volume description of sufficiently narrow resonances that takes into account the finite size corrections and mass shifts properly. Using predictions from form factor perturbation theory, we test the two methods against finite size data from truncated conformal space approach, and find excellent agreement which confirms both the theoretical framework and the numerical validity of the methods. Although our investigation is carried out in 1+1 dimensions, the extension to physical 3+1 space-time dimensions appears straightforward, given sufficiently accurate finite volume spectra

1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method

Directory of Open Access Journals (Sweden)

Szu-Hsien Peng

2012-01-01

Full Text Available The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.

The finite volume element (FVE) and multigrid method for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Gu Lizhen; Bao Weizhu

1992-01-01

The authors apply FVE method to discrete INS equations with the original variable, in which the bilinear square finite element and the square finite volume are chosen. The discrete schemes of INS equations are presented. The FMV multigrid algorithm is applied to solve that discrete system, where DGS iteration is used as smoother, DGS distributive mode for the INS discrete system is also presented. The sample problems for the square cavity flow with Reynolds number Re≤100 are successfully calculated. The numerical solutions show that the results with 1 FMV is satisfactory and when Re is not large, The FVE discrete scheme of the conservative INS equations and that of non-conservative INS equations with linearization both can provide almost same accuracy

The finite volume method in computational fluid dynamics an advanced introduction with OpenFOAM and Matlab

CERN Document Server

Moukalled, F; Darwish, M

2016-01-01

This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programm...

An adaptive grid refinement strategy for the simulation of negative streamers

International Nuclear Information System (INIS)

Montijn, C.; Hundsdorfer, W.; Ebert, U.

2006-01-01

The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers

A Study of the Transient Response of Duct Junctions: Measurements and Gas-Dynamic Modeling with a Staggered Mesh Finite Volume Approach

Directory of Open Access Journals (Sweden)

Antonio J. Torregrosa

2017-05-01

Full Text Available Duct junctions play a major role in the operation and design of most piping systems. The objective of this paper is to establish the potential of a staggered mesh finite volume model as a way to improve the description of the effect of simple duct junctions on an otherwise one-dimensional flow system, such as the intake or exhaust of an internal combustion engine. Specific experiments have been performed in which different junctions have been characterized as a multi-port, and that have provided precise and reliable results on the propagation of pressure pulses across junctions. The results obtained have been compared to simulations performed with a staggered mesh finite volume method with different flux limiters and different meshes and, as a reference, have also been compared with the results of a more conventional pressure loss-based model. The results indicate that the staggered mesh finite volume model provides a closer description of wave dynamics, even if further work is needed to establish the optimal calculation settings.

A three-dimensional electrostatic particle-in-cell methodology on unstructured Delaunay-Voronoi grids

International Nuclear Information System (INIS)

Gatsonis, Nikolaos A.; Spirkin, Anton

2009-01-01

The mathematical formulation and computational implementation of a three-dimensional particle-in-cell methodology on unstructured Delaunay-Voronoi tetrahedral grids is presented. The method allows simulation of plasmas in complex domains and incorporates the duality of the Delaunay-Voronoi in all aspects of the particle-in-cell cycle. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints. Electric potential and fields are derived from a finite-volume formulation of Gauss' law using the Voronoi-Delaunay dual. Boundary conditions and the algorithms for injection, particle loading, particle motion, and particle tracking are implemented for unstructured Delaunay grids. Error and sensitivity analysis examines the effects of particles/cell, grid scaling, and timestep on the numerical heating, the slowing-down time, and the deflection times. The problem of current collection by cylindrical Langmuir probes in collisionless plasmas is used for validation. Numerical results compare favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. The versatility of the methodology is demonstrated with the simulation of a complex plasma microsensor, a directional micro-retarding potential analyzer that includes a low transparency micro-grid.

Development of a higher-order finite volume method for simulation of thermal oil recovery process using moving mesh strategy

Energy Technology Data Exchange (ETDEWEB)

Ahmadi, M. [Heriot Watt Univ., Edinburgh (United Kingdom)

2008-10-15

This paper described a project in which a higher order up-winding scheme was used to solve mass/energy conservation equations for simulating steam flood processes in an oil reservoir. Thermal recovery processes are among the most complex because they require a detailed accounting of thermal energy and chemical reaction kinetics. The numerical simulation of thermal recovery processes involves localized phenomena such as saturation and temperatures fronts due to hyperbolic features of governing conservation laws. A second order accurate FV method that was improved by a moving mesh strategy was used to adjust for moving coordinates on a finely gridded domain. The Finite volume method was used and the problem of steam injection was then tested using derived solution frameworks on both mixed and moving coordinates. The benefits of using a higher-order Godunov solver instead of lower-order ones were qualified. This second order correction resulted in better resolution on moving features. Preferences of higher-order solvers over lower-order ones in terms of shock capturing is under further investigation. It was concluded that although this simulation study was limited to steam flooding processes, the newly presented approach may be suitable to other enhanced oil recovery processes such as VAPEX, SAGD and in situ combustion processes. 23 refs., 28 figs.

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

Science.gov (United States)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

Finite Boltzmann schemes

NARCIS (Netherlands)

Sman, van der R.G.M.

2006-01-01

In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

Finite element and finite difference methods in electromagnetic scattering

CERN Document Server

Morgan, MA

2013-01-01

This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca

A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces

Energy Technology Data Exchange (ETDEWEB)

Ju, Lili; Tian, Li; Wang, Desheng

2008-10-31

In this paper, we present a residual-based a posteriori error estimate for the finite volume discretization of steady convection– diffusion–reaction equations defined on surfaces in R3, which are often implicitly represented as level sets of smooth functions. Reliability and efficiency of the proposed a posteriori error estimator are rigorously proved. Numerical experiments are also conducted to verify the theoretical results and demonstrate the robustness of the error estimator.

Mixed isogeometric finite cell methods for the stokes problem

NARCIS (Netherlands)

Hoang, T.; Verhoosel, C.V.; Auricchio, F.; van Brummelen, E.H.; Reali, A.

2017-01-01

We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor-Hood, Sub-grid, Raviart-Thomas, and Nédélec

OGC and Grid Interoperability in enviroGRIDS Project

Science.gov (United States)

Gorgan, Dorian; Rodila, Denisa; Bacu, Victor; Giuliani, Gregory; Ray, Nicolas

2010-05-01

EnviroGRIDS (Black Sea Catchment Observation and Assessment System supporting Sustainable Development) [1] is a 4-years FP7 Project aiming to address the subjects of ecologically unsustainable development and inadequate resource management. The project develops a Spatial Data Infrastructure of the Black Sea Catchment region. The geospatial technologies offer very specialized functionality for Earth Science oriented applications as well as the Grid oriented technology that is able to support distributed and parallel processing. One challenge of the enviroGRIDS project is the interoperability between geospatial and Grid infrastructures by providing the basic and the extended features of the both technologies. The geospatial interoperability technology has been promoted as a way of dealing with large volumes of geospatial data in distributed environments through the development of interoperable Web service specifications proposed by the Open Geospatial Consortium (OGC), with applications spread across multiple fields but especially in Earth observation research. Due to the huge volumes of data available in the geospatial domain and the additional introduced issues (data management, secure data transfer, data distribution and data computation), the need for an infrastructure capable to manage all those problems becomes an important aspect. The Grid promotes and facilitates the secure interoperations of geospatial heterogeneous distributed data within a distributed environment, the creation and management of large distributed computational jobs and assures a security level for communication and transfer of messages based on certificates. This presentation analysis and discusses the most significant use cases for enabling the OGC Web services interoperability with the Grid environment and focuses on the description and implementation of the most promising one. In these use cases we give a special attention to issues such as: the relations between computational grid and

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

Science.gov (United States)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

Numerical study on flow fields and aerodynamics of tilt rotor aircraft in conversion mode based on embedded grid and actuator model

Directory of Open Access Journals (Sweden)

Ying Zhang

2015-02-01

Full Text Available A method combining rotor actuator disk model and embedded grid technique is presented in this paper, aimed at predicting the flow fields and aerodynamic characteristics of tilt rotor aircraft in conversion mode more efficiently and effectively. In this method, rotor’s influence is considered in terms of the momentum it impacts to the fluid around it; transformation matrixes among different coordinate systems are deduced to extend actuator method’s utility to conversion mode flow fields’ calculation. Meanwhile, an embedded grid system is designed, in which grids generated around fuselage and actuator disk are regarded as background grid and minor grid respectively, and a new method is presented for ‘donor searching’ and ‘hole cutting’ during grid assembling. Based on the above methods, flow fields of tilt rotor aircraft in conversion mode are simulated, with three-dimensional Navier–Stokes equations discretized by a second-order upwind finite-volume scheme and an implicit lower–upper symmetric Gauss–Seidel (LU-SGS time-stepping scheme. Numerical results demonstrate that the proposed CFD method is very effective in simulating the conversion mode flow fields of tilt rotor aircraft.

Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies

DEFF Research Database (Denmark)

Morningstar, Colin; Bulava, John; Singha, Bijit

2017-01-01

An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating...

Numerical analysis of the spacer grids' compression strength

International Nuclear Information System (INIS)

Schettino, C.F.M.; Gouvea, J.P.; Medeiros, N.

2013-01-01

Among the components of the fuel assembly, the spacer grids play an important structural role during the energy generation process, mainly for their requirement to have enough structural strength to withstand lateral impact loads, due to fuel assembly shipping/handling and due to forces outcome from postulated accidents (earthquake and LOCA). This requirement ensures a proper geometry for cooling and for guide thimble straightness in the fuel assembly. In this way, the understanding of the macroscopic mechanical behavior of this component becomes essential even to any subsequent geometrical modifications to optimize the flue assemblies' structural behavior. In the present work, three-dimensional finite element models destined to provide consistent predictions of 16X16-type spacer grids lateral strength were proposed. Firstly, buckling tests based on results available in the literature were performed to establish a methodology for spacer grid finite element-based modeling. The, by considering a spacer grid interesting geometry and some possible variations associated to its fabrication, tolerance, the proposed numerical models were submitted to compression conditions to calculate the buckling force. Also, these models were validated for comparison with experimental buckling load results. Comparison of buckling predictions combined to observations of actual and simulated deformed spacer grids geometries permitted to verify the consistency and applicability of the proposed models. Thus, these numerical results show a good agreement between the and the experimental results. (author)

Simulation of 3D parachute fluid–structure interaction based on nonlinear finite element method and preconditioning finite volume method

Directory of Open Access Journals (Sweden)

Fan Yuxin

2014-12-01

Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.

Interactive volume visualization of general polyhedral grids

KAUST Repository

Muigg, Philipp

2011-12-01

This paper presents a novel framework for visualizing volumetric data specified on complex polyhedral grids, without the need to perform any kind of a priori tetrahedralization. These grids are composed of polyhedra that often are non-convex and have an arbitrary number of faces, where the faces can be non-planar with an arbitrary number of vertices. The importance of such grids in state-of-the-art simulation packages is increasing rapidly. We propose a very compact, face-based data structure for representing such meshes for visualization, called two-sided face sequence lists (TSFSL), as well as an algorithm for direct GPU-based ray-casting using this representation. The TSFSL data structure is able to represent the entire mesh topology in a 1D TSFSL data array of face records, which facilitates the use of efficient 1D texture accesses for visualization. In order to scale to large data sizes, we employ a mesh decomposition into bricks that can be handled independently, where each brick is then composed of its own TSFSL array. This bricking enables memory savings and performance improvements for large meshes. We illustrate the feasibility of our approach with real-world application results, by visualizing highly complex polyhedral data from commercial state-of-the-art simulation packages. © 2011 IEEE.

Finite-volume discretizations and immersed boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2009-01-01

htmlabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed `Cartesian' grid. The essence of the present method

Finite-volume discretizations and immersed boundaries

NARCIS (Netherlands)

Y.J. Hassen (Yunus); B. Koren (Barry)

2010-01-01

textabstractIn this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is

Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics

KAUST Repository

Reynolds, Daniel R.

2012-01-01

We apply the automatic differentiation tool OpenAD toward constructing a preconditioner for fully implicit simulations of mapped grid visco-resistive magnetohydrodynamics (MHD), used in modeling tokamak fusion devices. Our simulation framework employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner, which typically requires knowledge of the Jacobian of the nonlinear residual function. However, due to significant nonlinearity within our PDE system, our mapped spatial discretization, and stencil adaptivity at physical boundaries, analytical derivation of these Jacobian entries is highly nontrivial. This paper therefore focuses on Jacobian construction using automatic differentiation. In particular, we discuss applying OpenAD to the case of a spatially-adaptive stencil patch that automatically handles differences between the domain interior and boundary, and configuring AD for reduced stencil approximations to the Jacobian. We investigate both scalar and vector tangent mode differentiation, along with simple finite difference approaches, to compare the resulting accuracy and efficiency of Jacobian construction in this application. © 2012 Springer-Verlag.

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

Science.gov (United States)

Renteria Marquez, I A; Bolborici, V

2017-05-01

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

KAUST Repository

Wheeler, Mary; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields

Analysis of Grid-Scored Sandwich Structures of Different Curvatures and Grid Sizes For Wind Turbine Blades

DEFF Research Database (Denmark)

Laustsen, Steffen; Thomsen, Ole Thybo; Lund, Erik

2012-01-01

The stress and strain field developed locally in-situ the core of grid-scored sandwich structures in wind turbine blades is investigated. Due to the many singularities occurring from the “tri-material corners”, a full 3D analysis of the sandwich structure in terms of the Finite Element Method is ...

ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

International Nuclear Information System (INIS)

Nagai, Katsuaki; Ushijima, Satoru

2010-01-01

A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.

ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

Science.gov (United States)

Nagai, Katsuaki; Ushijima, Satoru

2010-06-01

A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.

Adaptive Method Using Controlled Grid Deformation

Directory of Open Access Journals (Sweden)

Florin FRUNZULICA

2011-09-01

Full Text Available The paper presents an adaptive method using the controlled grid deformation over an elastic, isotropic and continuous domain. The adaptive process is controlled with the principal strains and principal strain directions and uses the finite elements method. Numerical results are presented for several test cases.

Coupling of a 3-D vortex particle-mesh method with a finite volume near-wall solver

Science.gov (United States)

Marichal, Y.; Lonfils, T.; Duponcheel, M.; Chatelain, P.; Winckelmans, G.

2011-11-01

This coupling aims at improving the computational efficiency of high Reynolds number bluff body flow simulations by using two complementary methods and exploiting their respective advantages in distinct parts of the domain. Vortex particle methods are particularly well suited for free vortical flows such as wakes or jets (the computational domain -with non zero vorticity- is then compact and dispersion errors are negligible). Finite volume methods, however, can handle boundary layers much more easily due to anisotropic mesh refinement. In the present approach, the vortex method is used in the whole domain (overlapping domain technique) but its solution is highly underresolved in the vicinity of the wall. It thus has to be corrected by the near-wall finite volume solution at each time step. Conversely, the vortex method provides the outer boundary conditions for the near-wall solver. A parallel multi-resolution vortex particle-mesh approach is used here along with an Immersed Boundary method in order to take the walls into account. The near-wall flow is solved by OpenFOAM® using the PISO algorithm. We validate the methodology on the flow past a sphere at a moderate Reynolds number. F.R.S. - FNRS Research Fellow.

Numerical analysis of the spacer grids' compression strength

Energy Technology Data Exchange (ETDEWEB)

Schettino, C.F.M.; Gouvea, J.P.; Medeiros, N., E-mail: carlosschettino@inb.gov.br, E-mail: jpg@metal.eeimvr.uff.br [Universidade Federal Fluminense (UFF), Volta Redonda, RJ (Brazil). Programa de Engenharia Metalurgica

2013-07-01

Among the components of the fuel assembly, the spacer grids play an important structural role during the energy generation process, mainly for their requirement to have enough structural strength to withstand lateral impact loads, due to fuel assembly shipping/handling and due to forces outcome from postulated accidents (earthquake and LOCA). This requirement ensures a proper geometry for cooling and for guide thimble straightness in the fuel assembly. In this way, the understanding of the macroscopic mechanical behavior of this component becomes essential even to any subsequent geometrical modifications to optimize the flue assemblies' structural behavior. In the present work, three-dimensional finite element models destined to provide consistent predictions of 16X16-type spacer grids lateral strength were proposed. Firstly, buckling tests based on results available in the literature were performed to establish a methodology for spacer grid finite element-based modeling. The, by considering a spacer grid interesting geometry and some possible variations associated to its fabrication, tolerance, the proposed numerical models were submitted to compression conditions to calculate the buckling force. Also, these models were validated for comparison with experimental buckling load results. Comparison of buckling predictions combined to observations of actual and simulated deformed spacer grids geometries permitted to verify the consistency and applicability of the proposed models. Thus, these numerical results show a good agreement between the and the experimental results. (author)

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

Science.gov (United States)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

KAUST Repository

Wheeler, Mary

2011-11-06

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.

Parallel SOR methods with a parabolic-diffusion acceleration technique for solving an unstructured-grid Poisson equation on 3D arbitrary geometries

Science.gov (United States)

Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.

2016-05-01

This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

International Nuclear Information System (INIS)

Kriventsev, Vladimir

2000-09-01

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

Characterization of large volume CdZnTe detectors with a quad-grid structure for the COBRA experiment

Energy Technology Data Exchange (ETDEWEB)

Rohatsch, Katja [TU Dresden, Institut fuer Kern- und Teilchenphysik, 01069 Dresden (Germany); Collaboration: COBRA-Collaboration

2016-07-01

The COBRA experiment uses room temperature semiconductor detectors made of Cadmium-Zinc-Telluride, which contains several double beta isotopes, to search for neutrinoless double beta-decay. To compensate for poor hole transport in CdZnTe the detectors are equipped with a coplanar grid (CPG) instead of a planar anode. Currently, a demonstrator setup consisting of 64 1 cm{sup 3} CPG-detectors is in operation at the LNGS in Italy to prove the concept and to determine the long-term stability of the detectors and the instrumentation. For a future large scale experiment it is planned to use larger CdZnTe detectors with a volume of 6 cm{sup 3}, because of the better surface-to-volume ratio and the higher full energy detection efficiency. This will also reduce the background contribution of surface contaminations. Before the installation at the LNGS the new detector design is validated and studied in detail. This talk presents a laboratory experiment for the characterization with γ-radiation of 6 cm{sup 3} CdZnTe quad-grid detectors. The anode of such a detector is divided into four sub-CPGs. The characterization routine consists of the determination of the optimal working point and two-dimensional spatially resolved scans with a highly collimated γ-source.

Workshop on Future Generation Grids

CERN Document Server

Laforenza, Domenico; Reinefeld, Alexander

2006-01-01

The Internet and the Web continue to have a major impact on society. By allowing us to discover and access information on a global scale, they have created entirely new businesses and brought new meaning to the term surf. In addition, however, we want processing, and increasingly, we want collaborative processing within distributed teams. This need has led to the creation of the Grid - an infrastructure that enables us to share capabilities, and integrate services and resources within and across enterprises. "Future Generation Grids" is the second in the "CoreGRID" series. This edited volume brings together contributed articles by scientists and researchers in the Grid community in an attempt to draw a clearer picture of the future generation Grids. This book also identifies some of the most challenging problems on the way to achieving the invisible Grid ideas

Impact of Considering 110 kV Grid Structures on the Congestion Management in the German Transmission Grid

Science.gov (United States)

Hoffrichter, André; Barrios, Hans; Massmann, Janek; Venkataramanachar, Bhavasagar; Schnettler, Armin

2018-02-01

The structural changes in the European energy system lead to an increase of renewable energy sources that are primarily connected to the distribution grid. Hence the stationary analysis of the transmission grid and the regionalization of generation capacities are strongly influenced by subordinate grid structures. To quantify the impact on the congestion management in the German transmission grid, a 110 kV grid model is derived using publicly available data delivered by Open Street Map and integrated into an existing model of the European transmission grid. Power flow and redispatch simulations are performed for three different regionalization methods and grid configurations. The results show a significant impact of the 110 kV system and prove an overestimation of power flows in the transmission grid when neglecting subordinate grids. Thus, the redispatch volume in Germany to dissolve bottlenecks in case of N-1 contingencies decreases by 38 % when considering the 110 kV grid.

A solution of two-dimensional magnetohydrodynamic flow using the finite volume method

Directory of Open Access Journals (Sweden)

Naceur Sonia

2014-01-01

Full Text Available This paper presents the two dimensional numerical modeling of the coupling electromagnetic-hydrodynamic phenomena in a conduction MHD pump using the Finite volume Method. Magnetohydrodynamic problems are, thus, interdisciplinary and coupled, since the effect of the velocity field appears in the magnetic transport equations, and the interaction between the electric current and the magnetic field appears in the momentum transport equations. The resolution of the Maxwell's and Navier Stokes equations is obtained by introducing the magnetic vector potential A, the vorticity z and the stream function y. The flux density, the electromagnetic force, and the velocity are graphically presented. Also, the simulation results agree with those obtained by Ansys Workbench Fluent software.

High‐order rotated staggered finite difference modeling of 3D elastic wave propagation in general anisotropic media

KAUST Repository

Chu, Chunlei

2009-01-01

We analyze the dispersion properties and stability conditions of the high‐order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high‐order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost‐effectively.

Application of the finite volume method in the simulation of saturated flows of binary mixtures

International Nuclear Information System (INIS)

Murad, M.A.; Gama, R.M.S. da; Sampaio, R.

1989-12-01

This work presents the simulation of saturated flows of an incompressible Newtonian fluid through a rigid, homogeneous and isotropic porous medium. The employed mathematical model is derived from the Continuum Theory of Mixtures and generalizes the classical one which is based on Darcy's Law form of the momentum equation. In this approach fluid and porous matrix are regarded as continuous constituents of a binary mixture. The finite volume method is employed in the simulation. (author) [pt

An outgoing energy flux boundary condition for finite difference ICRP antenna models

International Nuclear Information System (INIS)

Batchelor, D.B.; Carter, M.D.

1992-11-01

For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods

Picosecond studies of excitation transport in a finite volume: The clustered transport system octadecyl rhodamine B in triton X-100 micelles

International Nuclear Information System (INIS)

Ediger, M.D.; Domingue, R.P.; Fayer, M.D.

1984-01-01

A detailed experimental and theoretical examination of electronic excited state transport in the finite volume system, octadecyl rhodamine B molecules in triton X-100 micelles, is presented. Picosecond fluorescence mixing and transient grating techniques were used to examine systems in which the average number of chromophores per micelle ranged from 0.1 to 11. Because of the clustering of chromophores in the small micelles, the energy transport observed is extremely efficient. A statistical mechanical theory, based on a density expansion with a Pade approximant, is developed for donor--donor transport on a spherical surface. This theory accurately accounts for the experimental data with only the micelle radius as an adjustable parameter. The radius obtained from this procedure is in good agreement with determinations by other methods. This demonstrates that quantitative information about the spatial extent of chromophore distributions in small volumes can be obtained when appropriate finite volume energy transport theories are employed. It is shown that theories developed for infinite volumes are not applicable to systems such as the ones considered here. Finally the partitioning of rhodamine B and octadecyl rhodamine B between aqueous and micellar phases is measured, and lifetimes and rotation times are reported

Ion diode simulation with a finite-volume PIC approach for the numerical solution of the Maxwell-Lorentz system

Energy Technology Data Exchange (ETDEWEB)

Munz, C D; Schneider, R; Stein, E; Voss, U [Forschungszentrum Karlsruhe (Germany). Institut fuer Neutronenphysik und Reaktortechnik; Westermann, T [FH Karlsruhe (Germany). Fachbereich Naturwissenschaften; Krauss, M [Forschungszentrum Karlsruhe (Germany). Hauptabteilung Informations- und Kommunikationstechik

1997-12-31

The numerical concept realized in the the Karlsruhe Diode Code KADI2D is briefly reviewed. Several new aspects concerning the Maxwell field solver based on high resolution finite-volume methods are presented. A new approach maintaining charge conservation numerically for the Maxwell-Lorentz equations is shortly summarized. (author). 2 figs., 12 refs.

Ion diode simulation with a finite-volume PIC approach for the numerical solution of the Maxwell-Lorentz system

International Nuclear Information System (INIS)

Munz, C.D.; Schneider, R.; Stein, E.; Voss, U.; Westermann, T.; Krauss, M.

1996-01-01

The numerical concept realized in the the Karlsruhe Diode Code KADI2D is briefly reviewed. Several new aspects concerning the Maxwell field solver based on high resolution finite-volume methods are presented. A new approach maintaining charge conservation numerically for the Maxwell-Lorentz equations is shortly summarized. (author). 2 figs., 12 refs

Sensitivity analyses on natural convection in an 8:1 tall enclosure using finite-volume methods

International Nuclear Information System (INIS)

Ambrosini, Walter; Forgione, N.; Ferreri, Juan C.

2004-01-01

Full text: The results herein presented are an extension of those obtained in previous work by the Authors in a benchmark problem dealing with flow driven by buoyancy in an 8:1 tall enclosure. A simple finite-volume model purposely set up for this application has provided the preliminary results reported. The adopted modeling technique was a direct extension of the one previously adopted by the Authors to deal with single-phase natural convection and boiling channel instabilities. This extension to two-dimensional flow is based on a finite-volume scheme using first order approximation in time and space. Despite its simplicity, results were reasonably good and detected the flow instabilities due to proper selection of cell Courant number and a semi-implicit solution algorithm. In this paper, results using the same code with different discretisations are presented in a more detailed way and are further discussed. They show proper capture of all the main characteristics of the flow, also reported by other authors and considered as 'converged' solutions. Results show that, as expected, first order explicit or semi-implicit methods can be considered reliable tools when dealing with stability problems, if properly used. Some initial results obtained using a second order upwind method are also presented for the purpose of comparison. Additionally, results obtained using a commercial code (FLUENT) are also reported. (author)

Improving the performance parameters of metal cylindrical grid shell ...

African Journals Online (AJOL)

Improving the performance parameters of metal cylindrical grid shell structures. ... Finite element models are designed taking into account minimization of production and ... The force factors and deformation parameters of the basic circuits of a ...

Simulation of Jetting in Injection Molding Using a Finite Volume Method

Directory of Open Access Journals (Sweden)

Shaozhen Hua

2016-05-01

Full Text Available In order to predict the jetting and the subsequent buckling flow more accurately, a three dimensional melt flow model was established on a viscous, incompressible, and non-isothermal fluid, and a control volume-based finite volume method was employed to discretize the governing equations. A two-fold iterative method was proposed to decouple the dependence among pressure, velocity, and temperature so as to reduce the computation and improve the numerical stability. Based on the proposed theoretical model and numerical method, a program code was developed to simulate melt front progress and flow fields. The numerical simulations for different injection speeds, melt temperatures, and gate locations were carried out to explore the jetting mechanism. The results indicate the filling pattern depends on the competition between inertial and viscous forces. When inertial force exceeds the viscous force jetting occurs, then it changes to a buckling flow as the viscous force competes over the inertial force. Once the melt contacts with the mold wall, the melt filling switches to conventional sequential filling mode. Numerical results also indicate jetting length increases with injection speed but changes little with melt temperature. The reasonable agreements between simulated and experimental jetting length and buckling frequency imply the proposed method is valid for jetting simulation.

New results of GridPix TPCs

International Nuclear Information System (INIS)

Graaf, Harry van der

2009-01-01

The Gossip detector, being a GridPix TPC equipped with a thin layer of gas, is a promising alternative for Si tracking detectors. In addition, GridPix would be an interesting way to read out the gaseous phase volume of bi-phase Liquid Xe cryostats of v-less double beta decay and rare event (i.e. WIMP) search experiments.

New results of GridPix TPCs

Energy Technology Data Exchange (ETDEWEB)

Graaf, Harry van der, E-mail: vdgraaf@nikhef.n [Science Park 105 1098 XG Amsterdam (Netherlands)

2009-07-01

The Gossip detector, being a GridPix TPC equipped with a thin layer of gas, is a promising alternative for Si tracking detectors. In addition, GridPix would be an interesting way to read out the gaseous phase volume of bi-phase Liquid Xe cryostats of v-less double beta decay and rare event (i.e. WIMP) search experiments.

High Resolution 3-D Finite-Volume Coastal Ocean Modeling in Lower Campbell River and Discovery Passage, British Columbia, Canada

Directory of Open Access Journals (Sweden)

Yuehua Lin

2014-03-01

Full Text Available The 3-D unstructured-grid, Finite-Volume Coastal Ocean Model (FVCOM was used to simulate the flows in Discovery Passage including the adjoining Lower Campbell River, British Columbia, Canada. Challenges in the studies include the strong tidal currents (e.g., up to 7.8 m/s in Seymour Narrows and tailrace discharges, small-scale topographic features and steep bottom slopes, and stratification affected by the Campbell River freshwater discharges. Two applications of high resolution 3-D FVCOM modeling were conducted. One is for the Lower Campbell River extending upstream as far as the John Hart Hydroelectric dam. The horizontal resolution varies from 0.27 m to 32 m in the unstructured triangular mesh to resolve the tailrace flow. The bottom elevation decreases ~14 m within the distance of ~1.4 km along the river. This pioneering FVCOM river modeling demonstrated a very good performance in simulating the river flow structures. The second application is to compute ocean currents immediately above the seabed along the present underwater electrical cable crossing routes across Discovery Passage. Higher resolution was used near the bottom with inter-layer spacing ranging from 0.125 to 0.0005 of total water depth. The model behaves very well in simulating the strong tidal currents in the area at high resolution in both the horizontal and vertical. One year maximum near bottom tidal current along the routes was then analyzed using the model results.

A parallel adaptive finite difference algorithm for petroleum reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Hoang, Hai Minh

2005-07-01

Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)

New non-orthogonality treatment for atmospheric boundary layer flow simulation above highly non-uniform terrains

Directory of Open Access Journals (Sweden)

Mirkov Nikola S.

2016-01-01

Full Text Available In this paper we validate an improved finite volume approximation of Reynolds Averaged Navier-Stokes equations for simulation of wind flows in body-fitted grids generated by algebraic extrusion from digital terrain elevation data, proposed in N. Mirkov et. al. J. Comput. Phys. 287, 18-45(2015, [1]. The approach is based on second-order accurate finite volume method with collocated variable arrangement and pressure-velocity coupling trough SIMPLE algorithm. The main objective is the attenuation of spurious pressure field oscillations in regions with discontinuity in grid line slopes, as encountered in grids representing highly non-uniform terrains. Moreover, the approach relaxes the need for grid generation based on elliptic PDEs or grid smoothing by applying fixed point iterations (i.e. Gauss-Seidel to initial grid node positions resulting from algebraic grid generators. Drawbacks of previous approaches which ignored treatment of finite volume grid cell cases with intersection point offset in non-orthogonality corrections are removed. Application to real-life wind farm project at Dobrič (Srvljig, Serbia is used to assess the effectiveness of the method. The results validate the view in which accurate discretization of governing equations play more important role than the choice of turbulence modelling closures. [Projekat Ministarstva nauke Republike Srbije, br. TR-33036

Sanity check for NN bound states in lattice QCD with Lüscher’s finite volume formula – Disclosing Symptoms of Fake Plateaux –

Directory of Open Access Journals (Sweden)

Aoki Sinya

2018-01-01

Full Text Available The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Lüscher’s finite volume formula [1–3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4–5%. (ii The volume independence of plateaux in NPL2013 does not prove their correctness. (iii Effective range expansions (EREs in NPL2013 violate the physical pole condition. (iv Their comment is partly based on new data and analysis different from the original ones. (v Their new ERE does not satisfy the Lüscher’s finite volume formula.

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-01-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax

New ghost-node method for linking different models with varied grid refinement

Science.gov (United States)

James, S.C.; Dickinson, J.E.; Mehl, S.W.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Eddebbarh, A.-A.

2006-01-01

A flexible, robust method for linking grids of locally refined ground-water flow models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined "child" model that is contained within a larger and coarser "parent" model that is based on the iterative method of Steffen W. Mehl and Mary C. Hill (2002, Advances in Water Res., 25, p. 497-511; 2004, Advances in Water Res., 27, p. 899-912). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has matching grids (parent cells border an integer number of child cells) or nonmatching grids. The coupled grids are simulated by using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child-cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models. When the grids are nonmatching, model accuracy is slightly increased compared to that for matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to couple distinct models because the overall head and flow errors relative to the analytical solution are less than if only the regional coarse-grid model was used to simulate flow in the child model's domain.

Analysis of the neutron flux in an annular pulsed reactor by using finite volume method

Energy Technology Data Exchange (ETDEWEB)

Silva, Mário A.B. da; Narain, Rajendra; Bezerra, Jair de L., E-mail: mabs500@gmail.com, E-mail: narain@ufpe.br, E-mail: jairbezerra@gmail.com [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Centro de Tecnologia e Geociências. Departamento de Energia Nuclear

2017-07-01

Production of very intense neutron sources is important for basic nuclear physics and for material testing and isotope production. Nuclear reactors have been used as sources of intense neutron fluxes, although the achievement of such levels is limited by the inability to remove fission heat. Periodic pulsed reactors provide very intense fluxes by a rotating modulator near a subcritical core. A concept for the production of very intense neutron fluxes that combines features of periodic pulsed reactors and steady state reactors was proposed by Narain (1997). Such a concept is known as Very Intense Continuous High Flux Pulsed Reactor (VICHFPR) and was analyzed by using diffusion equation with moving boundary conditions and Finite Difference Method with Crank-Nicolson formalism. This research aims to analyze the flux distribution in the Very Intense Continuous Flux High Pulsed Reactor (VICHFPR) by using the Finite Volume Method and compares its results with those obtained by the previous computational method. (author)

Analysis of the neutron flux in an annular pulsed reactor by using finite volume method

International Nuclear Information System (INIS)

Silva, Mário A.B. da; Narain, Rajendra; Bezerra, Jair de L.

2017-01-01

Production of very intense neutron sources is important for basic nuclear physics and for material testing and isotope production. Nuclear reactors have been used as sources of intense neutron fluxes, although the achievement of such levels is limited by the inability to remove fission heat. Periodic pulsed reactors provide very intense fluxes by a rotating modulator near a subcritical core. A concept for the production of very intense neutron fluxes that combines features of periodic pulsed reactors and steady state reactors was proposed by Narain (1997). Such a concept is known as Very Intense Continuous High Flux Pulsed Reactor (VICHFPR) and was analyzed by using diffusion equation with moving boundary conditions and Finite Difference Method with Crank-Nicolson formalism. This research aims to analyze the flux distribution in the Very Intense Continuous Flux High Pulsed Reactor (VICHFPR) by using the Finite Volume Method and compares its results with those obtained by the previous computational method. (author)

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei

2012-05-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots

Directory of Open Access Journals (Sweden)

Grönemeyer Dietrich HW

2006-05-01

investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants. Results The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor. Conclusion The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute

Characterization of Slosh Damping for Ortho-Grid and Iso-Grid Internal Tank Structures

Science.gov (United States)

Westra, Douglas G.; Sansone, Marco D.; Eberhart, Chad J.; West, Jeffrey S.

2016-01-01

Grid stiffened tank structures such as Ortho-Grid and Iso-Grid are widely used in cryogenic tanks for providing stiffening to the tank while reducing mass, compared to tank walls of constant cross-section. If the structure is internal to the tank, it will positively affect the fluid dynamic behavior of the liquid propellant, in regard to fluid slosh damping. As NASA and commercial companies endeavor to explore the solar system, vehicles will by necessity become more mass efficient, and design margin will be reduced where possible. Therefore, if the damping characteristics of the Ortho-Grid and Iso-Grid structure is understood, their positive damping effect can be taken into account in the systems design process. Historically, damping by internal structures has been characterized by rules of thumb and for Ortho-Grid, empirical design tools intended for slosh baffles of much larger cross-section have been used. There is little or no information available to characterize the slosh behavior of Iso-Grid internal structure. Therefore, to take advantage of these structures for their positive damping effects, there is much need for obtaining additional data and tools to characterize them. Recently, the NASA Marshall Space Flight Center conducted both sub-scale testing and computational fluid dynamics (CFD) simulations of slosh damping for Ortho-Grid and Iso-Grid tanks for cylindrical tanks containing water. Enhanced grid meshing techniques were applied to the geometrically detailed and complex Ortho-Grid and Iso-Grid structures. The Loci-STREAM CFD program with the Volume of Fluid Method module for tracking and locating the water-air fluid interface was used to conduct the simulations. The CFD simulations were validated with the test data and new empirical models for predicting damping and frequency of Ortho-Grid and Iso-Grid structures were generated.

Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals

Science.gov (United States)

Deimert, C.; Potter, M. E.; Okoniewski, M.

2016-12-01

The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.

Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method

KAUST Repository

Efendiev, Yalchin R.

2015-06-05

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.

Optical strain measurements and its finite element analysis of cold ...

African Journals Online (AJOL)

International Journal of Engineering, Science and Technology ... Online video images of square grid were recorded during the deformation ... Finite element software ANSYS has been applied for the analysis of the upset forming process.

Grid-generated He II turbulence in a finite channel - experiment

International Nuclear Information System (INIS)

Niemela, J.J.; Skrbek, L.; Stalp, S.R.

2001-01-01

We present experimental data on decaying turbulence, generated by towing a grid through a stationary sample of He II. We describe in detail the experimental apparatus and physical principles that allow observation of up to six orders of magnitude of decaying vortex line density over three orders of magnitude in time using the second sound attenuation technique. (orig.)

Recent Developments in Grid Generation and Force Integration Technology for Overset Grids

Science.gov (United States)

Chan, William M.; VanDalsem, William R. (Technical Monitor)

1994-01-01

Recent developments in algorithms and software tools for generating overset grids for complex configurations are described. These include the overset surface grid generation code SURGRD and version 2.0 of the hyperbolic volume grid generation code HYPGEN. The SURGRD code is in beta test mode where the new features include the capability to march over a collection of panel networks, a variety of ways to control the side boundaries and the marching step sizes and distance, a more robust projection scheme and an interpolation option. New features in version 2.0 of HYPGEN include a wider range of boundary condition types. The code also allows the user to specify different marching step sizes and distance for each point on the surface grid. A scheme that takes into account of the overlapped zones on the body surface for the purpose of forces and moments computation is also briefly described, The process involves the following two software modules: MIXSUR - a composite grid generation module to produce a collection of quadrilaterals and triangles on which pressure and viscous stresses are to be integrated, and OVERINT - a forces and moments integration module.

New Ghost-node method for linking different models with varied grid refinement

International Nuclear Information System (INIS)

Mehl, Steffen W.; Hill, Mary Catherine; James, Scott Carlton; Leake, Stanley A.; Zyvoloski, George A.; Dickinson, Jesse E.; Eddebbarh, Al A.

2006-01-01

A flexible, robust method for linking grids of locally refined models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined 'child' model that is contained within a larger and coarser 'parent' model that is based on the iterative method of Mehl and Hill (2002, 2004). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has either matching grids (parent cells border an integer number of child cells; Figure 2a) or non-matching grids (parent cells border a non-integer number of child cells; Figure 2b). The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models (Mehl and Hill, 2002). When the grids are non-matching, model accuracy is slightly increased over matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models because the overall error is less than if only the regional model was used to simulate flow in the child model's domain

Numerical comparison of robustness of some reduction methods in rough grids

KAUST Repository

Hou, Jiangyong

2014-04-09

In this article, we present three nonsymmetric mixed hybrid RT 1 2 methods and compare with some recently developed reduction methods which are suitable for the single-phase Darcy flow problem with full anisotropic and highly heterogeneous permeability on general quadrilateral grids. The methods reviewed are multipoint flux approximation (MPFA), multipoint flux mixed finite element method, mixed-finite element with broken RT 1 2 method, MPFA-type mimetic finite difference method, and symmetric mixed-hybrid finite element method. The numerical experiments of these methods on different distorted meshes are compared, as well as their differences in performance of fluxes are discussed. © 2014 Wiley Periodicals, Inc.

The advanced smart grid edge power driving sustainability

CERN Document Server

Carvallo, Andres

2011-01-01

Placing emphasis on practical ""how-to"" guidance, this cutting-edge resource provides you with a first-hand, insider's perspective on the advent and evolution of smart grids in the 21st century (smart grid 1.0). You gain a thorough understanding of the building blocks that comprise basic smart grids, including power plant, transmission substation, distribution, and meter automation. Moreover, this forward-looking volume explores the next step of this technology's evolution. It provides a detailed explanation of how an advanced smart grid incorporates demand response with smart appliances and

Visualization of big SPH simulations via compressed octree grids

KAUST Repository

Reichl, Florian

2013-10-01

Interactive and high-quality visualization of spatially continuous 3D fields represented by scattered distributions of billions of particles is challenging. One common approach is to resample the quantities carried by the particles to a regular grid and to render the grid via volume ray-casting. In large-scale applications such as astrophysics, however, the required grid resolution can easily exceed 10K samples per spatial dimension, letting resampling approaches appear unfeasible. In this paper we demonstrate that even in these extreme cases such approaches perform surprisingly well, both in terms of memory requirement and rendering performance. We resample the particle data to a multiresolution multiblock grid, where the resolution of the blocks is dictated by the particle distribution. From this structure we build an octree grid, and we then compress each block in the hierarchy at no visual loss using wavelet-based compression. Since decompression can be performed on the GPU, it can be integrated effectively into GPU-based out-of-core volume ray-casting. We compare our approach to the perspective grid approach which resamples at run-time into a view-aligned grid. We demonstrate considerably faster rendering times at high quality, at only a moderate memory increase compared to the raw particle set. © 2013 IEEE.

Analysis of the optimized H type grid spring by a characterization test and the finite element method under the in-grid boundary

International Nuclear Information System (INIS)

Yoon, Kyung Ho; Lee, Kang Hee; Kang, Heung Seok; Song, Kee Nam

2006-01-01

Characterization tests (load vs. displacement curve) are conducted for the springs of Zirconium alloy spacer grids for an advanced LWR fuel assembly. Twofold testing is employed: strap-based and assembly-based tests. The assembly-based test satisfies the in situ boundary conditions of the spring within the grid assembly. The aim of the characterization test via the aforementioned two methods is to establish an appropriate assembly-based test method that fulfills the actual boundary conditions. A characterization test under the spacer grid assembly boundary condition is also conducted to investigate the actual behavior of the spring in the core. The stiffness of the characteristic curve is smaller than that of the strap-wised boundary condition. This phenomenon may cause the strap slit condition. A spacer grid consists of horizontal and vertical straps. The strap slit positions are differentiated from each other. They affords examination of the variation of the external load distribution in the grid spring. Localized regions of high stress and their values are analyzed, as they may be affected by the spring shape. Through a comparison of the results of the test and FE analysis, it is concluded that the present assembly-based analysis model and procedure are reasonably well conducted and can be used for spring characterization in the core. Guidelines for improving the mechanical integrity of the spring are also discussed

Electromagnetic and mechanical design of gridded radio-frequency cavity windows

Energy Technology Data Exchange (ETDEWEB)

Alsharo' a, Mohammad M. [Illinois Inst. of Technology, Chicago, IL (United States)

2004-12-01

Electromagnetic, thermal and structural analyses of radio-frequency (RF) cavities were performed as part of a developmental RF cavity program for muon cooling. RF cavities are necessary to provide longitudinal focusing of the muons and to compensate for their energy loss. Closing the cavity ends by electrically conducting windows reduces the power requirement and increases the on-axis electric field for a given maximum surface electric field. Many factors must be considered in the design of RF cavity windows. RF heating can cause the windows to deform in the axial direction of the cavity. The resulting thermal stresses in the window must be maintained below the yield stress of the window material. The out-of-plane deflection must be small enough so that the consequent frequency shift is tolerable. For example, for an 805 MHz cavity, the out-of-plane deflection must be kept below 25 microns to prevent the frequency of the cavity from shifting more than 10 kHz. In addition, the window design should yield smooth electric and magnetic fields, terminate field leakage beyond the window, and minimize beam scattering. In the present thesis, gridded-tube window designs were considered because of their high structural integrity. As a starting point in the analysis, a cylindrical pillbox cavity was considered as a benchmark problem. Analytical and finite element solutions were obtained for the electric and magnetic fields, power loss density, and temperature profile. Excellent agreement was obtained between the analytical and finite element results. The finite element method was then used to study a variety of gridded-tube windows. It was found that cooling of the gridded-tube windows by passing helium gas inside the tubes significantly reduces the out-of-plane deflection and the thermal stresses. Certain tube geometries and grid patterns were found to satisfy all of the design requirements.

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry

International Nuclear Information System (INIS)

Bernard-Champmartin, Aude; Ghidaglia, Jean-Michel; Braeunig, Jean-Philippe

2013-01-01

In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable h), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific up-winding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uh. (authors)

The CrossGrid project

International Nuclear Information System (INIS)

Kunze, M.

2003-01-01

There are many large-scale problems that require new approaches to computing, such as earth observation, environmental management, biomedicine, industrial and scientific modeling. The CrossGrid project addresses realistic problems in medicine, environmental protection, flood prediction, and physics analysis and is oriented towards specific end-users: Medical doctors, who could obtain new tools to help them to obtain correct diagnoses and to guide them during operations; industries, that could be advised on the best timing for some critical operations involving risk of pollution; flood crisis teams, that could predict the risk of a flood on the basis of historical records and actual hydrological and meteorological data; physicists, who could optimize the analysis of massive volumes of data distributed across countries and continents. Corresponding applications will be based on Grid technology and could be complex and difficult to use: the CrossGrid project aims at developing several tools that will make the Grid more friendly for average users. Portals for specific applications will be designed, that should allow for easy connection to the Grid, create a customized work environment, and provide users with all necessary information to get their job done

A finite volume alternate direction implicit approach to modeling selective laser melting

DEFF Research Database (Denmark)

Hattel, Jesper Henri; Mohanty, Sankhya

2013-01-01

Over the last decade, several studies have attempted to develop thermal models for analyzing the selective laser melting process with a vision to predict thermal stresses, microstructures and resulting mechanical properties of manufactured products. While a holistic model addressing all involved...... to accurately simulate the process, are constrained by either the size or scale of the model domain. A second challenging aspect involves the inclusion of non-linear material behavior into the 3D implicit FE models. An alternating direction implicit (ADI) method based on a finite volume (FV) formulation...... is proposed for modeling single-layer and few-layers selective laser melting processes. The ADI technique is implemented and applied for two cases involving constant material properties and non-linear material behavior. The ADI FV method consume less time while having comparable accuracy with respect to 3D...

Global 3-D FDTD Maxwell's-Equations Modeling of Ionospheric Disturbances Associated with Earthquakes Using an Optimized Geodesic Grid

Science.gov (United States)

Simpson, J. J.; Taflove, A.

2005-12-01

We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A

Buckling behavior analysis of spacer grid by lateral impact load

International Nuclear Information System (INIS)

Yoon, Kyung Ho; Kang, Heung Seok; Kim, Hyung Kyu; Song, Kee Nam

2000-05-01

The spacer grid is one of the main structural components in the fuel assembly, Which supports the fuel rods, guides cooling water, and protects the system from an external impact load, such as earthquakes. Therefore, the mechanical and structural properties of the spacer grids must be extensively examined while designing it. In this report, free fall type shock tests on the several kinds of the specimens of the spacer grids were also carried out in order to compare the results among the candidate grids. A free fall carriage on the specimen accomplishes the test. In addition to this, a finite element method for predicting the critical impact strength of the spacer grids is described. FE method on the buckling behavior of the spacer grids are performed for a various array of sizes of the grids considering that the spacer grid is an assembled structure with thin-walled plates and imposing proper boundary conditions by nonlinear dynamic impact analysis using ABAQUS/explicit code. The simulated results results also similarly predicted the local buckling phenomena and were found to give good correspondence with the shock test results

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

Science.gov (United States)

Keslerová, Radka; Trdlička, David

2015-09-01

This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

Study on the methodology for allocating costs of grid losses

International Nuclear Information System (INIS)

Aalberts, A.; Dekker, G.; Jaarsma, S.; Tieben, B.; Vlug, N.

2011-01-01

The research question in this report: 'Where are grid losses caused and in which (objective) manner can the costs of these grid losses be allocated to the buyers. The key questions answered in the research are: (1) In which locations of the electricity grid are losses caused and what is the volume of these losses?; (2) How are the costs of grid losses allocated to the various groups of end users?; and (3) What are alternative way(s) to allocate the costs of grid losses to the buyers?. [nl

Non-Galerkin Coarse Grids for Algebraic Multigrid

Energy Technology Data Exchange (ETDEWEB)

Falgout, Robert D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schroder, Jacob B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2014-06-26

Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

Program EAGLE User’s Manual. Volume 3. Grid Generation Code

Science.gov (United States)

1988-09-01

15 1. ompps.te Grid Structure ..... .. .................. . 15 2. Block Interfaces ......... ...................... . 18 3. Fundmental ...in principle it is possible to establish a correspondence between any physical region and a single empty rectangular block for general three...differences. Since this second surrounding layer is not involved in the grid generation, no further account will be taken of its presence in the present

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

Science.gov (United States)

Bijnens, Johan

2018-03-01

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

Finite Volume Element Predictor-corrector Method for a Class of Nonlinear Parabolic Systems%一类非线性抛物型方程组的有限体积元预估-校正方法

Institute of Scientific and Technical Information of China (English)

高夫征

2005-01-01

A finite volume element predictor-correetor method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.

Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

Science.gov (United States)

Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui

2018-06-01

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

Science.gov (United States)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Domain decomposition multigrid for unstructured grids

Energy Technology Data Exchange (ETDEWEB)

Shapira, Yair

1997-01-01

A two-level preconditioning method for the solution of elliptic boundary value problems using finite element schemes on possibly unstructured meshes is introduced. It is based on a domain decomposition and a Galerkin scheme for the coarse level vertex unknowns. For both the implementation and the analysis, it is not required that the curves of discontinuity in the coefficients of the PDE match the interfaces between subdomains. Generalizations to nonmatching or overlapping grids are made.

Finite volume thermal-hydraulics and neutronics coupled calculations - 15300

International Nuclear Information System (INIS)

Araujo Silva, V.; Campagnole dos Santos, A.A.; Mesquit, A.Z.; Bernal, A.; Miro, R.; Verdu, G.; Pereira, C.

2015-01-01

The computational power available nowadays allows the coupling of neutronics and thermal-hydraulics codes for reactor studies. The present methodology foresees at least one constraint to the separated codes in order to perform coupled calculations: both codes must use the same geometry, however, meshes can be different for each code as long as the internal surfaces stays the same. Using the finite volume technique, a 3D diffusion nodal code was implemented to deal with neutron transport. This code can handle non-structured meshes which allows for complicated geometries calculations and therefore more flexibility. A computational fluid dynamics (CFD) code was used in order to obtain the same level of details for the thermal hydraulics calculations. The chosen code is OpenFOAM, an open-source CFD tool. Changes in OpenFOAM allow simple coupled calculations of a PWR fuel rod with neutron transport code. OpenFOAM sends coolant density information and fuel temperature to the neutron transport code that sends back power information. A mapping function is used to average values when one node in one side corresponds to many nodes in the other side. Data is exchanged between codes by library calls. As the results of a fuel rod calculations progress, more complicated and processing demanding geometries will be simulated, aiming to the simulation of a real scale PWR fuel assembly

Task oriented design of robot kinematics using grid method and its application to nuclear power plant

International Nuclear Information System (INIS)

Chang, Pyung-Hun; Park, Joon-Young

2002-01-01

This paper presents a Task Oriented Design method for robot kinematics based on grid method, widely used in finite difference method and heat transfer/fluid flow analyses. This approach drastically reduces complexities and computational burden due to previous approaches. More specifically, the grid method with a new formulation simplifies the design to a problem of three-design-variable unit grid, which does not require to solve inverse/forward kinematics. The effectiveness of the grid method has been confirmed through a kinematics design of a robot for nuclear power plants. (author)

Effect of grid resolution on large eddy simulation of wall-bounded turbulence

Science.gov (United States)

Rezaeiravesh, S.; Liefvendahl, M.

2018-05-01

The effect of grid resolution on a large eddy simulation (LES) of a wall-bounded turbulent flow is investigated. A channel flow simulation campaign involving a systematic variation of the streamwise (Δx) and spanwise (Δz) grid resolution is used for this purpose. The main friction-velocity-based Reynolds number investigated is 300. Near the walls, the grid cell size is determined by the frictional scaling, Δx+ and Δz+, and strongly anisotropic cells, with first Δy+ ˜ 1, thus aiming for the wall-resolving LES. Results are compared to direct numerical simulations, and several quality measures are investigated, including the error in the predicted mean friction velocity and the error in cross-channel profiles of flow statistics. To reduce the total number of channel flow simulations, techniques from the framework of uncertainty quantification are employed. In particular, a generalized polynomial chaos expansion (gPCE) is used to create metamodels for the errors over the allowed parameter ranges. The differing behavior of the different quality measures is demonstrated and analyzed. It is shown that friction velocity and profiles of the velocity and Reynolds stress tensor are most sensitive to Δz+, while the error in the turbulent kinetic energy is mostly influenced by Δx+. Recommendations for grid resolution requirements are given, together with the quantification of the resulting predictive accuracy. The sensitivity of the results to the subgrid-scale (SGS) model and varying Reynolds number is also investigated. All simulations are carried out with second-order accurate finite-volume-based solver OpenFOAM. It is shown that the choice of numerical scheme for the convective term significantly influences the error portraits. It is emphasized that the proposed methodology, involving the gPCE, can be applied to other modeling approaches, i.e., other numerical methods and the choice of SGS model.

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

Directory of Open Access Journals (Sweden)

Bijnens Johan

2018-01-01

Full Text Available I present higher loop order results for several calculations in Chiral perturbation Theory. 1 Two-loop results at finite volume for hadronic vacuum polarization. 2 A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3 Chiral corrections to neutron-anti-neutron oscillations.

Quantitative evaluation of potential irradiation geometries for carbon-ion beam grid therapy.

Science.gov (United States)

Tsubouchi, Toshiro; Henry, Thomas; Ureba, Ana; Valdman, Alexander; Bassler, Niels; Siegbahn, Albert

2018-03-01

Radiotherapy using grids containing cm-wide beam elements has been carried out sporadically for more than a century. During the past two decades, preclinical research on radiotherapy with grids containing small beam elements, 25 μm-0.7 mm wide, has been performed. Grid therapy with larger beam elements is technically easier to implement, but the normal tissue tolerance to the treatment is decreasing. In this work, a new approach in grid therapy, based on irradiations with grids containing narrow carbon-ion beam elements was evaluated dosimetrically. The aim formulated for the suggested treatment was to obtain a uniform target dose combined with well-defined grids in the irradiated normal tissue. The gain, obtained by crossfiring the carbon-ion beam grids over a simulated target volume, was quantitatively evaluated. The dose distributions produced by narrow rectangular carbon-ion beams in a water phantom were simulated with the PHITS Monte Carlo code. The beam-element height was set to 2.0 cm in the simulations, while the widths varied from 0.5 to 10.0 mm. A spread-out Bragg peak (SOBP) was then created for each beam element in the grid, to cover the target volume with dose in the depth direction. The dose distributions produced by the beam-grid irradiations were thereafter constructed by adding the dose profiles simulated for single beam elements. The variation of the valley-to-peak dose ratio (VPDR) with depth in water was thereafter evaluated. The separation of the beam elements inside the grids were determined for different irradiation geometries with a selection criterion. The simulated carbon-ion beams remained narrow down to the depths of the Bragg peaks. With the formulated selection criterion, a beam-element separation which was close to the beam-element width was found optimal for grids containing 3.0-mm-wide beam elements, while a separation which was considerably larger than the beam-element width was found advantageous for grids containing 0.5-mm

On the modification of the Efimov spectrum in a finite cubic box

International Nuclear Information System (INIS)

Kreuzer, S.; Hammer, H.W.

2010-01-01

Three particles with large scattering length display a universal spectrum of three-body bound states called ''Efimov trimers''. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite-volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. We investigate the effects of partial-wave mixing and study the behavior of shallow trimers near the dimer energy. Moreover, we provide numerical evidence for universal scaling of the finite-volume corrections. (orig.)

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

Science.gov (United States)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains

Energy Technology Data Exchange (ETDEWEB)

Petersson, N. Anders; Sjögreen, Björn

2014-10-01

We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more

Analysis of a grid window structure for RF cavities in a Muon cooling channel

International Nuclear Information System (INIS)

Ladran, A.; Li, D.; Moretti, A.; Rimmer, R.; Staples, J.; Virostek, S.; Zisman, M.

2003-01-01

We report on the electromagnetic and thermal analysis of a grid window structure for high gradient, low frequency RF cavities. Windows may be utilized to close the beam iris and increase shunt impedance of closed-cell RF cavities. This work complements previous work presented for windows made of solid beryllium foil. An electromagnetic and thermal analysis of the thin wall tubes in a grid pattern was conducted using both MAFIA4 and ANSYS finite element analyses. The results from both codes agreed well for a variety of grid configurations and spacing. The grid configuration where the crossing tubes touched was found to have acceptable E-Fields and H-Fields performance. The thermal profiles for the grid will also be shown to determine a viable cooling profile

Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid

International Nuclear Information System (INIS)

Kageyama, Akira; Yoshida, Masaki

2005-01-01

We have developed finite difference codes based on the Yin-Yang grid for the geodynamo simulation and the mantle convection simulation. The Yin-Yang grid is a kind of spherical overset grid that is composed of two identical component grids. The intrinsic simplicity of the mesh configuration of the Yin-Yang grid enables us to develop highly optimized simulation codes on massively parallel supercomputers. The Yin-Yang geodynamo code has achieved 15.2 Tflops with 4096 processors on the Earth Simulator. This represents 46% of the theoretical peak performance. The Yin-Yang mantle code has enabled us to carry out mantle convection simulations in realistic regimes with a Rayleigh number of 10 7 including strongly temperature dependent viscosity with spatial contrast up to 10 6

A Finite-Volume computational mechanics framework for multi-physics coupled fluid-stress problems

International Nuclear Information System (INIS)

Bailey, C; Cross, M.; Pericleous, K.

1998-01-01

Where there is a strong interaction between fluid flow, heat transfer and stress induced deformation, it may not be sufficient to solve each problem separately (i.e. fluid vs. stress, using different techniques or even different computer codes). This may be acceptable where the interaction is static, but less so, if it is dynamic. It is desirable for this reason to develop software that can accommodate both requirements (i.e. that of fluid flow and that of solid mechanics) in a seamless environment. This is accomplished in the University of Greenwich code PHYSICA, which solves both the fluid flow problem and the stress-strain equations in a unified Finite-Volume environment, using an unstructured computational mesh that can deform dynamically. Example applications are given of the work of the group in the metals casting process (where thermal stresses cause elasto- visco-plastic distortion)

Microscopic deformation and strain hardening analysis of ferrite–bainite dual-phase steels using micro-grid method

International Nuclear Information System (INIS)

Ishikawa, Nobuyuki; Yasuda, Kyono; Sueyoshi, Hitoshi; Endo, Shigeru; Ikeda, Hiroshi; Morikawa, Tatsuya; Higashida, Kenji

2015-01-01

The local strain measurement method using nanometer-scaled micro grids printed on the surface of a specimen by an electron lithography technique (the micro-grid method) has been established. Microscopic deformation behavior of the ferrite–bainite steels with different bainite volume fraction, 16% and 40% of bainite, was evaluated. Strain localization in the ferrite phase adjacent to the ferrite/bainite boundary was clearly observed and visualized. Highly strained regions expanded toward the inner region of the ferrite phase and connected each other with an increase of macroscopic strain. The existence of hard bainite phase plays an important role for inducing strain localization in the ferrite phase by plastic constraint in the boundary parallel to the tensile direction. In order to obtain further understanding of microscopic deformation behavior, finite element analysis using the representative volume element, which is expressed by the axisymmetric unit cell containing a hard phase surrounded by a soft phase matrix, was conducted. It was found that the macroscopic stress–strain behavior of ferrite–bainite steels was well simulated by the unit cell models. Strain concentration in the ferrite phase was highly enhanced for the ferrite-40% bainite steel, and this imposed higher internal stress in the bainite phase, resulting in higher strain hardening rate in the early stage of the deformation. However, smaller ferrite volume fraction of ferrite-40% bainite steel induced bainite plastic deformation in order to fulfill the macroscopic strain of the steel. Accordingly, strain hardening capacity of the ferrite-40% bainite steel was reduced to a significant degree, resulting in a smaller uniform elongation than the ferrite-16% bainite steel

Storm Water Infiltration and Focused Groundwater Recharge in a Rain Garden: Finite Volume Model and Numerical Simulations for Different Configurations and Climates

Science.gov (United States)

Aravena, J.; Dussaillant, A. R.

2006-12-01

Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).

An unstructured finite volume solver for two phase water/vapour flows based on an elliptic oriented fractional step method

International Nuclear Information System (INIS)

Mechitoua, N.; Boucker, M.; Lavieville, J.; Pigny, S.; Serre, G.

2003-01-01

Based on experience gained at EDF and Cea, a more general and robust 3-dimensional (3D) multiphase flow solver has been being currently developed for over three years. This solver, based on an elliptic oriented fractional step approach, is able to simulate multicomponent/multiphase flows. Discretization follows a 3D full unstructured finite volume approach, with a collocated arrangement of all variables. The non linear behaviour between pressure and volume fractions and a symmetric treatment of all fields are taken into account in the iterative procedure, within the time step. It greatly enforces the realizability of volume fractions (i.e 0 < α < 1), without artificial numerical needs. Applications to widespread test cases as static sedimentation, water hammer and phase separation are shown to assess the accuracy and the robustness of the flow solver in different flow conditions, encountered in nuclear reactors pipes. (authors)

Counting Subspaces of a Finite Vector Space

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 11. Counting Subspaces of a Finite Vector Space – 1. Amritanshu Prasad. General Article Volume 15 Issue 11 November 2010 pp 977-987. Fulltext. Click here to view fulltext PDF. Permanent link:

A new variational formulation of kinetic plasma theory and the application of moving finite elements

International Nuclear Information System (INIS)

Glasser, A.H.

1991-01-01

A new variational formulation has been developed for the system of equations governing kinetic plasmas and electromagnetic fields. It is used to apply the method of Moving Finite Elements to the electromagnetic fields. The fields are expanded in a basis of linear finite elements on a movable, unstructured grid of triangles in 2D or tetrahedra in 3D, while the plasma distribution function is expanded in a basis of super particles. Minimization of the variational with respect to the time derivatives of the field quantities yields a coupled system of equations for simultaneously advancing the amplitudes and node positions, resulting in adaptive grid motion. The adaptivity of the grid may save a large factor in the size of the grid and the number of particles required in many problems. Minimization of the variational with respect to the time derivatives of the particle positions and velocities gives the equations of motion, providing consistent prescriptions for assigning particles to the grid and fields to the particles. Orthogonality conditions on the particles are derived as conditions for keeping their equations of motion independent. Collisions can be included in a natural way. The relationship between PIC methods and alternative methods of discretizing phase space is clarified

An h-adaptive finite element method for turbulent heat transfer

Energy Technology Data Exchange (ETDEWEB)

Carriington, David B [Los Alamos National Laboratory

2009-01-01

A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

KAUST Repository

Wheeler, Mary; Xue, Guangri; Yotov, Ivan

2013-01-01

We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method

Stress Analysis of Single Spacer Grid Support considering Fuel Rod

Energy Technology Data Exchange (ETDEWEB)

Yoo, Y. G.; Jung, D. H.; Kim, J. H. [Chungnam National University, Daejeon (Korea, Republic of); Park, J. K.; Jeon, K. L. [Korea Nuclear Fuel, Daejeon (Korea, Republic of)

2010-10-15

Pressurized water reactor (PWR) nuclear fuel assembly is mainly composed of a top-end piece, a bottom-end piece, lots of fuel rods, and several spacer grids. Among them, the main function of spacer grid is protecting fuel rods from Fluid Induced Vibration (FIV). The cross section of spacer grid assembled by laser welding in upper and lower point. When the fuel rod inserted in spacer gird, spring and dimple and around of welded area got a stresses. The main hypothesis of this analysis is the boundary area of HAZ and base metal can get a lot of damage than other area by FIV. So, design factors of spacer grid mainly considered to preventing the fatigue failure in HAZ and spring and dimple of spacer grid. From previous researching, the environment in reactor verified. Pressure and temperature of light water observed 15MPa and 320 .deg. C, and vibration of the fuel rod observed within 0 {approx} 50Hz. In this study, mechanical properties of zirconium alloy that extracted from the test and the spacer grid model which used in the PWR were applied in stress analyzing. General-purpose finite element analysis program was used ANSYS Workbench 12.0.1 version. 3-D CAD program CATIA was used to create spacer grid model

Prospects for investment in large-scale, grid-connected solar power in Africa

DEFF Research Database (Denmark)

Hansen, Ulrich Elmer; Nygaard, Ivan; Pedersen, Mathilde Brix

since the 1990s have changed the competiveness of solar PV in all markets, ranging from individual households via institutions to mini-grids and grid-connected installations. In volume and investment, the market for large-scale grid-connected solar power plants is by far the most important......-scale investments in grid-connected solar power plants and local assembly facilities for PV panels, have exceeded even optimistic scenarios. Finally, therefore, there seem to be bright prospects for investment in large-scale grid-connected solar power in Africa....

Adaptive hierarchical grid model of water-borne pollutant dispersion

Science.gov (United States)

Borthwick, A. G. L.; Marchant, R. D.; Copeland, G. J. M.

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection-diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection-diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection-diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.

Generating Free-Form Grid Truss Structures from 3D Scanned Point Clouds

Directory of Open Access Journals (Sweden)

Hui Ding

2017-01-01

Full Text Available Reconstruction, according to physical shape, is a novel way to generate free-form grid truss structures. 3D scanning is an effective means of acquiring physical form information and it generates dense point clouds on surfaces of objects. However, generating grid truss structures from point clouds is still a challenge. Based on the advancing front technique (AFT which is widely used in Finite Element Method (FEM, a scheme for generating grid truss structures from 3D scanned point clouds is proposed in this paper. Based on the characteristics of point cloud data, the search box is adopted to reduce the search space in grid generating. A front advancing procedure suit for point clouds is established. Delaunay method and Laplacian method are used to improve the quality of the generated grids, and an adjustment strategy that locates grid nodes at appointed places is proposed. Several examples of generating grid truss structures from 3D scanned point clouds of seashells are carried out to verify the proposed scheme. Physical models of the grid truss structures generated in the examples are manufactured by 3D print, which solidifies the feasibility of the scheme.

Finite size effects in lattice QCD with dynamical Wilson fermions

Energy Technology Data Exchange (ETDEWEB)

Orth, B.

2004-06-01

Due to limited computing resources choosing the parameters for a full lattice QCD simulation always amounts to a compromise between the competing objectives of a lattice spacing as small, quarks as light, and a volume as large as possible. Aiming at pushing unquenched simulations with the standard Wilson action towards the computationally expensive regime of small quark masses, the GRAL project addresses the question whether computing time can be saved by sticking to lattices with rather modest numbers of grid sites and extrapolating the finite-volume results to the infinite volume (prior to the usual chiral and continuum extrapolations). In this context we investigate in this work finite-size effects in simulated light hadron masses. Understanding their systematic volume dependence may not only help saving computer time in light quark simulations with the Wilson action, but also guide future simulations with dynamical chiral fermions which for a foreseeable time will be restricted to rather small lattices. We analyze data from hybrid Monte Carlo simulations with the N{sub f} = 2 Wilson action at two values of the coupling parameter, {beta} = 5.6 (lattice spacing {alpha} {approx} 0.08 fm) and {beta} = 5.32144 ({alpha} {approx} 0.13 fm). The larger {beta} corresponds to the coupling used previously by SESAM/T{chi}L. The considered hopping parameters {kappa} = 0.1575, 0.158 (at the larger {beta}) and {kappa} = 0.1665 (at the smaller {beta}) correspond to quark masses of 85, 50 and 36% of the strange quark mass, respectively. At each quark mass we study at least three different lattice extents in the range from L = 10 to L = 24 (0.85-2.04 fm). Estimates of autocorrelation times in the stochastic updating process and of the computational cost of every run are given. For each simulated sea quark mass we calculate quark propagators and hadronic correlation functions in order to extract the pion, rho and nucleon masses as well as the pion decay constant and the quark mass

A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

Energy Technology Data Exchange (ETDEWEB)

Melboe, Hallgeir

2001-10-01

This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution

Directory of Open Access Journals (Sweden)

Marco Carbone

2015-02-01

Full Text Available The increasing imperviousness of urban areas reduces the infiltration and evapotranspiration capacity of urban catchments and results in increased runoff. In the last few decades, several solutions and techniques have been proposed to prevent such impacts by restoring the hydrological cycle. A limiting factor in spreading the use of such systems is the lack of proper modelling tools for design, especially for the infiltration processes in a growing medium. In this research, a physically-based model, employing the explicit Finite Volume Method (FVM, is proposed for modelling infiltration into growing media. The model solves a modified version of the Richards equation using a formulation which takes into account the main characteristics of green infrastructure substrates. The proposed model was verified against the HYDRUS-1D software and the comparison of results confirmed the suitability of the proposed model for correctly describing the hydraulic behaviour of soil substrates.

Thermo-mechanical design of the extraction grids for RF negative ion source at HUST

Energy Technology Data Exchange (ETDEWEB)

Zuo, Chen; Liu, Kaifeng, E-mail: kfliuhust@hust.edu.cn; Li, Dong; Mei, Zhiyuan; Zhang, Zhe; Chen, Dezhi

2017-01-15

Highlights: • An extraction system with cooling channels has been designed for HUST negative ion source. • Corresponding heat loads onto three grids has been used in thermo-mechanical analysis. • The analysis results could be very useful for driving the engineering design. - Abstract: Huazhong University of Science and Technology (HUST) is developing a small radio frequency negative ion source experimental setup to promote research on neutral beam injection ion sources. The extraction system for the negative ion source is the key component to obtain the negative ions. The extraction system is composed of three grids: the plasma grid, the extraction grid and the grounded grid. Each grid is impacted by different heat loads. As the grids have to fulfil specific requirements regarding ion extraction, beam optics, and thermo-mechanical issues, grid cooling systems have been included for ensuring reliable operation. This paper focuses on the thermo-hydraulic and thermo-mechanical design of the grids. Finite element calculations have been carried out to analyse the temperature and deformation of the grids under heat loads using the fluid dynamics code CFX. Based on these results, the cooling circuit design and cooling parameters are optimised to satisfy the grid requirements.

Impact analysis of the spacer grid assembly and shape optimization of the attached spring

Energy Technology Data Exchange (ETDEWEB)

Park, K. J.; Lee, Z. N. [Hanyang University, Seoul (Korea)

2002-04-01

Spacer grids support fuel rods and maintain geometry from external impact loads. A simulation is performed for the strength of a spacer grid under the impact load. The critical impact load that leads to plastic deformation is identified by a free-fall test. A finite element model is established for the nonlinear simulation of the impact process. The simulation model is tuned based on the free-fall test. The model considers the aspects of welding and the contacts between components. Nonlinear finite element analysis is carried out using a software system called ABAQUS/EXPLICIT. The results are discussed from a design viewpoint. Design requirements are defined and a design process is established. The design process includes mathematical optimization as well as practical design method. The shape of the grid spring is designed to maintain its function during the lifetime of the fuel assembly. A structural optimization method is employed for the shape design. A good design is found. Commercial codes are utilized for structural analysis and optimization. 18 refs., 61 figs., 3 tabs. (Author)

On finite volume effects in the chiral extrapolation of baryon masses

CERN Document Server

Lutz, M F M; Kobdaj, C; Schwarz, K

2014-01-01

We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N^3LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-N_c sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Precise values for all counter terms relevant at N^3LO are predicted. In particular we extract a pion-nucleon sigma term of (39 +- 1) MeV and a strangeness sigma term of the nucleon of sigma_{sN} simeq (4 +- 1) MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with ( 802 +- 4 ) MeV and (1103 +- 6) MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei

2012-07-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation

International Nuclear Information System (INIS)

Li, Haisen S.; Romeijn, H. Edwin; Dempsey, James F.

2006-01-01

We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near mono-energetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the

Volume changes in hydrogels subjected to finite deformations

DEFF Research Database (Denmark)

Drozdov, Aleksey; Christiansen, Jesper de Claville

2013-01-01

Constitutive equations are derived for the elastic response of hydrogels under an arbitrary deformationwith finite strains. An expression is proposed for the free energy density of a hydrogel based on the Floryconcept of a network of flexible chains with constrained junctions whose reference conf...

Implicit finite-difference simulations of seismic wave propagation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

Implicit finite-difference simulations of seismic wave propagation

KAUST Repository

Chu, Chunlei

2012-03-01

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

Finite-Element 2D and 3D PIC Modeling of RF Devices with Applications to Multipacting

CERN Document Server

De Ford, John F; Petillo, John

2005-01-01

Multipacting currently limits the performance of many high power radio-frequency (RF) devices, particularly couplers and windows. Models have helped researchers understand and mitigate this problem in 2D structures, but useful multipacting models for complicated 3D structures are still a challenge. A combination of three recent technologies that have been developed in the Analyst and MICHELLE codes begin to address this challenge: high-order adaptive finite-element RF field calculations, advanced particle tracking on unstructured grids, and comprehensive secondary emission models. Analyst employs high-order adaptive finite-element methods to accurately compute driven RF fields and eigenmodes in complex geometries, particularly near edges, corners, and curved surfaces. To perform a multipacting analysis, we use the mesh and fields from Analyst in a modified version of the self-consistent, finite-element gun code MICHELLE. MICHELLE has both a fast, accurate, and reliable particle tracker for unstructured grids ...

Moving finite elements: A continuously adaptive method for computational fluid dynamics

International Nuclear Information System (INIS)

Glasser, A.H.; Miller, K.; Carlson, N.

1991-01-01

Moving Finite Elements (MFE), a recently developed method for computational fluid dynamics, promises major advances in the ability of computers to model the complex behavior of liquids, gases, and plasmas. Applications of computational fluid dynamics occur in a wide range of scientifically and technologically important fields. Examples include meteorology, oceanography, global climate modeling, magnetic and inertial fusion energy research, semiconductor fabrication, biophysics, automobile and aircraft design, industrial fluid processing, chemical engineering, and combustion research. The improvements made possible by the new method could thus have substantial economic impact. Moving Finite Elements is a moving node adaptive grid method which has a tendency to pack the grid finely in regions where it is most needed at each time and to leave it coarse elsewhere. It does so in a manner which is simple and automatic, and does not require a large amount of human ingenuity to apply it to each particular problem. At the same time, it often allows the time step to be large enough to advance a moving shock by many shock thicknesses in a single time step, moving the grid smoothly with the solution and minimizing the number of time steps required for the whole problem. For 2D problems (two spatial variables) the grid is composed of irregularly shaped and irregularly connected triangles which are very flexible in their ability to adapt to the evolving solution. While other adaptive grid methods have been developed which share some of these desirable properties, this is the only method which combines them all. In many cases, the method can save orders of magnitude of computing time, equivalent to several generations of advancing computer hardware

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun

2012-10-01

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan

2012-01-01

In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

Volume dependence of N-body bound states

Science.gov (United States)

König, Sebastian; Lee, Dean

2018-04-01

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

Finite-Difference Frequency-Domain Method in Nanophotonics

DEFF Research Database (Denmark)

Ivinskaya, Aliaksandra

Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...

3D Voronoi grid dedicated software for modeling gas migration in deep layered sedimentary formations with TOUGH2-TMGAS

Science.gov (United States)

Bonduà, Stefano; Battistelli, Alfredo; Berry, Paolo; Bortolotti, Villiam; Consonni, Alberto; Cormio, Carlo; Geloni, Claudio; Vasini, Ester Maria

2017-11-01

As is known, a full three-dimensional (3D) unstructured grid permits a great degree of flexibility when performing accurate numerical reservoir simulations. However, when the Integral Finite Difference Method (IFDM) is used for spatial discretization, constraints (arising from the required orthogonality between the segment connecting the blocks nodes and the interface area between blocks) pose difficulties in the creation of grids with irregular shaped blocks. The full 3D Voronoi approach guarantees the respect of IFDM constraints and allows generation of grids conforming to geological formations and structural objects and at the same time higher grid resolution in volumes of interest. In this work, we present dedicated pre- and post-processing gridding software tools for the TOUGH family of numerical reservoir simulators, developed by the Geothermal Research Group of the DICAM Department, University of Bologna. VORO2MESH is a new software coded in C++, based on the voro++ library, allowing computation of the 3D Voronoi tessellation for a given domain and the creation of a ready to use TOUGH2 MESH file. If a set of geological surfaces is available, the software can directly generate the set of Voronoi seed points used for tessellation. In order to reduce the number of connections and so to decrease computation time, VORO2MESH can produce a mixed grid with regular blocks (orthogonal prisms) and irregular blocks (polyhedron Voronoi blocks) at the point of contact between different geological formations. In order to visualize 3D Voronoi grids together with the results of numerical simulations, the functionality of the TOUGH2Viewer post-processor has been extended. We describe an application of VORO2MESH and TOUGH2Viewer to validate the two tools. The case study deals with the simulation of the migration of gases in deep layered sedimentary formations at basin scale using TOUGH2-TMGAS. A comparison between the simulation performances of unstructured and structured

Trends in life science grid: from computing grid to knowledge grid

Directory of Open Access Journals (Sweden)

Konagaya Akihiko

2006-12-01

Full Text Available Abstract Background Grid computing has great potential to become a standard cyberinfrastructure for life sciences which often require high-performance computing and large data handling which exceeds the computing capacity of a single institution. Results This survey reviews the latest grid technologies from the viewpoints of computing grid, data grid and knowledge grid. Computing grid technologies have been matured enough to solve high-throughput real-world life scientific problems. Data grid technologies are strong candidates for realizing "resourceome" for bioinformatics. Knowledge grids should be designed not only from sharing explicit knowledge on computers but also from community formulation for sharing tacit knowledge among a community. Conclusion Extending the concept of grid from computing grid to knowledge grid, it is possible to make use of a grid as not only sharable computing resources, but also as time and place in which people work together, create knowledge, and share knowledge and experiences in a community.

Lagrangian displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging.

Science.gov (United States)

Ma, Chi; Varghese, Tomy

2012-04-01

Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires Lagrangian description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. Lagrangian based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure Lagrangian description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our Lagrangian approach to strain estimation. Traditional Eulerian based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. Lagrangian displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-04-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

Magnetic and thermo-structural design optimization of the Plasma Grid for the MITICA neutral beam injector

Energy Technology Data Exchange (ETDEWEB)

Marconato, N., E-mail: nicolo.marconato@igi.cnr.it [Consorzio RFX, (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete SpA), C.so Stati Uniti 4, 35127 Padova (Italy); Agostinetti, P. [Consorzio RFX, (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete SpA), C.so Stati Uniti 4, 35127 Padova (Italy); Chitarin, G. [Consorzio RFX, (CNR, ENEA, INFN, Università di Padova, Acciaierie Venete SpA), C.so Stati Uniti 4, 35127 Padova (Italy); Department of Management and Engineering, University of Padova, Strad. S. Nicola 3, 36100 Vicenza (Italy)

2015-10-15

Highlights: • Latest status of the ITER NBI prototype (MITICA) design activity. • Finalization of the Plasma Grid design for optimal magnetic field intensity and uniformity. • Geometry optimization based on magnetic field calculation. • Assessment of the thermo-mechanical behavior of the grid by a 3D fully self-consistent fluid-thermal-structural model. - Abstract: MITICA is a prototype of the heating neutral beam (HNB) Injectors for ITER, built with the purpose of validating the injector design and optimizing its operation. Its goal is to produce a focused beam of neutral particles (H or D) with energy up to 1 MeV and power of 16 MW for 1 h. MITICA includes a Radio Frequency (RF) Plasma Source for the production of negative ions, a multi-stage electrostatic accelerator (up to 1 MV and 40 A), a neutralizer, a residual ion dump and a calorimeter. A transverse magnetic field in the Ion source and accelerator, including both a long-range component and a local component is crucial for obtaining the required Ion current and accelerator efficiency. The long-range component is produced by the current flowing through the plasma grid (PG) and related bus-bars. The PG current distribution and the uniformity of the resulting magnetic field have been optimized by detailed finite element (FEM) models. Hollow volumes in the thick copper part of the PG among beamlet groups allow a more uniform PG current distribution and a consequently uniform magnetic field in front of the grid. The paper describes in detail the PG geometry optimization procedure and the related magnetic and thermo-structural FEM analyses.

Grid interoperability: joining grid information systems

International Nuclear Information System (INIS)

Flechl, M; Field, L

2008-01-01

A grid is defined as being 'coordinated resource sharing and problem solving in dynamic, multi-institutional virtual organizations'. Over recent years a number of grid projects, many of which have a strong regional presence, have emerged to help coordinate institutions and enable grids. Today, we face a situation where a number of grid projects exist, most of which are using slightly different middleware. Grid interoperation is trying to bridge these differences and enable Virtual Organizations to access resources at the institutions independent of their grid project affiliation. Grid interoperation is usually a bilateral activity between two grid infrastructures. Recently within the Open Grid Forum, the Grid Interoperability Now (GIN) Community Group is trying to build upon these bilateral activities. The GIN group is a focal point where all the infrastructures can come together to share ideas and experiences on grid interoperation. It is hoped that each bilateral activity will bring us one step closer to the overall goal of a uniform grid landscape. A fundamental aspect of a grid is the information system, which is used to find available grid services. As different grids use different information systems, interoperation between these systems is crucial for grid interoperability. This paper describes the work carried out to overcome these differences between a number of grid projects and the experiences gained. It focuses on the different techniques used and highlights the important areas for future standardization

A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

International Nuclear Information System (INIS)

Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

2011-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

International Nuclear Information System (INIS)

Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

2010-01-01

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

2010-12-22

We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

The theory of finitely generated commutative semigroups

CERN Document Server

Rédei, L; Stark, M; Gravett, K A H

1966-01-01

The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single """"fundamental theorem"""" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before

On the use of Schwarz-Christoffel conformal mappings to the grid generation for global ocean models

Science.gov (United States)

Xu, S.; Wang, B.; Liu, J.

2015-10-01

In this article we propose two grid generation methods for global ocean general circulation models. Contrary to conventional dipolar or tripolar grids, the proposed methods are based on Schwarz-Christoffel conformal mappings that map areas with user-prescribed, irregular boundaries to those with regular boundaries (i.e., disks, slits, etc.). The first method aims at improving existing dipolar grids. Compared with existing grids, the sample grid achieves a better trade-off between the enlargement of the latitudinal-longitudinal portion and the overall smooth grid cell size transition. The second method addresses more modern and advanced grid design requirements arising from high-resolution and multi-scale ocean modeling. The generated grids could potentially achieve the alignment of grid lines to the large-scale coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the grids are orthogonal curvilinear, they can be easily utilized by the majority of ocean general circulation models that are based on finite difference and require grid orthogonality. The proposed grid generation algorithms can also be applied to the grid generation for regional ocean modeling where complex land-sea distribution is present.

High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves

DEFF Research Database (Denmark)

Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter

2012-01-01

is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...

High Resolution DNS of Turbulent Flows using an Adaptive, Finite Volume Method

Science.gov (United States)

Trebotich, David

2014-11-01

We present a new computational capability for high resolution simulation of incompressible viscous flows. Our approach is based on cut cell methods where an irregular geometry such as a bluff body is intersected with a rectangular Cartesian grid resulting in cut cells near the boundary. In the cut cells we use a conservative discretization based on a discrete form of the divergence theorem to approximate fluxes for elliptic and hyperbolic terms in the Navier-Stokes equations. Away from the boundary the method reduces to a finite difference method. The algorithm is implemented in the Chombo software framework which supports adaptive mesh refinement and massively parallel computations. The code is scalable to 200,000 + processor cores on DOE supercomputers, resulting in DNS studies at unprecedented scale and resolution. For flow past a cylinder in transition (Re = 300) we observe a number of secondary structures in the far wake in 2D where the wake is over 120 cylinder diameters in length. These are compared with the more regularized wake structures in 3D at the same scale. For flow past a sphere (Re = 600) we resolve an arrowhead structure in the velocity in the near wake. The effectiveness of AMR is further highlighted in a simulation of turbulent flow (Re = 6000) in the contraction of an oil well blowout preventer. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract Number DE-AC02-05-CH11231.

Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

International Nuclear Information System (INIS)

Bernal, A.; Roman, J.E.; Miró, R.; Verdú, G.

2016-01-01

Highlights: • A method is proposed to solve the eigenvalue problem of the Neutron Diffusion Equation in BWR. • The Neutron Diffusion Equation is discretized with the Finite Volume Method. • The currents are calculated by using a polynomial expansion of the neutron flux. • The current continuity and boundary conditions are defined implicitly to reduce the size of the matrices. • Different structured and unstructured meshes were used to discretize the BWR. - Abstract: The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.

Second order finite volume scheme for Maxwell's equations with discontinuous electromagnetic properties on unstructured meshes

Energy Technology Data Exchange (ETDEWEB)

Ismagilov, Timur Z., E-mail: ismagilov@academ.org

2015-02-01

This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.

Service Oriented Gridded Atmospheric Radiances (SOAR)

Science.gov (United States)

Halem, M.; Goldberg, M. D.; Tilmes, C.; Zhou, L.; Shen, S.; Yesha, Y.

2005-12-01

responsively meeting diverse user specified requests in terms of the spatial and temporal compositing of radiance fields. Moreover, the volume of sounder data records produced from current and future instruments varies from GB's to TB's per day and griding these sounding data can thin the volume to KB's to MB's per day making them easier to download to desktops and laptops. This not only will better serve a wider earth science community but makes these capabilities more readily useful to the education community. This presentation will describe the rationale for the project, an overview of the system architecture, a description of the framework for executing the applications on the distributed cluster and present examples of gridded service requests that are currently available. This demonstration project represents a foundation for the development of a distributed web service architecture that will be able to invoke requested services for temperature and moisture retrievals for arbitrary integrated gridded radiance data sets. We plan to extend the framework to accommodate such services for other earth observing instruments as well.

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

KAUST Repository

Wheeler, Mary

2013-11-16

We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

2011-01-01

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....

Effects of grid potentials and geometric dimensions on the multi-electrode probe measurements

International Nuclear Information System (INIS)

Elakshar, F.F.; Abdul El-Raoof, W.S.

1986-01-01

A hollow anode plasma source is used to produce low temperature plasma which is injected into a magnetic field. The effects of the grid potentials, collector potential and geometric dimensions on multi-electrode probe measurements, in the presence of a magnetic field, are investigated. It is found that the collector potential plays a substantial role in the measurement of temperatures and densities. The finite-size of the geometric dimensions of the probe influences the data and high values of temperature are obtained when a small ratio of the discriminator grid radius to the separation distance is used, providing that the repeller grid potentials is low. Reliable measurements can only be obtained if the multi-electrode probe is used in the presence of a magnetic field strong enough to reduce electron Larmor radii to less than the grid mesh radius. (author)

Trauma of the Frontal Region Is Influenced by the Volume of Frontal Sinuses. A Finite Element Study

Directory of Open Access Journals (Sweden)

Srbislav S. Pajic

2017-07-01

Full Text Available Anatomy of frontal sinuses varies individually, from differences in volume and shape to a rare case when the sinuses are absent. However, there are scarce data related to influence of these variations on impact generated fracture pattern. Therefore, the aim of this study was to analyse the influence of frontal sinus volume on the stress distribution and fracture pattern in the frontal region. The study included four representative Finite Element models of the skull. Reference model was built on the basis of computed tomography scans of a human head with normally developed frontal sinuses. By modifying the reference model, three additional models were generated: a model without sinuses, with hypoplasic, and with hyperplasic sinuses. A 7.7 kN force was applied perpendicularly to the forehead of each model, in order to simulate a frontal impact. The results demonstrated that the distribution of impact stress in frontal region depends on the frontal sinus volume. The anterior sinus wall showed the highest fragility in case with hyperplasic sinuses, whereas posterior wall/inner plate showed more fragility in cases with hypoplasic and undeveloped sinuses. Well-developed frontal sinuses might, through absorption of the impact energy by anterior wall, protect the posterior wall and intracranial contents.

Removal of apparent singularity in grid computations

International Nuclear Information System (INIS)

Jakubovics, J.P.

1993-01-01

A self-consistency test for magnetic domain wall models was suggested by Aharoni. The test consists of evaluating the ratio S = var-epsilon wall /var-epsilon wall , where var-epsilon wall is the wall energy, and var-epsilon wall is the integral of a certain function of the direction cosines of the magnetization, α, β, γ over the volume occupied by the domain wall. If the computed configuration is a good approximation to one corresponding to an energy minimum, the ratio is close to 1. The integrand of var-epsilon wall contains terms that are inversely proportional to γ. Since γ passes through zero at the centre of the domain wall, these terms have a singularity at these points. The integral is finite and its evaluation does not usually present any problems when the direction cosines are known in terms of continuous functions. In many cases, significantly better results for magnetization configurations of domain walls can be obtained by computations using finite element methods. The direction cosines are then only known at a set of discrete points, and integration over the domain wall is replaced by summation over these points. Evaluation of var-epsilon wall becomes inaccurate if the terms in the summation are taken to be the values of the integrand at the grid points, because of the large contribution of points close to where γ changes sign. The self-consistency test has recently been generalised to a larger number of cases. The purpose of this paper is to suggest a method of improving the accuracy of the evaluation of integrals in such cases. Since the self-consistency test has so far only been applied to two-dimensional magnetization configurations, the problem and its solution will be presented for that specific case. Generalisation to three or more dimensions is straight forward

Parallel implementation of a dynamic unstructured chimera method in the DLR finite volume TAU-code

Energy Technology Data Exchange (ETDEWEB)

Madrane, A.; Raichle, A.; Stuermer, A. [German Aerospace Center, DLR, Numerical Methods, Inst. of Aerodynamics and Flow Technology, Braunschweig (Germany)]. E-mail: aziz.madrane@dlr.de

2004-07-01

Aerodynamic problems involving moving geometries have many applications, including store separation, high-speed train entering into a tunnel, simulation of full configurations of the helicopter and fast maneuverability. Overset grid method offers the option of calculating these procedures. The solution process uses a grid system that discretizes the problem domain by using separately generated but overlapping unstructured grids that update and exchange boundary information through interpolation. However, such computations are complicated and time consuming. Parallel computing offers a very effective way to improve the productivity in doing computational fluid dynamics (CFD). Therefore the purpose of this study is to develop an efficient parallel computation algorithm for analyzing the flowfield of complex geometries using overset grids method. The strategy adopted in the parallelization of the overset grids method including the use of data structures and communication, is described. Numerical results are presented to demonstrate the efficiency of the resulting parallel overset grids method. (author)

Parallel implementation of a dynamic unstructured chimera method in the DLR finite volume TAU-code

International Nuclear Information System (INIS)

Madrane, A.; Raichle, A.; Stuermer, A.

2004-01-01

Aerodynamic problems involving moving geometries have many applications, including store separation, high-speed train entering into a tunnel, simulation of full configurations of the helicopter and fast maneuverability. Overset grid method offers the option of calculating these procedures. The solution process uses a grid system that discretizes the problem domain by using separately generated but overlapping unstructured grids that update and exchange boundary information through interpolation. However, such computations are complicated and time consuming. Parallel computing offers a very effective way to improve the productivity in doing computational fluid dynamics (CFD). Therefore the purpose of this study is to develop an efficient parallel computation algorithm for analyzing the flowfield of complex geometries using overset grids method. The strategy adopted in the parallelization of the overset grids method including the use of data structures and communication, is described. Numerical results are presented to demonstrate the efficiency of the resulting parallel overset grids method. (author)

3D magnetospheric parallel hybrid multi-grid method applied to planet–plasma interactions

Energy Technology Data Exchange (ETDEWEB)

Leclercq, L., E-mail: ludivine.leclercq@latmos.ipsl.fr [LATMOS/IPSL, UVSQ Université Paris-Saclay, UPMC Univ. Paris 06, CNRS, Guyancourt (France); Modolo, R., E-mail: ronan.modolo@latmos.ipsl.fr [LATMOS/IPSL, UVSQ Université Paris-Saclay, UPMC Univ. Paris 06, CNRS, Guyancourt (France); Leblanc, F. [LATMOS/IPSL, UPMC Univ. Paris 06 Sorbonne Universités, UVSQ, CNRS, Paris (France); Hess, S. [ONERA, Toulouse (France); Mancini, M. [LUTH, Observatoire Paris-Meudon (France)

2016-03-15

We present a new method to exploit multiple refinement levels within a 3D parallel hybrid model, developed to study planet–plasma interactions. This model is based on the hybrid formalism: ions are kinetically treated whereas electrons are considered as a inertia-less fluid. Generally, ions are represented by numerical particles whose size equals the volume of the cells. Particles that leave a coarse grid subsequently entering a refined region are split into particles whose volume corresponds to the volume of the refined cells. The number of refined particles created from a coarse particle depends on the grid refinement rate. In order to conserve velocity distribution functions and to avoid calculations of average velocities, particles are not coalesced. Moreover, to ensure the constancy of particles' shape function sizes, the hybrid method is adapted to allow refined particles to move within a coarse region. Another innovation of this approach is the method developed to compute grid moments at interfaces between two refinement levels. Indeed, the hybrid method is adapted to accurately account for the special grid structure at the interfaces, avoiding any overlapping grid considerations. Some fundamental test runs were performed to validate our approach (e.g. quiet plasma flow, Alfven wave propagation). Lastly, we also show a planetary application of the model, simulating the interaction between Jupiter's moon Ganymede and the Jovian plasma.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

Science.gov (United States)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

Tests of a 3D Self Magnetic Field Solver in the Finite Element Gun Code MICHELLE

CERN Document Server

Nelson, Eric M

2005-01-01

We have recently implemented a prototype 3d self magnetic field solver in the finite-element gun code MICHELLE. The new solver computes the magnetic vector potential on unstructured grids. The solver employs edge basis functions in the curl-curl formulation of the finite-element method. A novel current accumulation algorithm takes advantage of the unstructured grid particle tracker to produce a compatible source vector, for which the singular matrix equation is easily solved by the conjugate gradient method. We will present some test cases demonstrating the capabilities of the prototype 3d self magnetic field solver. One test case is self magnetic field in a square drift tube. Another is a relativistic axisymmetric beam freely expanding in a round pipe.

High order spectral volume and spectral difference methods on unstructured grids

Science.gov (United States)

Kannan, Ravishekar

The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed

CFD simulation of two-sail interaction about a sailing yacht; Sailing Yacht no niyoku kansho no CFD simulation

Energy Technology Data Exchange (ETDEWEB)

Lee, Y.; Miyata, H.; Sato, T. [The University of Tokyo, Tokyo (Japan). Faculty of Engineering

1997-06-01

Numerical analysis of sail characteristics was done by the finite volume method for an IACC class racing yacht, in compliance to the WISDAM-7 method for analyzing flow fields around the hull. The simulation code makes discrete the Navier-Stokes equation for non-compressive fluid in a conserved system by the finite volume method, and tries to find the solutions following the algorithm of the MAC method in a time-dependent manner. The H-H grids generated by an interface boundary technique for each sail are integrated for the two-sail configuration. It is found that combination of the finite volume method and grid integration is an adequate CFD procedure for simulation of interactions between the two sails. Performance of two-sail configuration, involving complex mechanisms such as interactions and separation of flows, is found by the method in which viscosity is taken into consideration. 5 refs., 20 figs., 3 tabs.

Adaptive moving grid methods for two-phase flow in porous media

KAUST Repository

Dong, Hao; Qiao, Zhonghua; Sun, Shuyu; Tang, Tao

2014-01-01

In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can

Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

International Nuclear Information System (INIS)

Al-Akhrass, Dina

2014-01-01

Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

Science.gov (United States)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

Grid Enabled Geospatial Catalogue Web Service

Science.gov (United States)

Chen, Ai-Jun; Di, Li-Ping; Wei, Ya-Xing; Liu, Yang; Bui, Yu-Qi; Hu, Chau-Min; Mehrotra, Piyush

2004-01-01

Geospatial Catalogue Web Service is a vital service for sharing and interoperating volumes of distributed heterogeneous geospatial resources, such as data, services, applications, and their replicas over the web. Based on the Grid technology and the Open Geospatial Consortium (0GC) s Catalogue Service - Web Information Model, this paper proposes a new information model for Geospatial Catalogue Web Service, named as GCWS which can securely provides Grid-based publishing, managing and querying geospatial data and services, and the transparent access to the replica data and related services under the Grid environment. This information model integrates the information model of the Grid Replica Location Service (RLS)/Monitoring & Discovery Service (MDS) with the information model of OGC Catalogue Service (CSW), and refers to the geospatial data metadata standards from IS0 19115, FGDC and NASA EOS Core System and service metadata standards from IS0 191 19 to extend itself for expressing geospatial resources. Using GCWS, any valid geospatial user, who belongs to an authorized Virtual Organization (VO), can securely publish and manage geospatial resources, especially query on-demand data in the virtual community and get back it through the data-related services which provide functions such as subsetting, reformatting, reprojection etc. This work facilitates the geospatial resources sharing and interoperating under the Grid environment, and implements geospatial resources Grid enabled and Grid technologies geospatial enabled. It 2!so makes researcher to focus on science, 2nd not cn issues with computing ability, data locztic, processir,g and management. GCWS also is a key component for workflow-based virtual geospatial data producing.

Generalized multiscale finite element methods for problems in perforated heterogeneous domains

KAUST Repository

Chung, Eric T.

2015-06-08

Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere. © 2015 Taylor & Francis

Finite-volume spectra of the Lee-Yang model

Energy Technology Data Exchange (ETDEWEB)

Bajnok, Zoltan [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,H-1525 Budapest 114, P.O.B. 49 (Hungary); Deeb, Omar el [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,H-1525 Budapest 114, P.O.B. 49 (Hungary); Physics Department, Faculty of Science, Beirut Arab University (BAU),Beirut (Lebanon); Pearce, Paul A. [School of Mathematics and Statistics, University of Melbourne,Parkville, Victoria 3010 (Australia)

2015-04-15

We consider the non-unitary Lee-Yang minimal model M(2,5) in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels (r,s)=(1,1),(1,2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ{sub 1,3} integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ{sub 1,3} integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A{sub 4} RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of (m,n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

Pacific Northwest Smart Grid Demonstration Project Technology Performance Report Volume 1: Technology Performance

Energy Technology Data Exchange (ETDEWEB)

Melton, Ron [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

2015-06-01

The Pacific Northwest Smart Grid Demonstration (PNWSGD), a $179 million project that was co-funded by the U.S. Department of Energy (DOE) in late 2009, was one of the largest and most comprehensive demonstrations of electricity grid modernization ever completed. The project was one of 16 regional smart grid demonstrations funded by the American Recovery and Reinvestment Act. It was the only demonstration that included multiple states and cooperation from multiple electric utilities, including rural electric co-ops, investor-owned, municipal, and other public utilities. No fewer than 55 unique instantiations of distinct smart grid systems were demonstrated at the projects’ sites. The local objectives for these systems included improved reliability, energy conservation, improved efficiency, and demand responsiveness. The demonstration developed and deployed an innovative transactive system, unique in the world, that coordinated many of the project’s distributed energy resources and demand-responsive components. With the transactive system, additional regional objectives were also addressed, including the mitigation of renewable energy intermittency and the flattening of system load. Using the transactive system, the project coordinated a regional response across the 11 utilities. This region-wide connection from the transmission system down to individual premises equipment was one of the major successes of the project. The project showed that this can be done and assets at the end points can respond dynamically on a wide scale. In principle, a transactive system of this type might eventually help coordinate electricity supply, transmission, distribution, and end uses by distributing mostly automated control responsibilities among the many distributed smart grid domain members and their smart devices.

Finite volume analysis of temperature effects induced by active MRI implants with cylindrical symmetry: 1. Properly working devices

Directory of Open Access Journals (Sweden)

Schnorr Jörg

2005-04-01

Full Text Available Abstract Background Active Magnetic Resonance Imaging implants are constructed as resonators tuned to the Larmor frequency of a magnetic resonance system with a specific field strength. The resonating circuit may be embedded into or added to the normal metallic implant structure. The resonators build inductively coupled wireless transmit and receive coils and can amplify the signal, normally decreased by eddy currents, inside metallic structures without affecting the rest of the spin ensemble. During magnetic resonance imaging the resonators generate heat, which is additional to the usual one described by the specific absorption rate. This induces temperature increases of the tissue around the circuit paths and inside the lumen of an active implant and may negatively influence patient safety. Methods This investigation provides an overview of the supplementary power absorbed by active implants with a cylindrical geometry, corresponding to vessel implants such as stents, stent grafts or vena cava filters. The knowledge of the overall absorbed power is used in a finite volume analysis to estimate temperature maps around different implant structures inside homogeneous tissue under worst-case assumptions. The "worst-case scenario" assumes thermal heat conduction without blood perfusion inside the tissue around the implant and mostly without any cooling due to blood flow inside vessels. Results The additional power loss of a resonator is proportional to the volume and the quality factor, as well as the field strength of the MRI system and the specific absorption rate of the applied sequence. For properly working devices the finite volume analysis showed only tolerable heating during MRI investigations in most cases. Only resonators transforming a few hundred mW into heat may reach temperature increases over 5 K. This requires resonators with volumes of several ten cubic centimeters, short inductor circuit paths with only a few 10 cm and a quality

Finite volume analysis of temperature effects induced by active MRI implants with cylindrical symmetry: 1. Properly working devices.

Science.gov (United States)

Busch, Martin H J; Vollmann, Wolfgang; Schnorr, Jörg; Grönemeyer, Dietrich H W

2005-04-08

Active Magnetic Resonance Imaging implants are constructed as resonators tuned to the Larmor frequency of a magnetic resonance system with a specific field strength. The resonating circuit may be embedded into or added to the normal metallic implant structure. The resonators build inductively coupled wireless transmit and receive coils and can amplify the signal, normally decreased by eddy currents, inside metallic structures without affecting the rest of the spin ensemble. During magnetic resonance imaging the resonators generate heat, which is additional to the usual one described by the specific absorption rate. This induces temperature increases of the tissue around the circuit paths and inside the lumen of an active implant and may negatively influence patient safety. This investigation provides an overview of the supplementary power absorbed by active implants with a cylindrical geometry, corresponding to vessel implants such as stents, stent grafts or vena cava filters. The knowledge of the overall absorbed power is used in a finite volume analysis to estimate temperature maps around different implant structures inside homogeneous tissue under worst-case assumptions. The "worst-case scenario" assumes thermal heat conduction without blood perfusion inside the tissue around the implant and mostly without any cooling due to blood flow inside vessels. The additional power loss of a resonator is proportional to the volume and the quality factor, as well as the field strength of the MRI system and the specific absorption rate of the applied sequence. For properly working devices the finite volume analysis showed only tolerable heating during MRI investigations in most cases. Only resonators transforming a few hundred mW into heat may reach temperature increases over 5 K. This requires resonators with volumes of several ten cubic centimeters, short inductor circuit paths with only a few 10 cm and a quality factor above ten. Using MR sequences, for which the MRI

11th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing

CERN Document Server

Barolli, Leonard; Amato, Flora

2017-01-01

P2P, Grid, Cloud and Internet computing technologies have been very fast established as breakthrough paradigms for solving complex problems by enabling aggregation and sharing of an increasing variety of distributed computational resources at large scale. The aim of this volume is to provide latest research findings, innovative research results, methods and development techniques from both theoretical and practical perspectives related to P2P, Grid, Cloud and Internet computing as well as to reveal synergies among such large scale computing paradigms. This proceedings volume presents the results of the 11th International Conference on P2P, Parallel, Grid, Cloud And Internet Computing (3PGCIC-2016), held November 5-7, 2016, at Soonchunhyang University, Asan, Korea.

User's manual for the HYPGEN hyperbolic grid generator and the HGUI graphical user interface

Science.gov (United States)

Chan, William M.; Chiu, Ing-Tsau; Buning, Pieter G.

1993-01-01

The HYPGEN program is used to generate a 3-D volume grid over a user-supplied single-block surface grid. This is accomplished by solving the 3-D hyperbolic grid generation equations consisting of two orthogonality relations and one cell volume constraint. In this user manual, the required input files and parameters and output files are described. Guidelines on how to select the input parameters are given. Illustrated examples are provided showing a variety of topologies and geometries that can be treated. HYPGEN can be used in stand-alone mode as a batch program or it can be called from within a graphical user interface HGUI that runs on Silicon Graphics workstations. This user manual provides a description of the menus, buttons, sliders, and typein fields in HGUI for users to enter the parameters needed to run HYPGEN. Instructions are given on how to configure the interface to allow HYPGEN to run either locally or on a faster remote machine through the use of shell scripts on UNIX operating systems. The volume grid generated is copied back to the local machine for visualization using a built-in hook to PLOT3D.

A staggered-grid convolutional differentiator for elastic wave modelling

Science.gov (United States)

Sun, Weijia; Zhou, Binzhong; Fu, Li-Yun

2015-11-01

The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.

Near-Body Grid Adaption for Overset Grids

Science.gov (United States)

Buning, Pieter G.; Pulliam, Thomas H.

2016-01-01

A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.

Interactive finite difference preprocessor for three-dimensional fluid flow systems. [PREFLO

Energy Technology Data Exchange (ETDEWEB)

Kleinstreuer, C. (Rensselaer Polytechnic Inst., Troy, NY); Patterson, M.R.

1981-06-01

A preprocessor, called PREFLO, consisting of data processing modules combined with a flexible finite difference grid generator is described. This economical, interactive computer code is a useful research tool contributing significantly to the accurate analysis and modeling of large and/or geometrically complex flow systems. PREFLO (PREprocessor for fluid FLOw problems), written in FORTRAN IV, consists of four modules which in turn call various subroutines. The main programs accomplish the following tasks: (1) system identification and selection of appropriate finite difference algorithms; (2) input devices for storage of natural flow boundaries; (3) interactive generation of finite difference meshes and display of computer graphics; (4) preparation of all data files for the source program. The computation of the velocity field near a power plant site is outlined to illustrate the capabilities and application of PREFLO.

Integrated Multi-Scale Data Analytics and Machine Learning for the Distribution Grid and Building-to-Grid Interface

Energy Technology Data Exchange (ETDEWEB)

Stewart, Emma M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hendrix, Val [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Deka, Deepjyoti [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-03-16

This white paper introduces the application of advanced data analytics to the modernized grid. In particular, we consider the field of machine learning and where it is both useful, and not useful, for the particular field of the distribution grid and buildings interface. While analytics, in general, is a growing field of interest, and often seen as the golden goose in the burgeoning distribution grid industry, its application is often limited by communications infrastructure, or lack of a focused technical application. Overall, the linkage of analytics to purposeful application in the grid space has been limited. In this paper we consider the field of machine learning as a subset of analytical techniques, and discuss its ability and limitations to enable the future distribution grid and the building-to-grid interface. To that end, we also consider the potential for mixing distributed and centralized analytics and the pros and cons of these approaches. Machine learning is a subfield of computer science that studies and constructs algorithms that can learn from data and make predictions and improve forecasts. Incorporation of machine learning in grid monitoring and analysis tools may have the potential to solve data and operational challenges that result from increasing penetration of distributed and behind-the-meter energy resources. There is an exponentially expanding volume of measured data being generated on the distribution grid, which, with appropriate application of analytics, may be transformed into intelligible, actionable information that can be provided to the right actors – such as grid and building operators, at the appropriate time to enhance grid or building resilience, efficiency, and operations against various metrics or goals – such as total carbon reduction or other economic benefit to customers. While some basic analysis into these data streams can provide a wealth of information, computational and human boundaries on performing the analysis

Mission Profile Translation to Capacitor Stresses in Grid-Connected Photovoltaic Systems

DEFF Research Database (Denmark)

Yang, Yongheng; Ma, Ke; Wang, Huai

2014-01-01

DC capacitors are widely adopted in grid-connected PhotoVoltaic(PV) systems for power stabilization and control decoupling. They have become one of the critical components in grid-connected PV inverters in terms of cost, reliability and volume. The electrical and thermal stresses of the DC...... stresses of the DC capacitors under both normal and abnormal grid conditions. As a consequence, this investigation provides new insights into the sizing and reliability prediction of those capacitors with respect to priorart studies. Two study cases on a single-stage PV inverter and a two-stage PV inverter...

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

Science.gov (United States)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media

KAUST Repository

Chung, Eric T.

2014-11-13

Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to their complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids. In this paper, we present a multiscale finite element method for wave propagation on a coarse grid. The proposed method is based on the generalized multiscale finite element method (GMsFEM) (see [Y. Efendiev, J. Galvis, and T. Hou, J. Comput. Phys., 251 (2012), pp. 116--135]). To construct multiscale basis functions, we start with two snapshot spaces in each coarse-grid block, where one represents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We use local spectral problems to identify important modes in each snapshot space. These local spectral problems are different from each other and their formulations are based on the analysis. To the best of knowledge, this is the first time that multiple snapshot spaces and multiple spectral problems are used and necessary for efficient computations. Using the dominant modes from local spectral problems, multiscale basis functions are constructed to represent the solution space locally within each coarse block. These multiscale basis functions are coupled via the symmetric interior penalty discontinuous Galerkin method which provides a block diagonal mass matrix and, consequently, results in fast computations in an explicit time discretization. Our methods\\' stability and spectral convergence are rigorously analyzed. Numerical examples are presented to show our methods\\' performance. We also test oversampling strategies. In particular, we discuss how the modes from different snapshot spaces can affect the proposed methods\\' accuracy.

Optimization of the cooling circuit and thermo-mechanical analysis for the extraction grid of ELISE

International Nuclear Information System (INIS)

Nocentini, R.; Gutser, R.; Heinemann, B.; Froeschle, M.; Riedl, R.

2011-01-01

The NNBI test facility ELISE ('Extraction from a Large Ion Source Experiment'), presently under construction at IPP, will have an extraction area with the same width and half the height of the ITER source, acceleration up to 60 kV, for 10 s, every 180 s, and plasma generation up to 1 h. Electrons are co-extracted from the ion source. Suppression magnets in the extraction grid deflect the electrons onto the extraction grid surface. For 30 mA/cm 2 extracted electron current density and 10 kV extraction voltage, localized power density is in the order of 39 MW/m 2 near the grid apertures and a total heat load of 150 kW is deposited onto each extraction grid segment. Heat removal is provided by a water circuit inside the grid. For ELISE, a new cooling circuit has been developed to provide a more reliable operation. The optimization of the cooling circuit and the thermo-mechanical analysis of the extraction grid of ELISE, considering maximum grid temperature, mechanical stresses and grid deformation, has been performed using the codes KOBRA3, TrajAn, the ANSYS finite element package and the fluid dynamics code CFX.

Parallel simulation of two-phase incompressible and immiscible flows in porous media using a finite volume formulation and a modified IMPES approach

International Nuclear Information System (INIS)

Da Silva, R S; De Carvalho, D K E; Antunes, A R E; Lyra, P R M; Willmersdorf, R B

2010-01-01

In this paper a finite volume method with a 'Modified Implicit Pressure, Explicit Saturation' (MIMPES) approach is used to model the 3-D incompressible and immiscible two-phase flow of water and oil in heterogeneous and anisotropic porous media. A vertex centered finite volume method with an edge-based data structure is adopted to discretize both the elliptic pressure and the hyperbolic saturation equations using parallel computers with distributed memory. Due to the explicit solution of the saturation equation in the IMPES method, severe time step restrictions are imposed on the simulation. In order to circumvent this problem, an edge-based implementation of the MIMPES method was used. In this method, the pressure equation is solved and the velocity field is computed much less frequently than the saturation field. Following the work of Hurtado, a mean relative variation of the velocity field throughout the simulation is used to automatically control the updating process, allowing for much larger time-steps in a very simple way. In order to run large scale problems, we have developed a parallel implementation using clusters of PC's. The simulator uses open source parallel libraries like FMDB, ParMetis and PETSc. Results of speed-up and efficiency are presented to validate the performance of the parallel simulator.

Development of a three-dimensional high-order strand-grids approach

Science.gov (United States)

Tong, Oisin

Development of a novel high-order flux correction method on strand grids is presented. The method uses a combination of flux correction in the unstructured plane and summation-by-parts operators in the strand direction to achieve high-fidelity solutions. Low-order truncation errors are cancelled with accurate flux and solution gradients in the flux correction method, thereby achieving a formal order of accuracy of 3, although higher orders are often obtained, especially for highly viscous flows. In this work, the scheme is extended to high-Reynolds number computations in both two and three dimensions. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable, and the Menter SST turbulence model, which blends the k-epsilon and k-o turbulence models for better accuracy. A major advantage of this high-order formulation is the ability to implement traditional finite volume-like limiters to cleanly capture shocked and discontinuous flows. In this work, this approach is explored via a symmetric limited positive (SLIP) limiter. Extensive verification and validation is conducted in two and three dimensions to determine the accuracy and fidelity of the scheme for a number of different cases. Verification studies show that the scheme achieves better than third order accuracy for low and high-Reynolds number flows. Cost studies show that in three-dimensions, the third-order flux correction scheme requires only 30% more walltime than a traditional second-order scheme on strand grids to achieve the same level of convergence. In order to overcome meshing issues at sharp corners and other small-scale features, a unique approach to traditional geometry, coined "asymptotic geometry," is explored. Asymptotic geometry is achieved by filtering out small-scale features in a level set domain through min/max flow. This approach is combined with a curvature based strand shortening

Design of a Carbon Fiber Composite Grid Structure for the GLAST Spacecraft Using a Novel Manufacturing Technique

Energy Technology Data Exchange (ETDEWEB)

Hicks, M

2004-04-12

The Gamma-Ray Large Area Space Telescope is an orbital observatory being planned as a joint DOE/NASA mission. The primary support of the instrument requires a grid structure which is very stiff, strong, light-weight, and thermally conductive. A carbon fiber composite grid design using a novel manufacture technique is proposed which meets or exceeds an aluminum design in all performance criteria and is economically competitive as well. Finite element analysis, confirmed by testing of a sample grid, is used to examine trade-offs for the materials and layups. Based on these analyses, recommendations are given for a viable design.

Smart Energy 2011. Smart Grid or the future of power industry; Smart Energy 2011. Smart Grid oder die Zukunft der Energiewirtschaft

Energy Technology Data Exchange (ETDEWEB)

Grossmann, Uwe; Kunold, Ingo (eds.)

2011-07-01

The demand for smart grids, energy information networks, smart metering, new tariffs offering incentives for load shifting to household customers and load reduction options to energy providers are discussed increasingly. The privacy protection of customers being threatened by detailed consumption profiles also needs attention. Practitioners and researches from enterprises and research institutions present results from their field of work in nine papers. This book mainly focusses on three topics: 'Energy 2020', 'Data protection and data security within smart grids' and 'Smart grid and energy information networks'. On the one hand this volume addresses researchers and practitioners from enterprises and research institutions, on the other hand teachers and students dealing with questions concerning the energy market of the future. (orig.)

Mapping PetaSHA Applications to TeraGrid Architectures

Science.gov (United States)

Cui, Y.; Moore, R.; Olsen, K.; Zhu, J.; Dalguer, L. A.; Day, S.; Cruz-Atienza, V.; Maechling, P.; Jordan, T.

2007-12-01

The Southern California Earthquake Center (SCEC) has a science program in developing an integrated cyberfacility - PetaSHA - for executing physics-based seismic hazard analysis (SHA) computations. The NSF has awarded PetaSHA 15 million allocation service units this year on the fastest supercomputers available within the NSF TeraGrid. However, one size does not fit all, a range of systems are needed to support this effort at different stages of the simulations. Enabling PetaSHA simulations on those TeraGrid architectures to solve both dynamic rupture and seismic wave propagation have been a challenge from both hardware and software levels. This is an adaptation procedure to meet specific requirements of each architecture. It is important to determine how fundamental system attributes affect application performance. We present an adaptive approach in our PetaSHA application that enables the simultaneous optimization of both computation and communication at run-time using flexible settings. These techniques optimize initialization, source/media partition and MPI-IO output in different ways to achieve optimal performance on the target machines. The resulting code is a factor of four faster than the orignial version. New MPI-I/O capabilities have been added for the accurate Staggered-Grid Split-Node (SGSN) method for dynamic rupture propagation in the velocity-stress staggered-grid finite difference scheme (Dalguer and Day, JGR, 2007), We use execution workflow across TeraGrid sites for managing the resulting data volumes. Our lessons learned indicate that minimizing time to solution is most critical, in particular when scheduling large scale simulations across supercomputer sites. The TeraShake platform has been ported to multiple architectures including TACC Dell lonestar and Abe, Cray XT3 Bigben and Blue Gene/L. Parallel efficiency of 96% with the PetaSHA application Olsen-AWM has been demonstrated on 40,960 Blue Gene/L processors at IBM TJ Watson Center. Notable

The MammoGrid Project Grids Architecture

CERN Document Server

McClatchey, Richard; Hauer, Tamas; Estrella, Florida; Saiz, Pablo; Rogulin, Dmitri; Buncic, Predrag; Clatchey, Richard Mc; Buncic, Predrag; Manset, David; Hauer, Tamas; Estrella, Florida; Saiz, Pablo; Rogulin, Dmitri

2003-01-01

The aim of the recently EU-funded MammoGrid project is, in the light of emerging Grid technology, to develop a European-wide database of mammograms that will be used to develop a set of important healthcare applications and investigate the potential of this Grid to support effective co-working between healthcare professionals throughout the EU. The MammoGrid consortium intends to use a Grid model to enable distributed computing that spans national borders. This Grid infrastructure will be used for deploying novel algorithms as software directly developed or enhanced within the project. Using the MammoGrid clinicians will be able to harness the use of massive amounts of medical image data to perform epidemiological studies, advanced image processing, radiographic education and ultimately, tele-diagnosis over communities of medical "virtual organisations". This is achieved through the use of Grid-compliant services [1] for managing (versions of) massively distributed files of mammograms, for handling the distri...

Finite volume method for radiative heat transfer in an unstructured flow solver for emitting, absorbing and scattering media

International Nuclear Information System (INIS)

Gazdallah, Moncef; Feldheim, Véronique; Claramunt, Kilian; Hirsch, Charles

2012-01-01

This paper presents the implementation of the finite volume method to solve the radiative transfer equation in a commercial code. The particularity of this work is that the method applied on unstructured hexahedral meshes does not need a pre-processing step establishing a particular marching order to visit all the control volumes. The solver simply visits the faces of the control volumes as numbered in the hexahedral unstructured mesh. A cell centred mesh and a spatial differencing step scheme to relate facial radiative intensities to nodal intensities is used. The developed computer code based on FVM has been integrated in the CFD solver FINE/Open from NUMECA Int. Radiative heat transfer can be evaluated within systems containing uniform, grey, emitting, absorbing and/or isotropically or linear anisotropically scattering medium bounded by diffuse grey walls. This code has been validated for three test cases. The first one is a three dimensional rectangular enclosure filled with emitting, absorbing and anisotropically scattering media. The second is the differentially heated cubic cavity. The third one is the L-shaped enclosure. For these three test cases a good agreement has been observed when temperature and heat fluxes predictions are compared with references taken, from literature.

Valuing modular nuclear power plants in finite time decision horizon

International Nuclear Information System (INIS)

Jain, Shashi; Roelofs, Ferry; Oosterlee, Cornelis W.

2013-01-01

Small and medium sized reactors, SMRs, (according to IAEA, ‘small’ refers to reactors with power less than 300 MWe, and ‘medium’ with power less than 700 MWe) are considered as an attractive option for investment in nuclear power plants. SMRs may benefit from flexibility of investment, reduced upfront expenditure, enhanced safety, and easy integration with small sized grids. Large reactors on the other hand have been an attractive option due to the economy of scale. In this paper we focus on the economic impact of flexibility due to modular construction of SMRs. We demonstrate, using real option analysis, the value of sequential modular SMRs. Numerical results under different considerations of decision time, uncertainty in electricity prices, and constraints on the construction of units, are reported for a single large unit and for modular SMRs. - Highlights: ► Real option value of modular construction in finite time decision horizon. ► Stochastic grid method is used to value the real option. ► Decisions in finite time can differ significantly from infinite decision time. ► Decisions depend on length of decision horizon and price volatilities

Comparison of Moving Boundary and Finite-Volume Heat Exchanger Models in the Modelica Language

Directory of Open Access Journals (Sweden)

Adriano Desideri

2016-05-01

Full Text Available When modeling low capacity energy systems, such as a small size (5–150 kWel organic Rankine cycle unit, the governing dynamics are mainly concentrated in the heat exchangers. As a consequence, the accuracy and simulation speed of the higher level system model mainly depend on the heat exchanger model formulation. In particular, the modeling of thermo-flow systems characterized by evaporation or condensation requires heat exchanger models capable of handling phase transitions. To this aim, the finite volume (FV and the moving boundary (MB approaches are the most widely used. The two models are developed and included in the open-source ThermoCycle Modelica library. In this contribution, a comparison between the two approaches is presented. An integrity and accuracy test is designed to evaluate the performance of the FV and MB models during transient conditions. In order to analyze how the two modeling approaches perform when integrated at a system level, two organic Rankine cycle (ORC system models are built using the FV and the MB evaporator model, and their responses are compared against experimental data collected on an 11 kWel ORC power unit. Additionally, the effect of the void fraction value in the MB evaporator model and of the number of control volumes (CVs in the FV one is investigated. The results allow drawing general guidelines for the development of heat exchanger dynamic models involving two-phase flows.

On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

KAUST Repository

Settle, Sean O.

2013-01-01

The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.

Using Micro-Synchrophasor Data for Advanced Distribution Grid Planning and Operations Analysis

Energy Technology Data Exchange (ETDEWEB)

Stewart, Emma [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Kiliccote, Sila [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); McParland, Charles [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Roberts, Ciaran [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2014-07-01

This report reviews the potential for distribution-grid phase-angle data that will be available from new micro-synchrophasors (µPMUs) to be utilized in existing distribution-grid planning and operations analysis. This data could augment the current diagnostic capabilities of grid analysis software, used in both planning and operations for applications such as fault location, and provide data for more accurate modeling of the distribution system. µPMUs are new distribution-grid sensors that will advance measurement and diagnostic capabilities and provide improved visibility of the distribution grid, enabling analysis of the grid’s increasingly complex loads that include features such as large volumes of distributed generation. Large volumes of DG leads to concerns on continued reliable operation of the grid, due to changing power flow characteristics and active generation, with its own protection and control capabilities. Using µPMU data on change in voltage phase angle between two points in conjunction with new and existing distribution-grid planning and operational tools is expected to enable model validation, state estimation, fault location, and renewable resource/load characterization. Our findings include: data measurement is outstripping the processing capabilities of planning and operational tools; not every tool can visualize a voltage phase-angle measurement to the degree of accuracy measured by advanced sensors, and the degree of accuracy in measurement required for the distribution grid is not defined; solving methods cannot handle the high volumes of data generated by modern sensors, so new models and solving methods (such as graph trace analysis) are needed; standardization of sensor-data communications platforms in planning and applications tools would allow integration of different vendors’ sensors and advanced measurement devices. In addition, data from advanced sources such as µPMUs could be used to validate models to improve

Finite Volumes Discretization of Topology Optimization Problems

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...

Viscoelastic response of hydrogel materials at finite strains

OpenAIRE

Skovly, Martin Johannessen

2015-01-01

Hydrogel materials are very soft materials consisting of polymer networks and solvent molecules. The materials may exhibit large volume changes depending on its external chemical and mechanical environment and have viscoelastic properties which is common for many polymeric materials. In order to model the material response with the finite element method, a hydrogel constitutive model have been combined with finite viscoelastic theory and the resulting viscoelastic hydrogel constitutive model ...

Non linear fe analysis on the static buckling behavior of the spacer grid structures

International Nuclear Information System (INIS)

Song, K.N.; Yoon, K.H.

2001-01-01

In this study considered is the static buckling behavior of spacer grids in the fuel assembly, which are required to have a sufficient strength against an accident like earthquake. Special attention is given to the finite element modeling of the spot-welding and the constraints between the spacer strips assembled together: it is found that a proper treatment of the constraints is critical for accurate assessment of the buckling behavior including strain localization at the point of spot welding. The buckling strength of the 17 x 17 spacer grid, which is difficult to analyze due to a large number of degrees of freedom, is estimated from analysis for the smaller models 3 x 3, 5 x 5, 7 x 7, and 9 x 9 spacer grids. (authors)

Investigation of nonlinear 2D bottom transportation dynamics in coastal zone on optimal curvilinear boundary adaptive grids

Directory of Open Access Journals (Sweden)

Sukhinov Alexander

2017-01-01

Full Text Available One of the practically important tasks of hydrophysics for sea coastal systems is the problem of modeling and forecasting bottom sediment transportation. A number of problems connected to ship safety traffic, water medium condition near the coastal line etc. depends on forecasting bottom deposit transportation under natural and technogenic influences. Coastal systems are characterized by a complicated form of coastline - the presence of long, narrow and curvilinear peninsulas and bays. Water currents and waves near the beach are strongly depend on complicated coastal line and in turn, exert on the bottom sediment transportation near the shore. The use of rectangular grids in the construction of discrete models leads to significant errors in both the specification of boundary conditions and in the modeling of hydrophysical processes in the coastal zone. In this paper, we consider the construction of a finite-element approximation of the initial-boundary value problem for the spatially two-dimensional linearized equation of sediment transportation using optimal boundary-adaptive grid. First, the linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed-when the coefficients of the equation that are nonlinearly dependent on the bottom relief function are set on the previous time layer, and the corresponding initial conditions are used on the first time layer. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional. On the constructed grid, finite element approximation using bilinear basis functions is performed, which completes the construction of a discrete model for the given problem. The using of curvilinear boundary adaptive grids leads to decreasing of total grid number in 5-20 times and respectively the total modeling time and/or it allows to improve modeling accuracy.

3D modeling of forces between magnet and HTS in a levitation system using new approach of the control volume method based on an unstructured grid

Energy Technology Data Exchange (ETDEWEB)

Alloui, L., E-mail: lotfi.alloui@lgep.supelec.fr [Laboratoire de Genie Electrique de Paris - LGEP, CNRS UMR 8507, Supelec, Universite Pierre et Marie Curie-Paris 6, Universite Paris Sud-Paris 11, Plateau de Moulon, 11 rue Joliot Curie, 91192 Gif-Sur-Yvette Cedex (France); Laboratoire de modelisation des systemes energetiques (LMSE), Universite de Biskra, 07000 Biskra (Algeria); Bouillault, F., E-mail: bouillault@lgep.supelec.fr [Laboratoire de Genie Electrique de Paris - LGEP, CNRS UMR 8507, Supelec, Universite Pierre et Marie Curie-Paris 6, Universite Paris Sud-Paris 11, Plateau de Moulon, 11 rue Joliot Curie, 91192 Gif-Sur-Yvette Cedex (France); Bernard, L., E-mail: laurent.bernardl@lgep.supelc.fr [Laboratoire de Genie Electrique de Paris - LGEP, CNRS UMR 8507, Supelec, Universite Pierre et Marie Curie-Paris 6, Universite Paris Sud-Paris 11, Plateau de Moulon, 11 rue Joliot Curie, 91192 Gif-Sur-Yvette Cedex (France); Leveque, J., E-mail: jean.leveque@green.uhp-nancy.fr [Groupe de recherche en electronique et electrotechnique de Nancy, Universite Henry Poincare, BP 239, 54506 Vandoeuvre les Nancy (France)

2012-05-15

In this paper we present new 3D numerical model to calculate the vertical and the guidance forces in high temperature superconductors taking into account the influence of the flux creep phenomena. In the suggested numerical model, we adopt a new approach of the control volume method. This approach is based on the use of an unstructured grid which can be used to model more complex geometries. A comparison of the control volume method results with experiments verifies the validity of this approach and the proposed numerical model. Based on this model, the levitation force's relaxation at different temperatures was also studied.

Finite element analysis of cylindrical indentation for determining plastic properties of materials in small volumes

International Nuclear Information System (INIS)

Lu, Y Charles; Kurapati, Siva N V R K; Yang Fuqian

2008-01-01

The cylindrical indentation is analysed, using the finite element method, for determining the plastic properties of elastic-plastic materials and the effect of strain hardening. The results are compared with those obtained from spherical indentation, the commonly used technique for measuring plastic properties of materials in small volumes. The analysis shows that the deformation under a cylindrical indenter quickly reaches a fully plastic state and that the size (diameter) of the plastic zone remains constant during further indentation. The indentation load is proportional to the indentation depth at large indentation depth, from which the indentation pressure P m at the onset of yielding can be readily extrapolated. The analysis of cylindrical indentation suggests that it does not need parameters such as impression radius (a) and contact stiffness (S) for determining the plastic behaviour of materials. Thus, the cylindrical indentation can suppress the uncertainties in measuring material properties

Validation of two gridded soil moisture products over India with in ...

Indian Academy of Sciences (India)

Home; Journals; Journal of Earth System Science; Volume 125; Issue 5. Validation of two gridded soil moisture products over India with in-situ observations. C K Unnikrishnan John P George Abhishek Lodh Devesh Kumar Maurya Swapan Mallick E N Rajagopal Saji Mohandas. Volume 125 Issue 5 July 2016 pp 935-944 ...

A treatment planning approach to spatially fractionated megavoltage grid therapy for bulky lung cancer

Energy Technology Data Exchange (ETDEWEB)

Costlow, Heather N. [Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, IN (United States); Zhang, Hualin, E-mail: hzhang@nmh.org [Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, IN (United States); Department of Radiation Oncology, Northwestern University Feinberg School of Medicine, Northwestern University, Northwestern Memorial Hospital, Chicago, IL (United States); Das, Indra J. [Department of Radiation Oncology, Indiana University School of Medicine, Indianapolis, IN (United States)

2014-10-01

The purpose of this study was to explore the treatment planning methods of spatially fractionated megavoltage grid therapy for treating bulky lung tumors using multileaf collimator (MLC). A total of 5 patients with lung cancer who had gross tumor volumes ranging from 277 to 635 cm{sup 3} were retrospectively chosen for this study. The tumors were from 6.5 to 9.6 cm at shortest dimension. Several techniques using either electronic compensation or intensity-modulated radiation therapy (IMRT) were used to create a variety of grid therapy plans on the Eclipse treatment planning system. The dose prescription point was calculated to the volume, and a dose of 20 Gy with 6-MV/15-MV beams was used in each plan. The dose-volume histogram (DVH) curves were obtained to evaluate dosimetric characteristics. In addition, DVH curves from a commercially available cerrobend grid collimator were also used for comparison. The linear-quadratic radiobiological response model was used to assess therapeutic ratios (TRs) and equivalent uniform doses (EUD) for all generated plans. A total of 6 different grid therapy plans were created for each patient. Overall, 4 plans had different electronic compensation techniques: Ecomps-Tubes, Ecomps-Circles, Ecomps-Squares, and Ecomps-Weave; the other 2 plans used IMRT and IMRT-Weave techniques. The DVH curves and TRs demonstrated that these MLC-based grid therapy plans can achieve dosimetric properties very similar to those of the cerrobend grid collimator. However, the MLC-based plans have larger EUDs than those with the cerrobend grid collimator. In addition, the field shaping can be performed for targets of any shape in MLC-based plans. Thus, they can deliver a more conformal dose to the targets and spare normal structures better than the cerrobend grid collimator can. The plans generated by the MLC technique demonstrated the advantage over the standard cerrobend grid collimator on accommodating targets and sparing normal structures. Overall, 6

Design and evaluation of a grid reciprocation scheme for use in digital breast tomosynthesis

Science.gov (United States)

Patel, Tushita; Sporkin, Helen; Peppard, Heather; Williams, Mark B.

2016-03-01

This work describes a methodology for efficient removal of scatter radiation during digital breast tomosynthesis (DBT). The goal of this approach is to enable grid image obscuration without a large increase in radiation dose by minimizing misalignment of the grid focal point (GFP) and x-ray focal spot (XFS) during grid reciprocation. Hardware for the motion scheme was built and tested on the dual modality breast tomosynthesis (DMT) scanner, which combines DBT and molecular breast tomosynthesis (MBT) on a single gantry. The DMT scanner uses fully isocentric rotation of tube and x-ray detector for maintaining a fixed tube-detector alignment during DBT imaging. A cellular focused copper prototype grid with 80 cm focal length, 3.85 mm height, 0.1 mm thick lamellae, and 1.1 mm hole pitch was tested. Primary transmission of the grid at 28 kV tube voltage was on average 74% with the grid stationary and aligned for maximum transmission. It fell to 72% during grid reciprocation by the proposed method. Residual grid line artifacts (GLAs) in projection views and reconstructed DBT images are characterized and methods for reducing the visibility of GLAs in the reconstructed volume through projection image flat-field correction and spatial frequency-based filtering of the DBT slices are described and evaluated. The software correction methods reduce the visibility of these artifacts in the reconstructed volume, making them imperceptible both in the reconstructed DBT images and their Fourier transforms.

Finite Volume Based Computer Program for Ground Source Heat Pump System

Energy Technology Data Exchange (ETDEWEB)

Menart, James A. [Wright State University

2013-02-22

This report is a compilation of the work that has been done on the grant DE-EE0002805 entitled ?Finite Volume Based Computer Program for Ground Source Heat Pump Systems.? The goal of this project was to develop a detailed computer simulation tool for GSHP (ground source heat pump) heating and cooling systems. Two such tools were developed as part of this DOE (Department of Energy) grant; the first is a two-dimensional computer program called GEO2D and the second is a three-dimensional computer program called GEO3D. Both of these simulation tools provide an extensive array of results to the user. A unique aspect of both these simulation tools is the complete temperature profile information calculated and presented. Complete temperature profiles throughout the ground, casing, tube wall, and fluid are provided as a function of time. The fluid temperatures from and to the heat pump, as a function of time, are also provided. In addition to temperature information, detailed heat rate information at several locations as a function of time is determined. Heat rates between the heat pump and the building indoor environment, between the working fluid and the heat pump, and between the working fluid and the ground are computed. The heat rates between the ground and the working fluid are calculated as a function time and position along the ground loop. The heating and cooling loads of the building being fitted with a GSHP are determined with the computer program developed by DOE called ENERGYPLUS. Lastly COP (coefficient of performance) results as a function of time are provided. Both the two-dimensional and three-dimensional computer programs developed as part of this work are based upon a detailed finite volume solution of the energy equation for the ground and ground loop. Real heat pump characteristics are entered into the program and used to model the heat pump performance. Thus these computer tools simulate the coupled performance of the ground loop and the heat pump

Study of the key factors affecting the triple grid lifetime of the LIPS-300 ion thruster

Science.gov (United States)

Mingming, SUN; Liang, WANG; Juntai, YANG; Xiaodong, WEN; Yongjie, HUANG; Meng, WANG

2018-04-01

In order to ascertain the key factors affecting the lifetime of the triple grids in the LIPS-300 ion thruster, the thermal deformation, upstream ion density and component lifetime of the grids are simulated with finite element analysis, fluid simulation and charged-particle tracing simulation methods on the basis of a 1500 h short lifetime test. The key factor affecting the lifetime of the triple grids in the LIPS-300 ion thruster is obtained and analyzed through the test results. The results show that ion sputtering erosion of the grids in 5 kW operation mode is greater than in the case of 3 kW. In 5 kW mode, the decelerator grid shows the most serious corrosion, the accelerator grid shows moderate corrosion, and the screen grid shows the least amount of corrosion. With the serious corrosion of the grids in 5 kW operation mode, the intercept current of the acceleration and deceleration grids increases substantially. Meanwhile, the cold gap between the accelerator grid and the screen grid decreases from 1 mm to 0.7 mm, while the cold gap between the accelerator grid and the decelerator grid increases from 1 mm to 1.25 mm after 1500 h of thruster operation. At equilibrium temperature with 5 kW power, the finite element method (FEM) simulation results show that the hot gap between the screen grid and the accelerator grid reduces to 0.2 mm. Accordingly, the hot gap between the accelerator grid and the decelerator grid increases to 1.5 mm. According to the fluid method, the plasma density simulated in most regions of the discharge chamber is 1 × 1018‑8 × 1018 m‑3. The upstream plasma density of the screen grid is in the range 6 × 1017‑6 × 1018 m‑3 and displays a parabolic characteristic. The charged particle tracing simulation method results show that the ion beam current without the thermal deformation of triple grids has optimal perveance status. The ion sputtering rates of the accelerator grid hole and the decelerator hole are 5.5 × 10‑14 kg s‑1 and

New challenges in grid generation and adaptivity for scientific computing

CERN Document Server

Formaggia, Luca

2015-01-01

This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). This book covers different, though related, aspects of the field: the generation of quality grids for complex three-dimensional geometries; parallel mesh generation algorithms; mesh adaptation, including both theoretical and implementation aspects; grid generation and adaptation on surfaces – all with an interesting mix of numerical analysis, computer science and strongly application-oriented problems.

Charging Schedule for Electric Vehicles in Danish Residential Distribution Grids

DEFF Research Database (Denmark)

Pillai, Jayakrishnan Radhakrishna; Huang, Shaojun; Bak-Jensen, Birgitte

2015-01-01

energy sources like wind in power systems. The EV batteries could be used to charge during periods of excess electricity production from wind power and reduce the charging rate or discharge on deficit of power in the grid, supporting system stability and reliability. By providing such grid services......The prospects of Electric Vehicles (EVs) in providing clean transportation and supporting renewable electricity is widely discussed in sustainable energy forums worldwide. The battery storage of EVs could be used to address the variability and unpredictability of electricity produced from renewable......, the vehicle owner, vehicle fleet operator and other parties involved in the process could economically benefit from the process. This paper investigates an optimal EV charging plan in Danish residential distribution grids in view of supporting high volumes of wind power in electricity grids. The results...

Effect of restoration volume on stresses in a mandibular molar: a finite element study.

Science.gov (United States)

Wayne, Jennifer S; Chande, Ruchi; Porter, H Christian; Janus, Charles

2014-10-01

There can be significant disagreement among dentists when planning treatment for a tooth with a failing medium-to-large--sized restoration. The clinician must determine whether the restoration should be replaced or treated with a crown, which covers and protects the remaining weakened tooth structure during function. The purpose of this study was to evaluate the stresses generated in different sized amalgam restorations via a computational modeling approach and reveal whether a predictable pattern emerges. A computer tomography scan was performed of an extracted mandibular first molar, and the resulting images were imported into a medical imaging software package for tissue segmentation. The software was used to separate the enamel, dentin, and pulp cavity through density thresholding and surface rendering. These tissue structures then were imported into 3-dimensional computer-aided design software in which material properties appropriate to the tissues in the model were assigned. A static finite element analysis was conducted to investigate the stresses that result from normal occlusal forces. Five models were analyzed, 1 with no restoration and 4 with increasingly larger restoration volume proportions: a normal-sized tooth, a small-sized restoration, 2 medium-sized restorations, and 1 large restoration as determined from bitewing radiographs and occlusal surface digital photographs. The resulting von Mises stresses for dentin-enamel of the loaded portion of the tooth grew progressively greater as the size of the restoration increased. The average stress in the normal, unrestored tooth was 4.13 MPa, whereas the smallest restoration size increased this stress to 5.52 MPa. The largest restoration had a dentin-enamel stress of 6.47 MPa. A linear correlation existed between restoration size and dentin-enamel stress, with an R(2) of 0.97. A larger restoration volume proportion resulted in higher dentin-enamel stresses under static loading. A comparison of the von Mises

Hybrid multicore/vectorisation technique applied to the elastic wave equation on a staggered grid

Science.gov (United States)

Titarenko, Sofya; Hildyard, Mark

2017-07-01

In modern physics it has become common to find the solution of a problem by solving numerically a set of PDEs. Whether solving them on a finite difference grid or by a finite element approach, the main calculations are often applied to a stencil structure. In the last decade it has become usual to work with so called big data problems where calculations are very heavy and accelerators and modern architectures are widely used. Although CPU and GPU clusters are often used to solve such problems, parallelisation of any calculation ideally starts from a single processor optimisation. Unfortunately, it is impossible to vectorise a stencil structured loop with high level instructions. In this paper we suggest a new approach to rearranging the data structure which makes it possible to apply high level vectorisation instructions to a stencil loop and which results in significant acceleration. The suggested method allows further acceleration if shared memory APIs are used. We show the effectiveness of the method by applying it to an elastic wave propagation problem on a finite difference grid. We have chosen Intel architecture for the test problem and OpenMP (Open Multi-Processing) since they are extensively used in many applications.

Direct solvers performance on h-adapted grids

KAUST Repository

Paszynski, Maciej; Pardo, David; Calo, Victor M.