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186
The nas parallel benchmarks
 The International Journal of Supercomputer Applications
, 1991
"... A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers. These benchmarks consist of ve \parallel kernel " benchmarks and three \simulated application" benchmarks. Together they mimic the computation and data movement characterist ..."
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Cited by 694 (9 self)
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A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers. These benchmarks consist of ve \parallel kernel &quot; benchmarks and three \simulated application&quot; benchmarks. Together they mimic the computation and data movement characteristics of large scale computational uid dynamics applications. The principal distinguishing feature of these benchmarks is their \pencil and paper &quot; speci cation  all details of these benchmarks are speci ed only algorithmically. In this way many of the di culties associated with conventional benchmarking approaches on highly parallel systems are avoided. 1
Analysis and Design of Numerical Schemes for Gas Dynamics 1 Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Accuracy and Multigrid Convergence
 INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
, 1995
"... The theory of nonoscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multidimensional problems on both structured and unstructured meshes, whi ..."
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Cited by 122 (45 self)
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The theory of nonoscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multidimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for onedimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multidimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with a modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.
Adaptive Local Refinement with Octree LoadBalancing for the Parallel Solution of ThreeDimensional Conservation Laws
 J. Parallel Distrib. Comput
, 1997
"... Conservation laws ae solved by a local Gaerkin finite element procedure with adapfive spacetime mesh refinement ad explicit time integration. The Courat stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to method ..."
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Cited by 68 (17 self)
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Conservation laws ae solved by a local Gaerkin finite element procedure with adapfive spacetime mesh refinement ad explicit time integration. The Courat stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. Processor load imbalaces, introduced at adaptive enrichment steps, are corrected by using traversals of an octtee representing a spatial decomposition of the domain. To accommodate the variable time steps, octtee partitioning is extended to use weights derived from element size. Partition boundary smoothing reduces the communications volume of partitioning procedures for a modest cost. Computational results comparing parallel octtee ad inertial partitioning procedures ae presented for the threedimensional Euler equations of compressible flow solved on an IBM SP2 computer.
On centraldifference and upwind schemes
 Journal of Computational Physics
, 1992
"... Israel A class of numerical dissipation models for centraldifference schemes constructed with second and fourthdifference terms is considered. The notion of matrix dissipation associated with upwind schemes is used to establish improved shock capturing capability for these models. In addition, c ..."
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Cited by 66 (12 self)
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Israel A class of numerical dissipation models for centraldifference schemes constructed with second and fourthdifference terms is considered. The notion of matrix dissipation associated with upwind schemes is used to establish improved shock capturing capability for these models. In addition, conditions are given that guarantee that such dissipation models produce a TVD scheme. Appropriate switches for this type of model to ensure satisfaction of the TVD property are presented. Significant improvements in the accuracy of a centraldifference scheme are demonstrated by computing both inviscid and viscous transonic airfoil flows. ';iozi For ' ;4:. cation
Multigrid Solution for HighOrder Discontinuous Galerkin . . .
, 2004
"... A highorder discontinuous Galerkin finite element discretization and pmultigrid solution procedure for the compressible NavierStokes equations are presented. The discretization has an elementcompact stencil such that only elements sharing a face are coupled, regardless of the solution space. Thi ..."
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Cited by 45 (16 self)
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A highorder discontinuous Galerkin finite element discretization and pmultigrid solution procedure for the compressible NavierStokes equations are presented. The discretization has an elementcompact stencil such that only elements sharing a face are coupled, regardless of the solution space. This limited coupling maximizes the effectiveness of the pmultigrid solver, which relies on an elementline Jacobi smoother. The elementline Jacobi smoother solves implicitly on lines of elements formed based on the coupling between elements in a p = 0 discretization of the scalar transport equation. Fourier analysis of 2D scalar convectiondiffusion shows that the elementline Jacobi smoother as well as the simpler element Jacobi smoother are stable independent of p and flow condition. Mesh refinement studies for simple problems with analytic solutions demonstrate that the discretization achieves optimal order of accuracy of O(h p+1). A subsonic, airfoil test case shows that the multigrid convergence rate is independent of p but weakly dependent on h. Finally, higherorder is shown to outperform grid refinement in terms of the time required to reach a desired accuracy level.
Positive schemes and shock modelling for compressible flows
 International Journal for Numerical Methods in Fluids
, 1995
"... A unified theory of nonoscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This l ..."
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Cited by 37 (2 self)
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A unified theory of nonoscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presmted which confirm the properties of these schemes. KEY WORDS computational aerodynamics; shock capturing; positive schemes 1.
Finite Volume Methods: Foundation and Analysis
 ENCYCLOPEDIA OF COMPUTATIONAL MECHANICS, VOLUME 1, FUNDAMENTALS
, 2004
"... Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, meteorology, electromagnetics, semiconductor device simulation, models of biologi ..."
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Cited by 35 (1 self)
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Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, meteorology, electromagnetics, semiconductor device simulation, models of biological processes and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article
A WellBalanced Scheme Using NonConservative Products Designed for Hyperbolic Systems of Conservation Laws With Source Terms
, 2001
"... The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a nonconservative reformulation of the zeroorder terms of the righthandside of the equations. In this context, we decided to use the ..."
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Cited by 30 (4 self)
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The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a nonconservative reformulation of the zeroorder terms of the righthandside of the equations. In this context, we decided to use the results of DalMaso, LeFloch and Murat [9] about nonconservative products, and the generalized Roe matrixes introduced by Toumi [36] to derive a firstorder linearized wellbalanced scheme in the sense of Greenberg and LeRoux [19]. As a main feature, this approach is able to preserve the right asymptotic behaviour of the original inhomogeneous system [31], which is not a obvious property [6]. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations. Key words: conservation laws, source terms. nonconservative products, balanced scheme. AMS subjects classification: 65M06, 76N15. 1 Current adress: Foundation for Research and Technology Hel...