Discretization of Unsteady Hyperbolic Conservation Laws
A basic target algorithm for approximating unsteady hyperbolic conservation laws uses a finite volume formulation in three steps: recovery or reconstruction of a more accurate approximation from a set of cell averages; solution of the conservation law to obtain interface fluxes averaged over a time...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2002, Vol.39 (5), p.1556-1597 |
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| container_title | SIAM journal on numerical analysis |
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| creator | Morton, K. W. |
| description | A basic target algorithm for approximating unsteady hyperbolic conservation laws uses a finite volume formulation in three steps: recovery or reconstruction of a more accurate approximation from a set of cell averages; solution of the conservation law to obtain interface fluxes averaged over a time step; and computation of new cell averages at the new time level. In this paper the target is achieved by bringing together ideas from Brenier's transport collapse operator-using Lin, Morton, and Süli's Riemann-Stieltjes interpretation, van Leer's MUSCL algorithm, Colella and Woodward's PPM algorithm, and Goodman and LeVeque's flux approximation. First, second, and third order accurate algorithms are developed for nonuniform one-dimensional grids, and extensions are described for unstructured triangular meshes. The MUSCL-type scheme in one dimension is proved to be TV-stable right up to the natural CFL limit, in which characteristics cross no more than one cell in one time step, and under the least restrictive necessary TVD condition on the recovery stage. |
| doi_str_mv | 10.1137/S0036142900373956 |
| format | Article |
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W.</creator><creatorcontrib>Morton, K. W.</creatorcontrib><description>A basic target algorithm for approximating unsteady hyperbolic conservation laws uses a finite volume formulation in three steps: recovery or reconstruction of a more accurate approximation from a set of cell averages; solution of the conservation law to obtain interface fluxes averaged over a time step; and computation of new cell averages at the new time level. In this paper the target is achieved by bringing together ideas from Brenier's transport collapse operator-using Lin, Morton, and Süli's Riemann-Stieltjes interpretation, van Leer's MUSCL algorithm, Colella and Woodward's PPM algorithm, and Goodman and LeVeque's flux approximation. First, second, and third order accurate algorithms are developed for nonuniform one-dimensional grids, and extensions are described for unstructured triangular meshes. 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W.</creatorcontrib><title>Discretization of Unsteady Hyperbolic Conservation Laws</title><title>SIAM journal on numerical analysis</title><description>A basic target algorithm for approximating unsteady hyperbolic conservation laws uses a finite volume formulation in three steps: recovery or reconstruction of a more accurate approximation from a set of cell averages; solution of the conservation law to obtain interface fluxes averaged over a time step; and computation of new cell averages at the new time level. In this paper the target is achieved by bringing together ideas from Brenier's transport collapse operator-using Lin, Morton, and Süli's Riemann-Stieltjes interpretation, van Leer's MUSCL algorithm, Colella and Woodward's PPM algorithm, and Goodman and LeVeque's flux approximation. First, second, and third order accurate algorithms are developed for nonuniform one-dimensional grids, and extensions are described for unstructured triangular meshes. The MUSCL-type scheme in one dimension is proved to be TV-stable right up to the natural CFL limit, in which characteristics cross no more than one cell in one time step, and under the least restrictive necessary TVD condition on the recovery stage.</description><subject>Accuracy</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Arithmetic mean</subject><subject>Conservation laws</subject><subject>Exact sciences and technology</subject><subject>Galerkin methods</subject><subject>Mathematical discontinuity</subject><subject>Mathematical integrals</subject><subject>Mathematics</subject><subject>Navier-Stokes equations</subject><subject>Numerical analysis</subject><subject>Numerical analysis. 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W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Discretization of Unsteady Hyperbolic Conservation Laws</atitle><jtitle>SIAM journal on numerical analysis</jtitle><date>2002</date><risdate>2002</risdate><volume>39</volume><issue>5</issue><spage>1556</spage><epage>1597</epage><pages>1556-1597</pages><issn>0036-1429</issn><eissn>1095-7170</eissn><coden>SJNAEQ</coden><abstract>A basic target algorithm for approximating unsteady hyperbolic conservation laws uses a finite volume formulation in three steps: recovery or reconstruction of a more accurate approximation from a set of cell averages; solution of the conservation law to obtain interface fluxes averaged over a time step; and computation of new cell averages at the new time level. In this paper the target is achieved by bringing together ideas from Brenier's transport collapse operator-using Lin, Morton, and Süli's Riemann-Stieltjes interpretation, van Leer's MUSCL algorithm, Colella and Woodward's PPM algorithm, and Goodman and LeVeque's flux approximation. First, second, and third order accurate algorithms are developed for nonuniform one-dimensional grids, and extensions are described for unstructured triangular meshes. The MUSCL-type scheme in one dimension is proved to be TV-stable right up to the natural CFL limit, in which characteristics cross no more than one cell in one time step, and under the least restrictive necessary TVD condition on the recovery stage.</abstract><cop>Philadelphia, PA</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/S0036142900373956</doi><tpages>42</tpages></addata></record> |
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| subjects | Accuracy Algorithms Approximation Arithmetic mean Conservation laws Exact sciences and technology Galerkin methods Mathematical discontinuity Mathematical integrals Mathematics Navier-Stokes equations Numerical analysis Numerical analysis. Scientific computation Partial differential equations, initial value problems and time-dependant initial-boundary value problems Scalars Sciences and techniques of general use Tensors Vertices Zero |
| title | Discretization of Unsteady Hyperbolic Conservation Laws |
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