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Title: High resolution finite volume methods on arbitrary grids via wave propagation. Final report

Abstract

A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

Authors:
Publication Date:
Research Org.:
National Aeronautics and Space Administration, Hampton, VA (USA). Langley Research Center
OSTI Identifier:
5543706
Report Number(s):
N-88-12979; NASA-CR-178397; ICASE-87-68; NAS-1.26:178397
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONSERVATION LAWS; NUMERICAL ANALYSIS; WAVE PROPAGATION; CARTESIAN COORDINATES; COORDINATES; MATHEMATICS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Leveque, R J. High resolution finite volume methods on arbitrary grids via wave propagation. Final report. United States: N. p., 1987. Web.
Leveque, R J. High resolution finite volume methods on arbitrary grids via wave propagation. Final report. United States.
Leveque, R J. 1987. "High resolution finite volume methods on arbitrary grids via wave propagation. Final report". United States.
@article{osti_5543706,
title = {High resolution finite volume methods on arbitrary grids via wave propagation. Final report},
author = {Leveque, R J},
abstractNote = {A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.},
doi = {},
url = {https://www.osti.gov/biblio/5543706}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Oct 01 00:00:00 EDT 1987},
month = {Thu Oct 01 00:00:00 EDT 1987}
}

Technical Report:
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