A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws

The finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, the artificial compression method of Harten, and Glimm's method, a random choice method, are di...

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Bibliographic Details
Published in:Journal of Computational Physics 1978-04, Vol.27 (1), p.1-31
Main Author: Sod, Gary A
Format: Article
Language:English
Subjects:
Civil Engineering
Dynamique, vibrations
Engineering Sciences
Mechanical engineering
Mechanics
Physics
Solid mechanics
Structural mechanics
Structures
Vibrations
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Summary:The finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, the artificial compression method of Harten, and Glimm's method, a random choice method, are discussed. The methods are used to integrate the one-dimensional Eulerian form of the equations of gas dynamics in Cartesian coordinates for an inviscid, nonheat-conducting fluid. The test problem was a typical shock tube problem. The results are compared and demonstrate that Glimm's method has several advantages.
ISSN:0021-9991
1090-2716
DOI:10.1016/0021-9991(78)90023-2