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 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.
- Publication Date:
- OSTI Identifier:
- Resource Type:
- Journal Article
- Resource Relation:
- Journal Name: J. Comput. Phys.; (United States); Journal Volume: 26:4
- Research Org:
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, and Lawrence Livermore Laboratory, P. O. Box 808, Livermore, California
- Country of Publication:
- United States
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; FINITE DIFFERENCE METHOD; REVIEWS; SHOCK TUBES; BOUNDARY-VALUE PROBLEMS; CONSERVATION LAWS; IDEAL FLOW; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; DOCUMENT TYPES; FLUID FLOW; ITERATIVE METHODS; NUMERICAL SOLUTION 658000* -- Mathematical Physics-- (-1987); 640410 -- Fluid Physics-- General Fluid Dynamics
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