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Title: Survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws

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.
Authors:
Publication Date:
OSTI Identifier:6812922
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
Language:English
Subject: 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