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

Journal Article · Sat Apr 01 04:00:00 EST 1978 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(78)90023-2· OSTI ID:6812922

Sod, G A

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.

• Research Organization: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, and Lawrence Livermore Laboratory, P. O. Box 808, Livermore, California
• OSTI ID: 6812922
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 26:4; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

640410 -- Fluid Physics-- General Fluid Dynamics
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY-VALUE PROBLEMS
CONSERVATION LAWS
DOCUMENT TYPES
FINITE DIFFERENCE METHOD
FLUID FLOW
IDEAL FLOW
ITERATIVE METHODS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
REVIEWS
SHOCK TUBES