Finite-difference approximations and entropy conditions for shocks

Journal Article · Thu Jan 01 04:00:00 EST 1976 · Commun. Pure Appl. Math.; (United States)

DOI:https://doi.org/10.1002/cpa.3160290305· OSTI ID:7231693

Harten, A; Hyman, J M; Lax, P D

Weak solutions of hyperbolic conservation laws are not uniquely determined by their initial values; an entropy condition is needed to pick out the physically relevant solution. The question arises whether finite-difference approximations converge to this particular solution. It is shown that, in the case of a single conservation law, monotone schemes, when convergent, always converge to the physically relevant solution. Numerical examples show that this is not always the case with nonmonotone schemes, such as the Lax--Wendroff scheme. 4 figures, 2 tables

• DOE Contract Number: E(11-1)-3077
• OSTI ID: 7231693
• Journal Information: Commun. Pure Appl. Math.; (United States), Journal Name: Commun. Pure Appl. Math.; (United States) Vol. 29; ISSN CPAMA
• Country of Publication: United States
• Language: English

Related Subjects

658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
ENTROPY
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
SERIES EXPANSION
SHOCK WAVES
THERMODYNAMIC PROPERTIES