Some Aspects of High Resolution Numerical Methods for Hyperbolic Systems of Conservation Laws, with Applications to Gas Dynamics

摘要

Discussed are several important aspects of finite difference methods for hyperbolic systems of conservation laws, from first-order upwind to second-order TVD schemes based on flux limiters and flux splitting, or on Godunov's method. Particular attention is given to the recent schemes of Sweby, Davis, and Goodman-LeVeque, which are second-order TVD versions of the Lax-Wendroff and Godunov schemes. An essential role is played by Harten's criterion for Total Variation Diminishing schemes.