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A comparative study of advanced shock-capturing schemes applied to Burgers’ equation. (English) Zbl 0759.76053

We have considered several variations of the TVD and FCT schemes and geometrical approaches such as MUSCL, ENO, and PPM. Included is an organized overview and classification of the schemes. Only essential features are described, and numerical implementation is discussed. Much of the mathematical theory is omitted, but a key source reference list is provided. We present a comparative study of these schemes applied to the Burgers’ equation. The objective is to assess their performance for problems involving formation and propagation of shocks, shock collisions, and expansion of discontinuities.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
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