Spurious oscillation of finite difference solutions near shock waves and a new formulation of “TVD” scheme
Through a model study, it was found that the spurious oscillations occuring near shock waves with finite difference equations are related to the dispersion term in the corresponding modified differential equation. If the sign of dispersion coefficient is properly adjusted so that the sign changes across shock waves, the undesirable oscillations can be totally suppressed. Based on this finding, an efficient finite difference scheme is developed. This scheme is one of “TVD”. Numerical results show that this algorithm is efficient and robust.
KeywordsShock Wave Mach Number Space Shuttle Inviscid Flow Mach Disk
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