Peculiarity of moving weak shock computations: Entropy generation analysis of numerically expressed shock waves

Shock-capturing schemes using a finite volume method represent shock waves using a specific number of cells. Although understanding the behavior of these “numerical shock waves” is crucial owing to their distinct characteristics, which differ from those of theoretical and physical shock waves, moving weak and moderate shock waves have not been thoroughly investigated. In this study, a numerical test and an analysis were conducted to elucidate the properties of numerical moving shock waves. Our numerical test revealed that the outcome is influenced by the shock strength and numerical flux functions. The final state of a moving shock wave can be classified into three regimes (dissipated, transitional, and thinly captured regimes) depending on the shock strength. Peculiarly, weak shocks faced the dissipated regime, and the dissipation was serious at a shock Mach number of 1.01. Computational results were examined with respect to the entropy generation resulting from the propagation of the numerical moving shock wave. The analysis clarified that the thickness of numerical moving shock waves was determined to ensure physically accurate entropy generation. Furthermore, it was clarified that a moving weak shock wave cannot be accurately represented with a thin profile owing to excessive entropy production. This difficulty in handling a small amount of entropy production resulted in the peculiarity of the weak shock wave computations.