On Peculiar Behaviors of Captured Very-Weak Moving Shockwaves

In this research, peculiar behaviors in calculations of weak and very-weak moving shock waves by two-dimensional finite volume methods are investigated. First-order accuracy calculations of moving shock wave with a shock Mach number of 1.01 show anomalous solutions. The observed anomalies are categorized into three types depending on numerical flux functions: unstable growth of shock wave width, overshoots in primitive variables, and failures of calculations. The κ =1/3 MUSCL scheme suppresses the unstable growth of shock wave thickness when numerical flux functions and limiters are carefully selected: A combination of SLAU2 and the van Albada-limited κ =1/3 MUSCL is found the best for computations of moving very-weak shock waves.