Due to its high resolution for discontinuities and high efficiency, the HLLEM scheme is a popular numerical method to calculate the conservative hyperbolic systems. When capturing multidimensional strong shock waves, however, it will encounter different forms of numerical oscillations, such as the odd-even decoupling and carbuncle phenomenon, which is a great hindrance to its application in hypersonic flow problems. In this paper the numerical shock instability of the HLLEM scheme is investigated from a mathematical perspective and a corresponding cure is proposed. A special linearized small p...
