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A common defect of the Roe scheme is the production of non-physical expansionshock and shock instability. An improved method with several advantages waspresented to suppress the shock instability. However, this method cannotprevent expansion shock and is incompatible with the traditional curing methodfor expansion shock. Therefore, the traditional curing mechanism is analyzed.The discussion explains the effectiveness of the traditional curing method andidentifies several defects, one of which leads to incompatibility betweencuring the shock instability and expansion shock. Consequently, a new improvedRoe scheme is proposed in this study. This scheme is concise, easy toimplement, low computational cost, and robust. More importantly, the scheme cansimultaneously cure the shock instability and expansion shock withoutadditional costs.

Cures for the Expansion Shock and the Shock Instability of the Roe Scheme