  A common defect of the Roe scheme is the production of non-physical expansion
shock and shock instability. An improved method with several advantages was
presented to suppress the shock instability. However, this method cannot
prevent expansion shock and is incompatible with the traditional curing method
for expansion shock. Therefore, the traditional curing mechanism is analyzed.
The discussion explains the effectiveness of the traditional curing method and
identifies several defects, one of which leads to incompatibility between
curing the shock instability and expansion shock. Consequently, a new improved
Roe scheme is proposed in this study. This scheme is concise, easy to
implement, low computational cost, and robust. More importantly, the scheme can
simultaneously cure the shock instability and expansion shock without
additional costs.
