  The shock instability phenomenon is a famous problem for the shock-capturing
scheme. By subdividing the numerical dissipation of the Roe scheme, the term of
pressure-difference-driven modification for the cell face velocity is regarded
as a version of the momentum interpolation method (MIM), which is necessary for
incompressible flows to suppress the pressure checkerboard problem. Through the
analysis and odd-even decoupling test, it is discovered that MIM plays the most
important role on the shock instability. In fact, for non-linear flows MIM
should be completely removed, but unexpected MIM is activated on the cell face
nearly parallel to the flow for high Mach number flows or low Mach number flows
in shock. For such conditions, two coefficients are designed based on local
Mach number and a shock detector, respectively, and then the improved Roe
scheme is proposed, which gives consideration to requirement of MIM for
incompressible and compressible flows and is validated for good performance of
avoiding odd-even decoupling. Therefore, the aim of decreasing rather than
increasing numerical dissipation to cure the shock instability can be achieved.
