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The shock instability phenomenon is a famous problem for the shock-capturingscheme. By subdividing the numerical dissipation of the Roe scheme, the term ofpressure-difference-driven modification for the cell face velocity is regardedas a version of the momentum interpolation method (MIM), which is necessary forincompressible flows to suppress the pressure checkerboard problem. Through theanalysis and odd-even decoupling test, it is discovered that MIM plays the mostimportant role on the shock instability. In fact, for non-linear flows MIMshould be completely removed, but unexpected MIM is activated on the cell facenearly parallel to the flow for high Mach number flows or low Mach number flowsin shock. For such conditions, two coefficients are designed based on localMach number and a shock detector, respectively, and then the improved Roescheme is proposed, which gives consideration to requirement of MIM forincompressible and compressible flows and is validated for good performance ofavoiding odd-even decoupling. Therefore, the aim of decreasing rather thanincreasing numerical dissipation to cure the shock instability can be achieved.

The Role of Momentum Interpolation Mechanism of the Roe Scheme in the Shock Instability