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The basic concept of multi-dimensional limiting process (MLP) on unstructuredgrids is inherited and modified for improving shock stabilities and reducingnumerical dissipation on smooth regions. A relaxed version of MLP condition,simply named as weak-MLP, is proposed for reducing dissipation. Moreover, astricter condition, that is the strict-MLP condition, is proposed to enhancethe numerical stability. The maximum/minimum principle is fulfilled by both thestrict- and weak-MLP condition. A differentiable pressure weight function isapplied for the combination of two novel conditions, and thus the modifiedlimiter is named as MLP-pw(pressure-weighted). A series of numerical test casesshow that MLP-pw limiter has improved stability and convergence, especially inhypersonic simulations. Furthermore, the limiter also shows lower dissipationin regions without significant pressure transition. Therefore, MLP-pw limitercan capture contact discontinuity and expansion accurately.

Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids