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

The basic concept of multi-dimensional limiting process (MLP) on unstructured grids is inherited and modified for improving shock stabilities and reducing numerical dissipation on smooth regions. A relaxed version of MLP condition, simply named as weak-MLP, is proposed for reducing dissipation. Moreover, a stricter condition, that is the strict-MLP condition, is proposed to enhance the numerical stability. The maximum/minimum principle is fulfilled by both the strictand weak-MLP condition. A differentiable pressure weight function is applied for the combination of two novel conditions, and thus the modified limiter is named as MLP-pw(pressure-weighted). A series of numerical test cases show that MLP-pw limiter has improved stability and convergence, especially in hypersonic simulations. Furthermore, the limiter also shows lower dissipation in regions without significant pressure transition. Therefore, MLPpw limiter can capture contact discontinuity and expansion accurately.