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 in this work for improving shock stability and reducing numerical dissipation in smooth flows. 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 and minimum principles are satisfied by both the strict- and weak-MLP conditions. A differentiable pressure weight function is applied to combine two novel conditions, and thus the modified limiter is named as MLP-pw (pressure-weighted) limiter. A series of numerical test cases show that MLP-pw limiter has improved stability and convergence, especially in hypersonic simulations. Moreover, the limiter also shows low numerical dissipation in simulating flow fields without shock-waves.