Multi-dimensional limiting process on triangular and tetrahedral meshes

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP), which has been quite successfully proposed on two- and three-dimensional structured meshes, onto the unstructured meshes. The basic idea of the present limiting strategy is to control the distribution of both cell-centered and cell-vertex physical properties to mimic a multi-dimensional nature of flow physics, which can be formulated as so called the MLP condition. The MLP condition can guarantee a high order spatial accuracy without yielding spurious oscillations. Starting from the MUSCL-type reconstruction on unstructured meshes followed by the efficient implementation of the MLP condition, MLP slope limiters on unstructured meshes are proposed. Through various numerical analyses and extensive computations, it is observed that the proposed limiters are quite effective in controlling numerical oscillations and very accurate in capturing both discontinuous and continuous multi-dimensional flow features on 2-D triangular meshes and 3-D tetrahedral meshes.