Modified far-upwind reconstruction methods for the implementation of NVSF schemes on unstructured grids

Abstract

Based on the analysis of the existing far-upwind reconstruction methods, three modified far-upwind reconstruction methods, named as NM-1, NM-2 and NM-3, are developed for the implementation of Normalized Variable and Space Formulation (NVSF) schemes on arbitrary unstructured grids. In the modified reconstruction methods, the locations of the cell centroids around the upwind cell are considered for the position reconstruction. And three interpolation techniques, including the nearest point interpolation, the inverse distance weighted interpolation and the gradient-considered inverse distance weighted interpolation are adopted for the value reconstruction. Moreover, a modified boundedness limitation is proposed to constrain the reconstructed value of the far-upwind node within a more reasonable scope. The pure advection tests demonstrate that NM-3 leads to a better overall performance in terms of accuracy and convergence comparing with the previous and the other modified reconstruction methods for seven classic NVSF schemes. Such advantage of NM-3 retains in the applications of multiphase flow (dam-break flow) and incompressible fluid flow (backward step flow and lid-driven cavity flow). Theoretical analysis implies that the good performance of NM-3 mainly attributes to that its position reconstruction better represents the ‘average position’ of the adjacent cell centroids around the upwind cell and its value reconstruction combines the advantages of the nearest point interpolation and the inverse distance weighted interpolation simultaneously.