A GRP-based tangential effects preserving, high resolution and efficient ghost fluid method for the simulation of two-dimensional multi-medium compressible flows

Abstract

This paper present the GRP-based GFM, which define the ghost fluid states by a local double-medium GRP established at the interface. The initial data of the GRP are linearly distributed, which are chosen by distance weighted least square fitting. The equations of the GRP have a source term associated with the tangential direction, which is necessary because of the Galilean invariance of the two-dimensional Euler equations. The intermediate states of the GRP are linearly distributed in numerical calculation. Modify the fluid states and their spatial derivatives along the normal direction of the interface in the real fluid regions near the interface by making use of the linearly distributed intermediate states. Then extend the fluid states and spatial derivatives in the real fluid regions near the interface to the ghost fluid regions by linear and constant extrapolating. The advantages of our proposed GRP-based GFM over the traditional RP-based GFM are as follows: (i) Reflect the effects of the source term associated with the tangential direction. (ii) Maintain the continuity of the material derivatives along the normal direction of the interface of pressure and normal velocity, and almostly eliminate the pressure and normal velocity mismatch errors near the interface. (iii) Comparing with choosing the initial data by bilinear interpolation, choosing the initial data by weighted least square fitting can improve the simulation results. (iv) Comparing with extending the ghost fluid states by solving the Eikonal equations iteratively, extending the ghost fluid states by linearly and constantly extrapolating can improve the numerical efficiency. Several typical numerical examples prove the superiority of our algorithm.