An adaptive ghost fluid finite volume method for compressible gas–water simulations

Abstract

An adaptive ghost fluid finite volume method is developed for one- and two-dimensional compressible multi-medium flows in this work. It couples the real ghost fluid method (GFM) [C.W. Wang, T.G. Liu, B.C. Khoo, A real-ghost fluid method for the simulation of multi-medium compressible flow, SIAM J. Sci. Comput. 28 (2006) 278–302] and the adaptive moving mesh method [H.Z. Tang, T. Tang. Moving mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487–515; H.Z. Tang, T. Tang, P.W. Zhang, An adaptive mesh redistribution method for non-linear Hamilton–Jacobi equations in two- and three-dimensions, J. Comput. Phys. 188 (2003) 543–572], and thus combines their advantages. This work shows that the local mesh clustering in the vicinity of the material interface can effectively reduce both numerical and conservative errors caused by the GFM around the material interface and other discontinuities. Besides the improvement of flow field resolution, the adaptive GFM also largely increases the computational efficiency. Several numerical experiments are conducted to demonstrate robustness and efficiency of the current method. They include several 1D and 2D gas–water flow problems, involving a large density gradient at the material interface and strong shock-interface interactions. The results show that our algorithm can capture the shock waves and the material interface accurately, and is stable and robust even for solutions with large density and pressure gradients.