A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems (Communications in Computational Physics, 2021)
In this paper, we develop a novel approach by combining a new robust finite difference Hermite weighted essentially non-oscillatory (HWENO) method [51]with the modified ghost fluid method (MGFM) [25] to simulate the compressible two-medium flow problems. The main idea is that we first use the technique of the MGFMto transform a two-medium flow problem to two single-medium cases by defining theghost fluids status based on the predicted interface status. Then the efficient and robustHWENO finite difference method is applied for solving the single-medium flow cases.By using immediate neighbor information to deal with both the solution and its derivatives, the fifth order finite difference HWENO scheme adopted in this paper is morecompact and has higher resolution than the classical fifth order finite difference WENOscheme of Jiang and Shu [14]. Furthermore, by combining the HWENO scheme withthe MGFM to simulate the two-medium flow problems, less ghost point informationis needed than that in using the classical WENO scheme in order to obtain the samenumerical accuracy. Various one-dimensional and two-dimensional two-medium flowproblems are solved to illustrate the good performances of the proposed method.