WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-dimensional Compressible Two-medium Flows

摘要

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in 32, 7, 6. Recently, it has been observed in 3 that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in 7, based on the high order finite volume WENO scheme with subcell resolution and utilizing the exact Riemann solver to catch the right paths at the discontinuities, is proposed to improve its computational performance and to overcome some of the shortcomings. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.