An efficient hybrid multi-resolution WCNS scheme for solving compressible flows

Abstract

A hybrid finite difference fifth-order multi-resolution weighted compact nonlinear scheme (WCNS) is presented for simulating the inviscid and viscous compressible flows in this paper. This scheme borrows and improves the idea of the recently developed multi-resolution WENO scheme for node-to-midpoint nonlinear interpolation procedures of the WCNS scheme, which implements higher-order approximate interpolation at midpoints based on a series of nested stencils. This strategy can achieve the expected design accuracy under different linear weights, and can gradually decrease from high-order accuracy to first-order accuracy near the discontinuities. In addition, a hybridization strategy is proposed to further improve the computational efficiency of the presented multi-resolution WCNS scheme. The strategy does not depend on a specific problem to be solved, nor does it contain any problem-related artificial parameters. Finally, some benchmark examples are used to verify the performance of the presented scheme in terms of numerical accuracy, shock capture capability, robustness, computational efficiency, etc.