Improved Weighted Compact Nonlinear Scheme for Flows with Shocks and Material Interfaces: Algorithm and Assessment

摘要

Simulations of single- and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative hybrid weighted interpolation method (HW6-LD). In smooth regions, the scheme applies the central nonlinear interpolation with minimum dissipation to capture highly turbulent features while in regions around shock waves and discontinuities, the scheme stabilizes the solutions by hybridizing the central interpolation with the more dissipative upwind-biased nonlinear interpolation. In capturing material interfaces between different species, a quasi-conservative five equation model that can conserve mass of each species is used to prevent pressure oscillations across the interfaces. Compared to the classical upwind-biased interpolation and the adaptive central-upwind interpolation with improved scale-separation capability, it is shown that the proposed localized dissipative hybrid weighted interpolation method has better performance to simultaneously capture discontinuities and preserve highly fluctuating flow features in a series of one- and multi-dimensional test problems.