65 / 2019-09-27 16:56:36

An improved third-order compact nonlinear scheme

third order,compact nonlinear schemes,nonlinear interpolation,ENO property,compressible flow

Reynolds-averaged Navier-Stokes (RANS) simulations based on second-order numerical methods are widely used by commercial codes, and work as dominating tools for most industry related applications. They, however, suffer from limitations in accurate and reliable predictions of skin-friction drag and aerodynamic heating, as well as in simulations of complex flows such as large-scale separation and transition. A remedy for this is the development of high-order schemes, by which numerically-induced dissipation and dispersion errors of low-order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high resolution nonlinear shock-capturing methods. A stencil-selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third-order WCNS. It is demonstrated that the new scheme has shown reduced dissipation and dispersion errors than WCNSs using two typical nonlinear weights by approximate dispersion relation (ADR) analysis. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh-Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multi-scales phenomena.