High order all-speed semi-implicit weighted compact nonlinear scheme for the isentropic Navier–Stokes equations

Abstract

This paper presents a high order all-speed semi-implicit weighted compact nonlinear scheme (WCNS) for the isentropic Navier–Stokes system. To avoid the severe CFL stability restriction, the pressure and viscous terms are treated implicitly in time, while the other terms are treated explicitly in time. The third-order IMEX Runge–Kutta methods and the fifth-order WCNS are used for time discretization and spatial discretization, respectively. The generated linear equations of velocity components are solved by the GMRES iterative algorithm. Numerical results in one, two and three dimensions in both compressible and incompressible regimes are presented to show the performance of the designed scheme.