71 / 2019-09-29 08:42:15

High order semi-implicit weighted compact nonlinear scheme for the viscous burgers' equations

Semi-implicit, IMEX, WCNS, Burgers' equations

This paper combines the hybrid cell-edge and cell-node weighted compact nonlinear scheme (WCNS) with the semi-implicit time-stepping method to solve the viscous burgers' equations. The advection terms are treated explicitly, while viscosity terms are treated implicitly to avoid severe CFL restrictions. Numerical examples are given to verify the high order accuracy, high resolution and efficiency of the semi-implicit WCNS.