Implicit eighth-order central compact scheme for the numerical simulation of steady and unsteady incompressible Navier–Stokes equations

Abstract

The pseudo-compressibility method, with an implicit eighth-order central compact scheme, is proposed to solve the steady and unsteady incompressible Navier–Stokes equations. In this method, the spatial discretisation comprises an eighth-order compact scheme with stable boundary closures and a tenth-order numerical filter operator. Moreover, a Lower–Upper Symmetric Gauss-Seidel time integration method is adopted for the pseudo time sub-iteration, whereas the dual-time step method is used to improve time accuracy. The reliability of the proposed procedure is verified by simulating the phenomenon of Taylor decaying vortices, the separated flow over a backward-facing step, and the low Reynolds number steady and unsteady viscous incompressible flow over a circular cylinder. The results of the present algorithm have been proven consistent, both with exact solutions and with experimental data.