Based On The Projection Method For Solving Incompressible Flow, Numerical Methods

In this paper, based on the Kim and Moin projection methods, we develop a high-order compact scheme with spatial order 4 and temporal order 2 for the solution of the incompressible Navier-Stokes equations.In particular, we propose a new compact discretization formula for the Neumann boundary condition of pressure.Some classical numerical experiments are performed to validate the accuracy and robustness of the present scheme. First, the simulation of the decaying vortices proves that present projection methods are indeed full second-order temporal accuracy and high order accuracy in space with the high order compact scheme we choose. The simulation results of the steady flow and asymptotic flow 2D regularized driven cavity with different Reynolds number are in good agreement with other solutions in the literature. The reliability of the compact scheme projection is further illustrated by a back-facing step problem, this experiment also checks present methods accuracy as the reattachment length is a function of Reynolds number.All of the computational results show that, besides including the excellent performances in accuracy, efficiency and stability, present methods have the advantage of better scale resolution with smaller number of gird nodes and large potential of extending to direct numerical simulation of the complex flows with high Reynolds number.