The Study On The Finite Volume Compact Scheme And The Boundary Treatment Of The Compact Finite Difference Scheme

A fourth-order finite volume compact scheme for the discretization of the two-dimensional unsteady incompressible Navier-Stokes equations is presented.The scheme is constructed on a staggered grid.The numerical method of integrating the Navier-Stokes equations comprises a compact finite volume formulation of the sliding average convective and diffusive fluxes.The pressure term is achieved by solving pressure Poisson equation,and a new fourth-order finite volume compact scheme is used to discrete the equation.Time advancement uses a low storage three-stage Runge-Kutta method. Compared with normal finite volume noncompact scheme,Fourier analysis shows that finite volume compact scheme can achieve higher resolution .Validation of the method is presented by calculating the Taylor's vortex array and a double layer flow problem. Finally,the boundary treatment of the compact finite difference scheme is discussed and compared with the numerical result with periodic boundary conditions.