求解不可压流体Navier-Stokes方程的四阶精度有限容积紧致格式  

A fourth-order finite volume compact method for the incompressible Navier-Stokes equations

作　　者：周筱洁[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《苏州大学学报（自然科学版）》2005年第3期1-8,共8页Journal of Soochow University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(20476065)

摘　　要：采用四阶精度的有限容积紧致格式在交错网格上对二维非定常不可压流体的Navier-Stokes方程中的对流项和扩散项进行离散.压力项则由压力Poisson方程求得,并给出了新的压力Poisson方程的四阶精度有限容积紧致格式的离散表达式.用低存贮的三阶Runge-Kutta方法对Navier-Stokes方程进行时间推进.Fourier分析表明,有限容积紧致格式比一般的有限容积非紧致格式有更高的分辨率.最后以Taylor涡为例,得到了很好的结果.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 methold of integrating the Navier-Stokes equations comprises a compact finite volume formulation of the average convective and diffusive fluxes. The pressure term is achieved via the solution of Poisson equation, and a new fourth-order finite volume compact scheme is used to discrete the pressure Poisson equation. Time advancement uses a low store three-order Runge-Kutta method. Compared with finite normal volume noncompact scheme, Fourier analysis shows that finite volume compact scheme can achieve higher resolution. Validation of the method is presented by calculating of Taylor＇s vortex array.

关 键 词：NAVIER-STOKES方程 有限容积法 紧致格式 高分辨率 

分 类 号：O357.1[理学—流体力学]