局部网格加密方法计算不可压N-S方程

LOCAL MESH REFINEMENT FOR THE INCOMPRESSIBLE N-S EQUATIONS

本文发展了二维非定常不可压N-S方程的局部网格加密方法(LMR):需加密区域预先指定;仅对空间方向加密,分粗细二层网格,细网格覆盖在粗网格上;粗和细网格上分别用显式和隐式差分格式。结合压力修正法类的余量型差分格式,恰当地处理了粗细网格之间的信息传递,使得粗细网格交接面上质量守恒,即满足连续性条件。粗网格通过插值给细网格边界值影响细网格;细网格通过粗细网格压力Poisson方程耦合求解影响粗网格,并且由于压力Poisson方程从动量方程形成,在细网格覆盖下的粗网格上,压力Poisson方程是细网格方程的组合,从而耦合求解时粗细网格压力Poisson方程不需迭代。 本文中计算了二维方腔内的自然对流模型问题,Rayleigh数是10~6。粗网格用显式ULWC格式,细网格用隐式余量型近似因式分解格式。Poisson方程用快速直接算法PO1STG(在FISHPACK中)。粗网格距△=1/16,细网格距△=1/64,加密1/4区域,计算到定常局部网格加密方法所需CPU时间比同等均匀网格(△=1/64)节约一倍以上。

A local mesh refinement method is developed for the time-dependent incompressible N-S equations. A two-level grid system is considered, in which the fine grids are overlaid on the coarse grids, Refinement is in space only and the refined subdomains are specified. Explicit and implicit finite difference schemes are used respectively on the coarse and fine grids Using the delta-form finite difference schemes of the pressure correction method and appropriately treating information exchange between the coarse and fine grids, mass is conserved on the interface between the coarse and fine grids, mass is conserved on the interface betweem the coarse and fine grids, i. e the continuity condition is satisfied. The coarse grids influence the fine grids by interpolation of the coarse grid values for the boundary conditions on the fine grids. The fine grids influence the coarse grids by the coupled solution of the pressure Poisson equations. Because the pressure Poisson equations are formed from the momentum equations, for the coarse grid overlaid by fine grids, the pressure Poisson equation is simply the average of the fine grid equations. So, the coupled solution of the pressure Poisson equations do not need iteration.The standard example of bouyancy-driven natural convection flow in an upright enclosed square cavity at high Rayleigh number Ra = 106 is calculated. The explicit scheme ULWC is used on the coarse grids and the implicit delta-form approximate factorization scheme on the fine grids. Poisson equations are solved by the faster solver POISTG in FISHPACK . The mesh widths of the coarse and fine grids are 1/16 and 1/64 respectively. Local refined subdomain is one quarter of the entire domain. The total CPU time of the LMR method is less tha n one half that of the uniform grid (△= 1/64).