在半交错网格上求非定常不可压N－S方程的差分解

THE FINITE DIFFERENCE SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NMIEIR-STOKES EQUATIONS ON THEHALF-STAGGERED MESH

在半交错网格上求非定常不可压Ｎ－Ｓ方程的差分解黄兰洁，伍亚丹（中国科学院计算数学与科学工程计算研究所）ＴＨＥＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＳＯＬＵＴＩＯＮＯＦＴＨＥＵＮＳＴＥＡＤＹＩＮＣＯＭＰＲＥＳＳＩＢＬＥＮＭＩＥＩＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯ...

Abstract The numerical solution of the unsteady incompressible Navier-Stokes equationson the half-staggered mesh is discussed in this paper. This type of mesh has manyad￣ages in extension to the curvilinear case3 but the resulting discrete pressurePoisson equation requires two constraints for solution and leads to two degrees offreedom for the solution. The added constraint (over that of the staggered mesh)can usually be satisfied; and the added degree of freedom, causing possible oscillation in the pressure solution, does not affect the velocity solution. Furthermore,the Poisson equation can be efficiently solved by the muitigrid method. In thiswork, the conservative centered-difference Crank-Nicholson scheme is used withthe pressure correction projection method, which results in second order accuracyin space and in time. Numerical experiments confirm these conclusions and showthat the above algorithm to work well for realistic low Reynolds number flow.