非スタガード差分法による非圧縮性ナビェ・ストークス方程式の数値解

概要

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A new method for solving the primitive variable formulation of the incompressible Navier-Stokes equations on the non-staggered grid is presented. The spatial derivatives of the momentum equations are discretized by the second-order centered finite difference approximation on the cell interfaces, and the fluxes on the non-staggered grid are estimated from the simple average of the cell interfaces. The resulting system of ordinary differential equations in time is integrated by the forward Euler scheme. The Poisson equation for the pressure is discretized in the same manner as the momentum equations and solved by the successive-overrelaxation (SOR) method. The present method satisfies the divergence-free condition, i.e., the continuity equation, at each time step. As the test problem, square driven cavity flows are considered. The results obtained by the present method are compared with those of the marker-and-cell (MAC) method. The results show that the present method gives solutions comparable to the MAC solutions, and that the allowable time step is larger than in the MAC method.
一般社団法人日本機械学会の論文
1996-07-25