A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations
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摘要: 微分求积法(DQM)能以较少的网格点求得微分方程的高精度数值解,但采用单纯的微分求积法求解二维不可压缩Navier-Stokes方程时,只能对低雷诺数流动获得较好的数值解,当雷诺数较高时会导致数值解不收敛。为此,提出了一种微分求积法与迎风差分法混合求解二维不可压缩Navier-Stokes方程的预估-校正数值格式,用伪时间相关算法以较少的网格点获得了较高雷诺数流动的数值解。作为算例,对1:1和1:2驱动方腔内的流动进行了计算,得到了较好的数值结果。
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关键词:
- 数值方法 /
- 微分求积法 /
- Navier-Stokes方程
Abstract: Differential quadrature method(DQM)is able to obtain highly accurate numerical solutions of differential equations just using a few grid points.But using purely differential quadrature method, good numerical solutions of two-dimensional incompressible Navier-Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow.For this reason,in this paper a combinative predicting-correcting numerical scheme for solving two-dimensional incompressible Navier-Stokes equations is presented by mixing upwind difference method into differential quadrature one.Using this scheme and pseudo-time-dependent algorithm,numerical solutions of high Reynolds number flow are obtained with only a few grid points.For example,1:1 and 1:2 driven cavity flows are calculated and good numerical solutions are obtained. -
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