Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations

Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations
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DOI：
10.1007/978-3-642-56103-0_26
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发表时间：
2003
期刊：
--
影响因子：
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通讯作者：
S. Tiwari;J. Kuhnert
S. Tiwari;J. Kuhnert
中科院分区：
其他
文献类型：
--
作者：
S. Tiwari;J. Kuhnert

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将拉格朗日粒子格式应用于不可压缩Navier-Stokes方程的投影方法。利用加权最小二乘法求出空间导数的近似。利用最小二乘法对压力泊松方程进行局部迭代求解。对二维情况进行了数值试验。介绍了库埃特流、泊塞勒流和驱动腔流。得到了静、静两种情况下的数值解，并与通道流动的解析解进行了比较。最后，考虑了单位方阵内受驱动的空腔流动，并与有限元法的平稳解进行了比较。
A Lagrangian particle scheme is applied to the projection method for the incompressible Navier-Stokes equations. The approximation of spatial derivatives is obtained by the weighted least squares method. The pressure Poisson equation is solved by a local iterative procedure with the help of the least squares method. Numerical tests are performed for two dimensional cases. The Couette flow, Poisseulle flow and the driven cavity flow are presented. The numerical solutions are obtained for stationary as well as instationary cases and are compared with the analyatical solutions for channel flows. Finally, the driven cavity flow in a unit square is considered and the stationary solution obtained from this scheme is compared with that from the finite element method!