不可压缩流动的无网格Galerkin方法模拟

Characteristic-based Split Meshfree Method for Incompressible Flow Problems

Galerkin型无网格方法在求解不可压缩流动问题时,会遇到对流占优、速度-压力失耦等问题,本文基于CBS有限元方法的基本思想,提出了无网格CBS方法来解决上述问题.通过对平面Poiseuille流动的计算表明:无网格CBS方法在采用压力速度等线性基近似的情况下,当时间步长大于某个临界值时可很好地解决速度-压力失耦问题,且具有相当高的计算精度.

The standard Galerkin meshfree method for incompressible flow may suffer from numerical instabilities due to the advection-dominated and the improper coupling of velocity and pressure.In order to eliminate these instabilities,based on characteristic-based split scheme in finite element framework,an element free characteristic-based split（EFCBS） method is developed.Meanwhile the presented method is applied to planar Poiseuille flow problem;and the numerical results indicate that the EFCBS method with equal low-order basis function approximation for velocity-pressure variables under the time-step more than a critical time-step can effectively avoid the pressure oscillations;moreover the method has good accuracy.