不可压缩流动的无网格Galerkin方法模拟  

Characteristic-based Split Meshfree Method for Incompressible Flow Problems

作　　者：张小华[1] 

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《三峡大学学报（自然科学版）》2010年第5期32-35,共4页Journal of China Three Gorges University：Natural Sciences

基　　金：湖北省教育厅重点科研项目(D200729002);三峡大学科学基金(KJ2009B058)

摘　　要：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.

关 键 词：无网格方法 不可压缩流 CBS格式 速度-压力耦合 

分 类 号：O351.3[理学—流体力学]