改进节点积分的无单元Galerkin法及其在流动问题中的应用

无单元Galerkin法需要在背景网格上积分,计算量大,且在求解对流占优问题时会出现非物理的数值伪振荡现象。为此,基于局部Taylor展开思想,采用节点处的局部Taylor展开计算积分,建立了局部Taylor展开积分无单元Galerkin法。该方法同时解决了标准的无单元Galerkin法计算量大和对流占优时会出现数值伪振荡的问题。一维定常对流扩散方程和二维Burgers方程的求解说明了该方法的有效性,且计算效率远高于无单元Galerkin法。

An improved nodal integration Element-Free Galerkin method and its application in flow problems

Element-Free Galerkin(EFG) method is intensive computation due to the requirement of background cells quadrature,and may appear non-physical oscillations in solving convection dominated problems.To solve these problems,a local Taylor expansion integration Element-Free Galerkin(LTEI-EFG) method is proposed in this paper,which based on the idea of integration for local Taylor expansion.This method can not only save computation cost but also eliminate non-physical oscillation in solving convection dominated problem.Numerical examples of one-dimensional convection diffusion equation and two-dimensional Burgers’ equation show that the LTEI-EFG method is accurate and much more efficient than EFG method.