对流扩散方程的QC3无网格法

QC3 Meshless Method of Convection-diffusion Equation

对流扩散方程作为偏微分运动方程的分支,在流体力学、气体动力学等领域有着重要应用.为解决对流扩散方程难以通过解析法得到解析解的难题,采用二阶一致3点积分(Quadratically Consistent 3-Point Integration,简称QC3)提高无网格法的计算效率,通过对积分点上形函数导数的修正,改善无网格法的精度和收敛性.本文将QC3无网格法拓展到对流扩散方程问题中,时域离散采用广义特征线Galerkin法,空间离散采用QC3法.数值结果表明,应用QC3无网格法得到的对流扩散问题数值解与解析解十分接近,验证了QC3无网格法解决对流扩散问题的可行性.

The convection-diffusion equation,as a branch of the partial differential motion equation,has important applications in the fields of fluid mechanics and gas dynamics.In order to solve the problem that the convection-diffusion equation is difficult to obtain the analytical solution by the analytical method,Quadratically Consistent 3-Point Integration(QC3)is used to improve the computational efficiency of the meshless method.Correction to improve the accuracy and convergence of the meshless method.In this paper,the QC3 meshless method is extended to the convection-diffusion equation problem.The generalized characteristic line Galerkin method is used for time domain dispersion,the QC3 method is used for spatial dispersion.The numerical results show that the numerical solution and the analytical solution of the convection diffusion problem obtained by the QC3 meshless method are very close,and the feasibility of the QC3 meshless method to solve the convection diffusion problem is verified.