Numerical Simulation of Nonlinear Flow Based on Element-Free Galerkin Method

基于无网格伽辽金法的非线性流动数值模拟

Key Laboratory for Unmanned Underwater Vehicle, School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

^* E-mail: panguang@nwpu.edu.cn

Received: 12 March 2018

Abstract

This paper focuses on the studying on some flow problems of nonlinear based on the Element Free Galerkin method. First the Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction respectively. And the penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. Then the flow problem of stationary nonlinear is studied. The flow problem of water in the rectangular domain squeezed by the two plates distributed above and below the calculated domain is studied with the method of EFG. The accuracy of the direct linear alternating interation method is shown by contrast with the analytical solution. Then the flow problem of unsteady nonlinear is studied. The θ-weighted method is used to discrete the time term of the N-S equation and the unsteady nonlinear solution matrix of EFG is established. The flow problem of flow around the square column is studied with the method of EFG and the flows under a series of low Reynolds are stimulated.

摘要

基于无网格伽辽金方法针对典型的非线性流动问题进行数值研究，对Navier-Stokes方程使用Galerkin方法离散，方程中的惯性项分别采取速度项提出法和直接推导法进行离散，使用罚函数法施加压力和速度边界条件，建立了基于EFG法的二维N-S方程的离散形式。针对定常非线性流动问题，对矩形域上下平板相向运动流动进行数值模拟，结果表明该方法求解精度比较高，计算误差不超过3.66%；针对非定常非线性流动问题，采取θ加权法对N-S方程中的时间项进行离散，建立了EFG法非定常求解方程。以方柱绕流问题为例，证明了文中所建立的非定常算法的精度及收敛性。