基于无网格伽辽金法的非线性流动数值模拟  

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

作　　者：孟俊男 潘光[1] 曹永辉[1] 李林丰 黎针岑 周冰 MENG Junnan;PAN Guang;CAO Yonghui;LI Linfeng;LI Zhencen;ZHOU Bing(Key Laboratory for Unmanned Underwater Vehicle, School of Marine Science and Technology, Northwestern Polytechnical University, Xi′an 710072, China)

机构地区：[1]西北工业大学航海学院西北工业大学无人水下运载技术重点实验室,陕西西安710072

出　　处：《西北工业大学学报》2019年第1期70-79,共10页Journal of Northwestern Polytechnical University

基　　金：国家重点研发计划(2016YFC0301300);国家自然科学基金(11502210;51709229;5149170)资助

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。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.

关 键 词：无网格伽辽金法 罚函数法 NAVIER-STOKES方程 直接线性交替迭代法 

分 类 号：O357.1[理学—流体力学]