基于无网格自然邻接点Petrov-Galerkin法求解带源参数瞬态热传导问题

基于无网格自然邻接点Petrov-Galerkin法,本文建立了一种求解带源参数瞬态热传导问题的新方法.为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻接点插值构造试函数.在局部多边形子域上采用局部Petrov-Galerkin方法建立瞬态热传导问题的积分弱形式.这些多边形子域可由Delaunay三角形创建.时间域则通过传统的两点差分法进行离散.最后通过算例验证了该数值算法的有效性和正确性.

Analysis of transient heat conduction problems with a source parameter based on meshless natural neighbour Petrov-Galerkin method

Based on meshless natural neighbour petrov Galerkin method, a novel meshless method was developed to solve transient heat conduction problems with a source parameter. The essential boundary conditions cannot be enforced directly when the non interpolative moving least squares (MLS) approximation is used. In order to overcome this difficulty, the natural neighbour interpolation was employed instead of the moving least squares approximation to construct trial functions. The local weak forms of the transient heat conduction problems were satisfied locally in a series of polygonal sub domains, which can be constructed easily with Delaunay tessellations. The traditional two point difference technique was selected for the time discretization scheme. A numerical example demonstrates the validity and effectiveness of the presented method.