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

摘要

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 over-come this difficulty,the natural neighbour interpolation was employed instead of the moving least squares approxi-mation 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.%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。