A local Petrov-Galerkin approach with moving Kriging interpolation for solving transient heat conduction problems

摘要

A meshless Local Petrov-Galerkin approach based on the moving Kriging interpolation (Local Kriging method; LoKriging hereafter) is employed for solving partial different equations that govern the heat flow in two- and three-dimensional spaces. The method is developed based on the moving Kriging interpolation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for domain integral in symmetric weak form. As the shape functions possess the Kronecker delta function property, essential boundary conditions can be implemented without any difficulties. The traditional two-point difference method is selected for the time discretization scheme. For computation of 3D problems, a novel local sub-domain from the polyhedrons is used for evaluating the integrals. Several selected numerical examples are presented to illustrate the performance of the LoKriging method.