Meshfree Stabilized Collocation Method for the Transient Heat Conduction Problems

Abstract

The stabilized collocation method (SCM) based on reproducing kernel (RK) approximation is demonstrated to solve the transient heat conduction problems. SCM is a truly mesh-free method (MFM) that can perform accurate integration in the subdomains with high efficiency. RK approximation satisfying high-order consistency conditions and performing subdomain integration on the strong form ensures high-order consistency of integration, which enhances the accuracy and stability of the algorithm. Because the corresponding integration subdomain depends solely on the particle positions and remains independent of the problem’s domain shape and deformation, it can be employed for problems in any domain shape. To deal with the transient heat conduction problems precisely and stably, SCM is first used and the numerical examples of one-, two- and three-dimensional transient heat conduction problems exhibit the high accuracy and good stability of the presented method.