Solution of Convection-Dominated Problems on Irregular Meshes by Collocated Discrete Least Squares Mesh-Less (CDLSM) Method

Abstract

In this paper, a study is performed on the e ect of irregularity of domain discretization on the performance of the CDLSM method for the solution of convection-dominated problems. The method is based on minimizing a least squares functional of the residuals of the governing di erential equations and its boundary conditions over a set of collocation points. Four convection-dominated benchmark examples are solved using CDLSM method on three di erent sets of nodal distribution with di erent levels of irregularity and the results are presented. These experiments show that CDLSM method is capable of producing stable and accurate results for hyperbolic problems with shocked or high gradient solutions even on highly irregular mesh of nodes. Mesh-less methods as alternative numerical approaches to eliminate the well-known drawbacks of mesh-based methods have attracted much attention in the past decade due to their exibility and their potentiality in negating the need for the human-labor intensive process of constructing geometric meshes in a domain. Exploiting this ability, however, requires that the method could solve the problem under consideration on unstructured distribution of nodes. This is particularly important when a re nement strategy is to be used to improve the performances of these methods.