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


Department of Civil Engineering,Iran University of Science and Technology


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.