Application of Meshless Local Petrov-Galerkin (MLPG) Approach to Simulation of Incompressible Flow

Abstract

ABSTRACT The meshless local Petrov-Galerkin (MLPG) method is an effective local mesh-free method for solving partial differential equations using moving least-squares (MLS) approximation and local weak form. In this article, the MLPG formulation is used with some modifications to simulate the incompressible flow within an irregular domain with scattered nodal distribution. The governing equations are taken in terms of vorticity–stream functions. It is found that the results agree very well with the available results in the literature. The numerical examples show that the MLPG method is a very promising method for computational fluid dynamics (CFD) problems, as the requirement for a global mesh is removed.