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The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations

H. Lin, S.N. Atluri1
Center for Aerospace Research and Education, 7704 Boelter Hall, University of California, Los Angeles, CA 90095-1600

Computer Modeling in Engineering & Sciences 2001, 2(2), 117-142. https://doi.org/10.3970/cmes.2001.002.117

Abstract

The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems.

Keywords

MLPG, MLS, Babus~ka-Brezzi conditions, upwinding scheme, incompressible flow, Navier-Stokes equations.

Cite This Article

Lin, H., Atluri, S. (2001). The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations. CMES-Computer Modeling in Engineering & Sciences, 2(2), 117–142.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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