Open Access

ARTICLE

MLPG6 for the Solution of Incompressible Flow Equations

V. C. Loukopoulos¹, G. C. Bourantas²

1 Department of Physics, University of Patras, Patras, 26500, Rion, Greece
2 King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia

Computer Modeling in Engineering & Sciences 2012, 88(6), 531-558. https://doi.org/10.3970/cmes.2012.088.531

Abstract

Meshless Local Petrov-Galerkin (MLPG) approach is used for the solution of the Navier-Stokes and energy equations. More specific as a special case we apply the MLPG6 approach. In the MLPG6 method, the test function is chosen to be the same as the trial function (Galerkin method). The MLPG local weak form is written over a local sub-domain which is completely independent from the trial or test functions. The sizes of nodal trial and test function domains, as well as the size of the local sub-domain over which the local weak-form is considered, can be arbitrary. This may lead to either symmetric or unsymmetric stiffness matrices, which are sparse and well-conditioned. Additionally, the effect of the support domain (SD) and local sub-domain (LSD) sizes on the MLPG approach are examined. Forced convection and natural (or free) convection flows, with essential and natural boundary conditions, are studied numerically with MLPG6 for regular and irregular spatial domains and the following characteristics of the method are demonstrated: i) truly mesh free implementation, without the need of a background mesh; ii) simplicity of the method using lower-order polynomial basis and smaller support sizes; and iii) accuracy and computational efficiency.

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Keywords

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