The DMLPG method for numerical solution of Rayleigh-Benard natural convection in porous medium

Abstract

This paper proposes the direct meshless local Petrov–Galerkin (DMLPG) type 2 method to obtain a numerical solution of the Rayleigh-Benard problem Natural convection in porous medium. In DMLPG method, the Dirac’s delta function is used as the test function and shape function is recovery directly from nodes via classical moving least squares (MLS) function. This causes the DMLPG is cheaper and simpler than classical MLPG method. Numerical results are presented in the form of isotherm, streamlines and average Nusselt number. As the results, the Benard convection multicellular patern formation can be simulated well. Comparing the numerical results obtained using the proposed method with those obtained using the conventional methods shows good agreement.