Natural convection heat transfer at high Rayleigh numbers – Extended meshless local Petrov–Galerkin (MLPG) primitive variable method

The meshless local Petrov–Galerkin (MLPG) method is extended using an improved primitive variable formulation to solve the two-dimensional laminar natural convection equations. The extended method solves the natural convection heat transfer problems at high Rayleigh numbers. The method uses the fractional step scheme for discretization, and the moving least square (MLS) interpolation for approximation of the field variables. For the proposed technique, a weighting function of unity is used. The improved method considers the natural convection in a square cavity for up to and including Ra=108Ra=108, in a concentric square outer cylinder and circular inner cylinder annulus for up to and including Ra=107Ra=107, and in a two concentric circular cylinders annulus for up to and including Ra=105Ra=105. Comparing the results of the three test cases obtained using the present method with those obtained using the conventional methods shows very good agreement existing among the appropriate results, hence, verifying the proposed improved meshless numerical technique.