Stabilized MLPG-VF-based method with CBS scheme for laminar flow at high Reynolds and Rayleigh numbers

In the present work, the meshless local Petrov-Galerkin vorticity-stream function (MLPG-VF) method is extended to solve two-dimensional laminar fluid flow and heat transfer equations for high Reynolds and Rayleigh numbers. The characteristic-based split (CBS) scheme which uses unity test function is employed for discretization, and the moving least square (MLS) method is used for interpolation of the field variables. Four test cases are considered to evaluate the present algorithm, namely lid-driven cavity flow with Reynolds numbers up to and including 104, flow over a backward-facing step at Reynolds number of 800, natural convection in a square cavity for Rayleigh numbers up to and including 108, and natural convection in a concentric square outer cylinder and circular inner cylinder annulus for Rayleigh numbers up to and including 10(7). In each case, the result obtained using the proposed algorithm is either compared with the results from the literatures or with those obtained using conventional numerical techniques. The present algorithm shows stable results at lower or equal computational cost compared to the other upwinding schemes usually employed in the MLPG method. Close agreements between the compared results as well as higher accuracy of the proposed method show the ability of this stabilized algorithm.