Two-step Taylor-characteristic-based MLPG method for fluid flow and heat transfer applications

A stabilized two-step Taylor-characteristic-based meshless local Petrov–Galerkin (2S-TCBMLPG) method is proposed to solve laminar fluid flow and heat transfer problems using the primitive variables form of the Navier–Stokes equations. In this method, a two-step Taylor-characteristic-based scheme is employed in order to obtain stable solutions for the field variables at high Peclet and Reynolds numbers. The test function in the weighted-residual forms of the governing equations is chosen to be unity, and the field variables are approximated using the moving least-squares (MLS) interpolations. Five test cases, namely, Poiseuille flow between parallel plates, lid-driven cavity flow, Couette flow between two eccentric cylinders, non-isothermal flow past a bundle of tubes, and mixed convection heat transfer in a differentially-heated square cavity, are solved in order to examine the effectiveness of the proposed method. Very good agreements exist between the results obtained using the proposed meshless method with those obtained using the conventional methods for the considered test cases. Close agreements among the appropriate results demonstrates a step forward toward further development of stabilized algorithms for solving the primitive variables form of the Navier–Stokes equations by the MLPG method.