Meshless Local Petrov-Galerkin Method- Steady, Non-Isothermal Fluid Flow Applications

The meshless local Petrov-Galerkin method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for a driven cavity flow for moderate Reynolds numbers using different point distributions. The L2-norm of the error as a function of the size of the control volumes is presented for different cases; and the rate of convergence of the method is established. The results of this study show that the proposed method is applicable in solving a variety of non-isothermal fluid flow problems.