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

Abstract

Abstract : 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.

Keywords

• Keywords: meshless
• control volume
• Petrov-Galerkin
• stream function
• vorticity