Meshless Local Petrov-Galerkin Method with Unity Test Function for Non-Isothermal Fluid Flow
A. Arefmanesh; M. Najafi; and H. Abdi

doi:10.3970/cmes.2008.025.009
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 25, No. 1, pp. 9-22, 2008
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Keywords meshless, control volume, Petrov-Galerkin, stream function, vorticity
Abstract The meshless local Petrov-Galerkin (MLPG) 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 different test cases. This present study considers the implementation of the method on a non-isothermal lid-driven cavity flow, the lid-driven cavity flow with an inlet and outlet, and also on the non-isothermal flow over an obstacle. Nonuniform point distribution is employed for all the test cases for the numerical simulations. The flow streamlines for each test case is depicted. The$L^{2}$-norm of the error as a function of the size of the control volumes is presented for moderate Reynolds numbers and the rate of convergence of the method is established. Close agreements of the obtained results with those of the other numerical techniques show that the proposed method is applicable in solving a variety of non-isothermal fluid flow problems.
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