A Hybrid Multi-Region BEM / LBIE-RBF Velocity-Vorticity Scheme for the Two-Dimensional Navier-Stokes Equations
E.J. Sellountos; and A. Sequeira

doi:10.3970/cmes.2008.023.127
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 23, No. 2, pp. 127-148, 2008
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Keywords Local Boundary Integral Equation (LBIE), Boundary Elements Method (BEM) Navier-Stokes, Radial Basis Functions (RBF), RBF discontinuity, velocity-vorticity.
Abstract In this work a hybrid velocity-vorticity scheme for the solution of the 2D Navier-Stokes equations is presented. The multi-region Local Boundary Integral Equation (LBIE) combined with Radial Basis Functions (RBF) interpolation is used for the solution of the kinematics and the multi-region BEM for the solution of the transport kinetics. The final system of equations is in band form for both methods. The issue of RBF discontinuities is resolved by constructing the RBF matrix locally in every region. The kinematics integral equation is used in three different forms, for coupling the velocity field on the boundary, on interior points and on points belonging to interfaces. The convective velocity is decomposed into a constant and a variable part, and the constant part is a term of the parabolic-diffusion fundamental solution resulting on a very effective upwind technique for the transport kinetics. The complete absence of the derivatives and the same nodal discretization for both equations give a very strong coupling between the kinematics and the kinetics.
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