The Influence Of RBF Differentiation On The Accuracy Of The Alternative LBIE Method For Solving The Navier-Stokes Equations
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E. H. Ooi & V. Popov
In this paper, the local boundary integral equation (LBIE) method employing the simplified approach for imposing the boundary conditions is used to solve the lid driven cavity problem described by the velocity-vorticity formulations of the Navier-Stokes equations. The objective of this study is to investigate how the differentiation of the radial basis functions carried out to approximate the spatial gradients in the simplified approach affects the accuracy of the numerical solutions in problems where knowledge of the spatial gradients is of significance. The numerical results were compared with benchmark solutions and with those obtained using the radial basis integral equation method; an integral equation based meshless method that does not involve the differentiation of the RBF to approximate the spatial gradients. Keywords: velocity-vorticity formulation, radial basis functions, meshless methods, Navier-Stokes equations, integral equations.
velocity-vorticity formulation, radial basis functions, meshless methods, Navier-Stokes equations, integral equations