Sanyasiraju VSS Yedida

In this paper, two radial basis function (RBF)-based local grid-free upwind schemes have been discussed for convection-diffusion equations. The schemes have been validated over some convection-diffusion problems with sharp boundary layers. It is found that one of the upwind schemes realizes the boundary layers more accurately than the rest. Comparisons with the analytical solutions demonstrate that the local RBF grid-free upwind schemes based on the exact velocity direction are stable and produce accurate results on domains discretized even with scattered distribution of nodal points. Copyright © 2009 John Wiley & Sons, Ltd.

A 'local' radial basic function (RBF) based gridfree scheme has been developed to solve unsteady, incompressible Navier-Stokes equations in primitive variables. The velocity-pressure decoupling is obtained by making use of a fractional step algorithm. The scheme is validated over a variety of benchmark problems and found a very good agreement with the existing results. Comparisons with the benchmark solutions show that the developed local RBF gridfree scheme is stable and produces accurate results on domains discretized even with non-uniform distribution of nodal points. © 2008 Elsevier Inc. All rights reserved.

This paper describes the application of radial basis function (RBF) based finite difference type scheme (RBF-FD) for solving steady convection-diffusion equations. Numerical studies are made using multiquadric (MQ) RBF. By varying the shape parameter in MQ, the accuracy of the solution is seen to be highly improved for large values of Reynolds' numbers. The developed scheme has been compared with the corresponding finite difference scheme and found that the solutions obtained using the former are non-oscillatory. Copyright © 2007 John Wiley & Sons, Ltd.