A RBF Based Local Gridfree Scheme for Unsteady Convection-Diffusion Problems

摘要

In this work a Radial Basis Function (RBF) based local gridfree scheme has been presented for unsteady convection diffusion equations. Numerical studies have been made using multiquadric (MQ) radial function. Euler and a three stage Runge-Kutta schemes have been used for temporal discretization. The developed scheme is compared with the corresponding finite difference (FD) counterpart and found that the solutions obtained using the former are more superior. As expected, for a fixed time step and for large nodal densities, thought the Runge-Kutta scheme is able to maintain higher order of accuracy over the Euler method, the temporal discretization is independent of the improvement in the solution which in the developed scheme has been achived by optimizing the shape parameter of the RBF.