Radial basis function solution of the lid-driven cavity problem using the stream function formulation

Abstract

An RBF meshless method for the solution of the steady incompressible Navier-Stokes equations using the streamfunction-vorticity formulation is presented. This approach reduces the problem to the solution of a nonlinear biharmonic equation describing the stream function. The method is used to compute the solution of the lid-driven cavity flow problem for different Reynolds numbers. For the Stokes problem (Re = 0), the accuracy deteriorates in the neighborhood of the singularities in the two upper corners. Enlarging the space spanned by the RBF basis functions with additional functions that capture the singular behavior of the solution restores the spectral convergence of the RBF method. © Civil-Comp Press, 2009.