Direct Solution Of Navier-Stokes Equations By Radial Basis Functions

Abstract

The pressure-velocity formulation of the Navier-Stokes (N-S) equation is solved using the radial basis functions (RBF) collocation method. The non-linear collocated equations are solved using the Levenberg-Marquardt method. The primary novelty of this approach is that the N-S equation is solved directly, instead of using an iterative algorithm for the primitive variables. Two flow situations are considered: Couette flow with and without pressure gradient, and 2D laminar flow in a duct with and without flow obstruction. The approach is validated by comparing the Couette flow results with the analytical solution and the 2D results with those obtained using the well-validated CFD-ACE™ commercial package. © 2007