The Boundary Knot Method for Simulating Unsteady Incompressible Fluid Flow

This article presents a numerical algorithm using the Boundary knot (BK) method for the incompressible Navier-Stokes equations. To deal with time derivatives, the forward time differences are employed yielding the Poisson's equation. The BK method with the general solution of the Helmholtz equation and dual reciprocity (DR) principle is chosen to solve the Poisson's equation. In numerical examples the reverse principle with thin plate spline (TPS) radial basis functions (RBF) is used to construct the particular solution. It is found that BKM with a classical DR principle gives reasonable results with the advantage of BKM spectral convergence; however the accuracy of the solution is affected by the accuracy of particular solution created using DR.