Simulation of solid body motion in a Newtonian fluid using a vorticity-based pseudo-spectral immersed boundary method augmented by the radial basis functions

Abstract

The moving boundary conditions are implemented into the Fourier pseudo-spectral solution of the two-dimensional incompressible Navier–Stokes equations (NSE) in the vorticity-velocity form, using the radial basis functions (RBF). Without explicit definition of an external forcing function, the desired immersed boundary conditions are imposed by direct modification of the convection and diffusion terms. At the beginning of each time-step the solenoidal velocities, satisfying the desired moving boundary conditions, along with a modified vorticity are obtained and used in modification of the convection and diffusion terms of the vorticity evolution equation. Time integration is performed by the explicit fourth-order Runge–Kutta method and the boundary conditions are set at the beginning of each sub-step. The method is applied to a couple of moving boundary problems and more than second-order of accuracy in space is demonstrated for the Reynolds numbers up to Re = 550. Moreover, performance of the method is shown in comparison with the classical Fourier pseudo-spectral method.