Simulation of Solid Body Motion in a Newtonian Fluid Using a Vorticity-Based Parallel Pseudo-Spectral Immersed Boundary Method

A numerical method is presented for the simulation of the two-way interaction of a rigid body with an incompressible Newtonian fluid in a two-dimensional configuration. In this method, the moving boundaries which are modeled by the radial base functions, are implemented on a Fourier pseudo-spectral solver of the Navier-Stokes equations in the vorticity-velocity formulation. At the beginning of each time step, the conservative velocity fields, satisfying the immersed boundary conditions along with a modified vorticity field, are implemented to the pseudo-spectral solver. The Poisson equations are solved in parallel, because the velocity boundary conditions obtain independently. The dynamics of the solid body is followed by a second-order method in which the forces are obtained from a vorticity-based integral method. The time integration is performed using a third-order parallel Runge-Kutta method. Employing a parallel fast Fourier pseudo-spectral solver along with parallelization of the time integrations, in combination with modeling of the solid boundaries using the radial base functions result in a very fast and efficient solver that makes it possible real-time simulations (which requires at least 21 flow snapshots per second). The accuracy and efficiency of the method is demonstrated by solving some sample problems.