Fast Computation of Domain Boundary Conditions Using Splines in Penalized VIC Method

In the vortex-in-cell method combined with the penalization method, fluid particles are traced by continuously updating their positions and strengths from the grid solution. To evaluate particle velocity, the velocity field is computed by solving a Poisson equation for the vector potential, namely del(2)psi = -omega, where u = del x psi, and its computation can be greatly accelerated by the use of a fast Poisson solver. While this method offers an efficient way to simulate unsteady viscous flows, the computation of the boundary values when solving the Poisson equation can become a computation time bottleneck. Although adopting the fast multipole method can lead to saving further computation time, its disadvantage is that it requires complicated hierarchical data structures such as a quad-tree and oct-tree. In this paper, we introduce and assess an approximation method for specifying domain boundary values using splines. Using the proposed spline approximation method we achieve significant savings in both computation time and memory consumption.