An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows

We formulate the penalization problem inside a vortex particle-mesh method as a linear system. This system has to be solved at every wall boundary condition enforcement within a time step. Furthermore, because the underlying problem is a Poisson problem, the solution of this linear system is computationally expensive. For its solution, we here use a recycling iterative solver, rBiCGStab, in order to reduce the number of iterations and therefore decrease the computational cost of the penalization step. For the recycled subspace, we use the orthonormalized previous solutions as only the right hand side changes from the solution at one time to the next. This method is validated against benchmark results: the impulsively started cylinder, with validation at low Reynolds number (Re=550) and computational savings assessments at moderate Reynolds number (Re=9500); then on a flat plate benchmark (Re=1000). By improving the convergence behavior, the approach greatly reduces the computational cost of iterative penalization, at a moderate cost in memory overhead.