Speaker
Daniel Fortunato, Flatiron Institute
Abstract
Consider the flow of a dense suspension of rigid bodies in a Stokesian fluid. Such flows are difficult to compute numerically due to the presence of close-to-touching interactions between the bodies, which may require a large number of unknowns to discretize, a large number of GMRES iterations to solve, and an extremely small time step. A common way of dealing with these difficulties is to introduce an artificial repulsion force between the bodies to prevent them from getting too close, but this is non-physical and may fundamentally alter the results of a simulation.
For suspensions of identical discs in 2D, we present a fast and accurate boundary integral method that mitigates these challenges without introducing artificial forces. Through precomputation, compression, and interpolation of the close-to-touching part of the interaction operator, our method—termed “”interpolated compressed inverse preconditioning””—efficiently handles close-to-touching interactions down to distances of $10^{-10}$ with only a coarse discretization of the boundary. Additionally, we present a preconditioner that significantly reduces the number of GMRES iterations required to solve the Stokes mobility problem at each time step by effectively reusing the Krylov subspace from previous time steps. Coupled with high-order, adaptive time-stepping using spectral deferred correction, we are able to take larger time steps, mitigating the temporal stiffness resulting from close-to-touching interactions.