Parallel preconditioners for the unsteady Navier–Stokes equations and applications to hemodynamics simulations

We are interested in the numerical solution of the unsteady Navier–Stokes equations on large scale parallel architectures. We consider efficient preconditioners, such as the Pressure Convection-Diffusion (PCD), the Yosida preconditioner, the SIMPLE preconditioner, and the algebraic additive Schwarz preconditioner, for the linear systems arising from finite element discretizations using tetrahedral unstructured meshes and time advancing finite difference schemes. To achieve parallel efficiency, we introduce approximate versions of these preconditioners, based on their factorizations where each factor can be either inverted exactly or using an add-hoc preconditioner. We investigate their strong scalability for both classical benchmark problems and simulations relevant to hemodynamics, using up to 8192 cores.