Preconditioning for Linear Systems Arising from IgA Discretized Incompressible Navier-Stokes Equations

摘要

We deal with efficient techniques for numerical simulation of the incompressible fluid flow based on the Navier-Stokes equations discretized using the isogeometric analysis approach. Typically, the most time-consuming part of the simulation is solving the large saddle-point type linear systems arising from the discretization. These systems can be efficiently solved by Krylov subspace methods, but the choice of the preconditioner is crucial. In our study we test several preconditioners developed for the incompressible Navier-Stokes equations discretized by a finite element method, which can be found in the literature. We study their efficiency for the linear systems arising from the IgA discretization, where the matrix is usually less sparse compared to those from finite elements. Our aim is to develop a fast solver for a specific problem of flow in a water turbine. It brings several complications like periodic boundary conditions at nonparallel boundaries and computation in a rotating frame of reference. This makes the system matrix even less sparse with a more complicated sparsity pattern.