Block preconditioning for saddle point systems with indefinite (1, 1) block
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
On the accuracy of the rotation form in simulations of the Navier-Stokes equations
Journal of Computational Physics
Short Note: New connections between finite element formulations of the Navier-Stokes equations
Journal of Computational Physics
A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations
Applied Numerical Mathematics
SIAM Journal on Matrix Analysis and Applications
A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations
Journal of Computational Physics
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We consider preconditioned iterative methods applied to discretizations of the linearized Navier-Stokes equations in two- and three-dimensional bounded domains. Both unsteady and steady flows are considered. The equations are linearized by Picard iteration. We make use of the rotation form of the momentum equations, which has several advantages from the linear algebra point of view. We focus on a preconditioning technique based on the Hermitian/skew-Hermitian splitting of the resulting nonsymmetric saddle point matrix. We show that this technique can be implemented efficiently when the rotation form is used. We study the performance of the solvers as a function of mesh size, Reynolds number, time step, and algorithm parameters. Our results indicate that fast convergence independent of problem parameters is achieved in many cases. The preconditioner appears to be especially attractive in the case of low viscosity and for unsteady problems.