Recycling augmented Lagrangian preconditioner in an incompressible fluid solver

Abstract

The paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for non-symmetric saddle point linear algebraic systems. The strategy is applied to solve two-dimensional incompressible fluid problems with efficiency rates independent of the Reynolds number. The solver is then tested to simulate motion of a surface fluid, an example of a 2D flow motivated by an interest in lateral fluidity of inextensible viscous membranes. Numerical examples include the Kelvin--Helmholtz instability problem posed on the sphere and on the torus. Some new eigenvalue estimates for the AL preconditioner are derived.

15 pages, 5 figures, 3 tables

References in corpus (3)

• A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
• An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow
• Error analysis of higher order trace finite element methods for the surface Stokes equations

Cited by in corpus (2)

• A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow
• Uniform block-diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes equations and the linear elasticity equations