Recycling augmented Lagrangian preconditioner in an incompressible fluid solver

Abstract

AbstractThe paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for nonsymmetric 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 two‐dimensional 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.