Recycling augmented Lagrangian preconditioner in an incompressible fluid solver

TL;DR

This paper introduces a recycled augmented Lagrangian preconditioner for efficient 2D incompressible fluid simulations, demonstrating independence from Reynolds number and applying it to complex flow problems.

Contribution

It presents a novel reuse of matrix factorizations within AL preconditioners, improving efficiency for non-symmetric saddle point systems in fluid dynamics.

Findings

Solver efficiency independent of Reynolds number

Successful simulation of surface fluid motion

New eigenvalue estimates for AL preconditioner

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.