Predictor-Corrector Preconditioners for Newton-Krylov Solvers in Fluid Problems

TL;DR

This paper introduces a predictor-corrector preconditioning method for Newton-Krylov solvers in fluid problems, enabling easier integration with existing semi-implicit codes to improve solver efficiency.

Contribution

It presents a novel implementation of preconditioning that reuses existing semi-implicit schemes within a predictor-corrector framework for fully implicit nonlinear problems.

Findings

Effective preconditioning for nonlinear diffusion and flow problems.

Minimal code modifications needed for implementation.

Improved solver performance demonstrated on benchmark problems.

Abstract

We propose an alternative implementation of preconditioning techniques for the solution of non-linear problems. Within the framework of Newton-Krylov methods, preconditioning techniques are needed to improve the performance of the solvers. We propose a different implementation approach to re-utilize existing semi-implicit methods to precondition fully implicit non-linear schemes. We propose a predictor-corrector approach where the fully non-linear scheme is the corrector and the pre-existing semi-implicit scheme is the predictor. The advantage of the proposed approach is that it allows to retrofit existing codes, with only minor modifications, in particular avoiding the need to reformulate existing methods in terms of variations, as required instead by other approaches now currently used. To test the performance of the approach we consider a non-linear diffusion problem and the standard driven cavity problem for incompressible flows.