A staggered-grid multilevel incomplete LU for steady incompressible flows

TL;DR

This paper introduces a parallel multilevel incomplete LU preconditioner for 3D stationary incompressible Navier-Stokes equations, improving robustness and efficiency for solving linear systems in fluid flow simulations.

Contribution

It develops a novel staggered-grid multilevel incomplete LU method based on and extending the two-level scheme by Wubs and Thies, with improvements for better robustness.

Findings

Demonstrates superior robustness over SIMPLE-type preconditioner.

Effective in solving 3D lid-driven cavity benchmark problems.

Shows potential for use in complex flow simulations requiring robust linear solvers.

Abstract

Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this paper, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner.