An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids

TL;DR

This paper introduces an asynchronous incomplete LU preconditioner tailored for parallel fluid dynamics simulations on unstructured grids, demonstrating improved convergence and scalability over previous methods.

Contribution

The paper develops a block variant of asynchronous ILU preconditioning for compressible Navier-Stokes equations on unstructured grids, with extended convergence theory and practical ordering strategies.

Findings

Block variant outperforms scalar ILU in convergence and scalability.

Preconditioning effectiveness depends on grid cell ordering for viscous flows.

Experimental results confirm improved performance on steady-state test cases.

Abstract

We present a study of the effectiveness of asynchronous incomplete LU factorization preconditioners for the time-implicit solution of compressible flow problems while exploiting thread-parallelism within a compute node. A block variant of the asynchronous fine-grain parallel preconditioner adapted to a finite volume discretization of the compressible Navier-Stokes equations on unstructured grids is presented, and convergence theory is extended to the new variant. Experimental (numerical) results on the performance of these preconditioners on inviscid and viscous laminar two-dimensional steady-state test cases are reported. It is found, for these compressible flow problems, that the block variant performs much better in terms of convergence, parallel scalability and reliability than the original scalar asynchronous ILU preconditioner. For viscous flow, it is found that the ordering of unknowns may determine the success or failure of asynchronous block-ILU preconditioning, and an ordering of grid cells suitable for solving viscous problems is presented.