Preconditioning a NewtonKrylov solver for allspeed melt pool flow physics
Abstract
n this paper, we introduce a multigrid blockbased preconditioner for solving linear systems arising from a Discontinuous Galerkin discretization of the allspeed NavierStokes equations with phase change. The equations are discretized in conservative form with a reconstructed Discontinuous Galerkin (rDG) method and integrated with fullyimplicit time discretization schemes. To robustly converge the numerically stiff systems, we use the NewtonKrylov framework with a primitivevariable formulation (pressure, velocity, and temperature), which is better conditioned than the conservativevariable form at lowMach number. In the limit of large acoustic CFL number and viscous Fourier number, there is a strong coupling between the velocitypressure system and the linear systems become nondiagonally dominant. To effectively solve these illconditioned systems, an approximate block factorization preconditioner is developed, which uses the Schur complement to reduce a 3 x 3 block system into a sequence of two 2 x 2 block systems: velocitypressure,v P, and velocitytemperature, v T. We compare the performance of the v Pv T Schur complement preconditioner to classic preconditioning strategies: monolithic algebraic multigrid (AMG), elementblock SOR, and primitive variable block GaussSeidel. The performance of the preconditioned solver is investigated in the limit of large CFL and Fourier numbers for lowMach liddriven cavity flow, RayleighBénard meltmore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Univ. of California, Davis, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1577941
 Report Number(s):
 LLNLJRNL745515
Journal ID: ISSN 00219991; 900481
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 397; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Block preconditioning; Physicsbased preconditioning; Fully implicit; Newton Krylov; All speed fluid dynamics; Reconstructed discontinuous Galerkin method
Citation Formats
Weston, Brian, Nourgaliev, Robert, Delplanque, Jean Pierre, and Barker, Andrew T. Preconditioning a NewtonKrylov solver for allspeed melt pool flow physics. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.07.045.
Weston, Brian, Nourgaliev, Robert, Delplanque, Jean Pierre, & Barker, Andrew T. Preconditioning a NewtonKrylov solver for allspeed melt pool flow physics. United States. doi:10.1016/j.jcp.2019.07.045.
Weston, Brian, Nourgaliev, Robert, Delplanque, Jean Pierre, and Barker, Andrew T. Thu .
"Preconditioning a NewtonKrylov solver for allspeed melt pool flow physics". United States. doi:10.1016/j.jcp.2019.07.045. https://www.osti.gov/servlets/purl/1577941.
@article{osti_1577941,
title = {Preconditioning a NewtonKrylov solver for allspeed melt pool flow physics},
author = {Weston, Brian and Nourgaliev, Robert and Delplanque, Jean Pierre and Barker, Andrew T.},
abstractNote = {n this paper, we introduce a multigrid blockbased preconditioner for solving linear systems arising from a Discontinuous Galerkin discretization of the allspeed NavierStokes equations with phase change. The equations are discretized in conservative form with a reconstructed Discontinuous Galerkin (rDG) method and integrated with fullyimplicit time discretization schemes. To robustly converge the numerically stiff systems, we use the NewtonKrylov framework with a primitivevariable formulation (pressure, velocity, and temperature), which is better conditioned than the conservativevariable form at lowMach number. In the limit of large acoustic CFL number and viscous Fourier number, there is a strong coupling between the velocitypressure system and the linear systems become nondiagonally dominant. To effectively solve these illconditioned systems, an approximate block factorization preconditioner is developed, which uses the Schur complement to reduce a 3 x 3 block system into a sequence of two 2 x 2 block systems: velocitypressure,vP, and velocitytemperature, vT. We compare the performance of the vPvT Schur complement preconditioner to classic preconditioning strategies: monolithic algebraic multigrid (AMG), elementblock SOR, and primitive variable block GaussSeidel. The performance of the preconditioned solver is investigated in the limit of large CFL and Fourier numbers for lowMach liddriven cavity flow, RayleighBénard melt convection, compressible internally heated convection, and 3D laserinduced melt pool flow. Here, numerical results demonstrate that the vPvT Schur complement preconditioned solver scales well both algorithmically and in parallel, and is robust for highly illconditioned systems, for all tested rDG discretization schemes (up to 4thorder).},
doi = {10.1016/j.jcp.2019.07.045},
journal = {Journal of Computational Physics},
issn = {00219991},
number = C,
volume = 397,
place = {United States},
year = {2019},
month = {7}
}