Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Jacobian-free multigrid preconditioner for DG-SEM for atmospheric flow

Birken, Philipp LU ; Dedner, Andreas ; Kasimir, Johannes LU and Klöfkorn, Robert LU orcid (2024) 9th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2024
Abstract

High fidelity fluid simulations have important applications in science and engineering, examples include numerical weather prediction and simulation aided design. Discontinuous Galerkin (DG) methods are promising high order discretizations for simulating unsteady compressible fluid flow in three dimensions. Systems arising from such discretizations are often stiff and require implicit time integration. This motivates the study of fast, parallel, low-memory solvers for the resulting algebraic equation systems. For (low order) finite volume (FV) discretizations, multigrid (MG) methods have been successfully applied to steady and unsteady fluid flows. But for high order DG methods applied to flow problems, such solvers are currently... (More)

High fidelity fluid simulations have important applications in science and engineering, examples include numerical weather prediction and simulation aided design. Discontinuous Galerkin (DG) methods are promising high order discretizations for simulating unsteady compressible fluid flow in three dimensions. Systems arising from such discretizations are often stiff and require implicit time integration. This motivates the study of fast, parallel, low-memory solvers for the resulting algebraic equation systems. For (low order) finite volume (FV) discretizations, multigrid (MG) methods have been successfully applied to steady and unsteady fluid flows. But for high order DG methods applied to flow problems, such solvers are currently lacking. The lack of efficient solvers suitable for contemporary computer architectures inhibits wider adoption of DG methods. This motivates our research to construct a Jacobian-free preconditioner for high order DG discretizations. The preconditioner is based on a multigrid method constructed for a low order finite volume discretization defined on a subgrid of the DG mesh. Numerical experiments on atmospheric flow problems show the benefit of this approach.

(Less)
Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to conference
publication status
published
subject
keywords
atmospheric, DGSEM, DUNE, DUNE-FEM, FV, implicit, matrix-free, multigrid, preconditioner
conference name
9th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2024
conference location
Lisbon, Portugal
conference dates
2024-06-03 - 2024-06-07
external identifiers
  • scopus:105012422493
project
Partial differential equations
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2024, Scipedia S.L., All rights reserved.
id
cbb65663-0624-4ba1-b5ca-3b1ab9ccfa60
date added to LUP
2026-02-05 13:28:58
date last changed
2026-02-05 13:30:06
@misc{cbb65663-0624-4ba1-b5ca-3b1ab9ccfa60,
  abstract     = {{<p>High fidelity fluid simulations have important applications in science and engineering, examples include numerical weather prediction and simulation aided design. Discontinuous Galerkin (DG) methods are promising high order discretizations for simulating unsteady compressible fluid flow in three dimensions. Systems arising from such discretizations are often stiff and require implicit time integration. This motivates the study of fast, parallel, low-memory solvers for the resulting algebraic equation systems. For (low order) finite volume (FV) discretizations, multigrid (MG) methods have been successfully applied to steady and unsteady fluid flows. But for high order DG methods applied to flow problems, such solvers are currently lacking. The lack of efficient solvers suitable for contemporary computer architectures inhibits wider adoption of DG methods. This motivates our research to construct a Jacobian-free preconditioner for high order DG discretizations. The preconditioner is based on a multigrid method constructed for a low order finite volume discretization defined on a subgrid of the DG mesh. Numerical experiments on atmospheric flow problems show the benefit of this approach.</p>}},
  author       = {{Birken, Philipp and Dedner, Andreas and Kasimir, Johannes and Klöfkorn, Robert}},
  keywords     = {{atmospheric; DGSEM; DUNE; DUNE-FEM; FV; implicit; matrix-free; multigrid; preconditioner}},
  language     = {{eng}},
  title        = {{Jacobian-free multigrid preconditioner for DG-SEM for atmospheric flow}},
  year         = {{2024}},
}