Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

Franciolini, Matteo; Fidkowski, Krzysztof J.; Crivellini, Andrea

doi:10.1016/j.compfluid.2020.104542

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

Journal Article · Sat Apr 18 00:00:00 EDT 2020 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2020.104542· OSTI ID:1802092

Franciolini, Matteo ^[1]; Fidkowski, Krzysztof J. ^[2]; Crivellini, Andrea ^[3]

Univ. of Michigan, Ann Arbor, MI (United States); Polytechnic Univ. of Marche, Ancona (Italy); NASA Ames Research Center (ARC), Moffett Field, Mountain View, CA (United States); OSTI
Univ. of Michigan, Ann Arbor, MI (United States)
Polytechnic Univ. of Marche, Ancona (Italy)

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Finally, additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0010341

OSTI ID:: 1802092

Alternate ID(s):: OSTI ID: 1616207

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Journal Issue: C Vol. 203; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
DG
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computer science
high-order
mechanics
p-multigrid
parallel efficiency
preconditioners

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

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