Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

Pazner, Will; Persson, Per -Olof

doi:10.1016/j.jcp.2017.01.050

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

Journal Article · Thu Jan 26 23:00:00 EST 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.01.050· OSTI ID:1543560

^[1]; Persson, Per -Olof ^[2]

Brown Univ., Providence, RI (United States)
Univ. of California, Berkeley, CA (United States)

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge–Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming the resulting linear system of equations, one can obtain a method which is much less computationally expensive than the untransformed formulation, and which compares competitively with other time-integration schemes, such as diagonally implicit Runge–Kutta (DIRK) methods. We develop and test several ILU-based preconditioners effective for these large systems. We additionally employ a parallel-in-time strategy to compute the Runge–Kutta stages simultaneously. Numerical experiments are performed on the Navier–Stokes equations using Euler vortex and 2D and 3D NACA airfoil test cases in serial and in parallel settings. In conclusion, the fully implicit Radau IIA Runge–Kutta methods compare favorably with equal-order DIRK methods in terms of accuracy, number of GMRES iterations, number of matrix–vector multiplications, and wall-clock time, for a wide range of time steps.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1543560

Alternate ID(s):: OSTI ID: 1398120

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 335; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method Pazner, Will; Persson, Per-Olof Journal of Scientific Computing, Vol. 80, Issue 1 https://doi.org/10.1007/s10915-019-00942-1	journal	March 2019
Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations Jeon, Yonghyeon; Bak, Soyoon; Bu, Sunyoung Mathematics, Vol. 7, Issue 12 https://doi.org/10.3390/math7121158	journal	December 2019
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Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method Romor, Francesco; Tezzele, Marco; Lario, Andrea arXiv https://doi.org/10.48550/arxiv.2008.12083	text	January 2020
Evaluation of Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations Jameson, Antony Journal of Scientific Computing, Vol. 73, Issue 2-3 https://doi.org/10.1007/s10915-017-0476-x	journal	July 2017
Analysis and entropy stability of the line-based discontinuous Galerkin method Pazner, Will; Persson, Per-Olof arXiv https://doi.org/10.48550/arxiv.1809.09815	text	January 2018

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97 MATHEMATICS AND COMPUTING
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Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

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