Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

Brachet, Matthieu; Debreu, Laurent; Eldred, Christopher

doi:10.1016/j.apnum.2022.05.006

Title: Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

Journal Article · 20 May 2022 · Applied Numerical Mathematics

DOI:https://doi.org/10.1016/j.apnum.2022.05.006· OSTI ID:1872031

; Debreu, Laurent ^[1];

^[2]

University of Grenoble Alpes, Grenoble (France)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

We report the time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); French National Research Agency; European Union’s Horizon 2020

Grant/Contract Number:: NA0003525; ANR-18-CE46-0008; 821926

OSTI ID:: 1872031

Report Number(s):: SAND2022-6879J; 706614

Journal Information:: Applied Numerical Mathematics, Vol. 180; ISSN 0168-9274

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
shallow water equations
time stepping
exponential integrators
finite differences
Krylov methods

Title: Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

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