A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models

Journal Article · 15 April 2024 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2024.116975 · OSTI ID:2376290

Connors, Jeffrey M. ^[1]; Owen, Justin  ^[2]; Kuberry, Paul Allen ^[2]; Bochev, Pavel  ^[2]

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1. Univ. of Connecticut, Storrs, CT (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: NA0003525
• OSTI ID: 2376290
• Report Number(s): SAND--2024-07807J
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: 116975 Vol. 426; ISSN 0045-7825
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English