Affordable Access

Access to the full text

On the theoretical foundation of overset grid methods for hyperbolic problems : Well-posedness and conservation

Authors
  • Kopriva, David A.
  • Nordström, Jan
  • Gassner, Gregor J.
Publication Date
Jan 01, 2022
Identifiers
DOI: 10.1016/j.jcp.2021.110732
OAI: oai:DiVA.org:liu-179908
Source
DiVA - Academic Archive On-line
Keywords
Language
English
License
Green
External links

Abstract

We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space dimension, for both scalar equations and systems of equations, the problem where one domain partially oversets another is well-posed when characteristic coupling conditions are used. If a system cannot be diagonalized, as is usually the case in multiple space dimensions, then the energy method does not give proper bounds in terms of initial and boundary data. For those problems, we propose a novel penalty approach. We show, by using a global energy that accounts for the energy in the overlap region of the domains, that under well-defined conditions on the coupling matrices the penalized overset domain problems are energy bounded, conservative, well-posed and have solutions equivalent to the original single domain problem. / <p>Funding: Simons Foundation [426393]; Vetenskapsradet, SwedenSwedish Research Council [2018-05084 VR]; Swedish e-Science Research Center (SeRC); Klaus-Tschira Stiftung; European Research CouncilEuropean Research Council (ERC)European Commission [71448]</p>

Report this publication

Statistics

Seen <100 times