A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions

Jan Nordström, Andrew R. Winters

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We derive boundary conditions and estimates based on the energy and entropy analysis of systems of the nonlinear shallow water equations in two spatial dimensions. It is shown that the energy method provides more details, but is fully consistent with the entropy analysis. The details brought forward by the nonlinear energy analysis allow us to pinpoint where the difference between the linear and nonlinear analysis originate. We find that the result from the linear analysis does not necessarily hold in the nonlinear case. The nonlinear analysis leads in general to a different minimal number of boundary conditions compared with the linear analysis. In particular, and contrary to the linear case, the magnitude of the flow does not influence the number of required boundary conditions.

Original languageEnglish
Article number111254
JournalJournal of Computational Physics
Volume463
DOIs
Publication statusPublished - 15 Aug 2022

Keywords

  • Boundary conditions
  • Energy stability
  • Entropy stability
  • Nonlinear hyperbolic equations
  • Shallow water equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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