Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms

N. A. Matskevich, L. B. Chubarov

Research output: Contribution to journalArticlepeer-review

Abstract

We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth’s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

Original languageEnglish
Pages (from-to)234-250
Number of pages17
JournalNumerical Analysis and Applications
Volume12
Issue number3
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • bottom friction
  • Coriolis force
  • exact solutions
  • free surface
  • large-particle method
  • mathematical modeling
  • numerical algorithms
  • ordinary differential equations
  • shallow water equations
  • verification
  • wave run-up

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