Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods

A. I. Delis*, Th Katsaounis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

A generalization and extension of a finite difference method for calculating numerical solutions of the two dimensional shallow water system of equations is investigated. A previously developed non-oscillatory relaxation scheme is generalized as to included problems with source terms in two dimensions, with emphasis given to the bed topography, resulting to a class of methods of first- and second-order in space and time. The methods are based on classical relaxation models combined with TVD Runge-Kutta time stepping mechanisms where neither Riemann solvers nor characteristic decompositions are needed. Numerical results are presented for several test problems with or without the source term present. The wetting and drying process is also considered. The presented schemes are verified by comparing the results with documented ones.

Original languageEnglish (US)
Pages (from-to)754-783
Number of pages30
JournalApplied Mathematical Modelling
Volume29
Issue number8
DOIs
StatePublished - Aug 1 2005

Keywords

  • Finite differences
  • Relaxation schemes
  • Source terms
  • TVD
  • Two-dimensional shallow water equations

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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