Simple treatment of non-aligned boundaries in a Cartesian grid shallow flow model

Qiuhua Liang*, Alistair G. L. Borthwick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A simple method is proposed for treating Curved or irregular boundaries in Cartesian grid shallow flow models. It directly evaluates fictional values in 'ghost' cells adjacent to boundary cells and requires no interpolation or generation of cut cells. The boundary treatment is implemented in a dynamically adaptive quadtree grid-based solver of the hyperbolic shallow water equations and validated against several test cases with analytical or alternative numerical solutions. The method is easy to code, accurate, and demonstrably effective in dealing with irregular computational domains in shallow flow simulations. Results are presented for still water in a basin of complicated geometry, steady hydraulic jump in an open channel with a converging sidewall, wind-induced circulation in a circular shallow lake, and shock wave diffraction in a channel containing a contraction and expansion. Copyright (C) 2007 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)2091-2110
Number of pages20
JournalInternational Journal for Numerical Methods in Fluids
Volume56
Issue number11
DOIs
Publication statusPublished - 20 Apr 2008

Keywords

  • Cartesian method
  • boundary fitness
  • shallow flow
  • Godunov-type scheme
  • quadtree grid
  • Riemann solver
  • FINITE-VOLUME ALGORITHM
  • GODUNOV-TYPE SCHEME
  • WATER EQUATIONS
  • QUADTREE GRIDS
  • DAM-BREAK
  • SIMULATION
  • MESHES

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