1-D numerical modelling of shallow flows with variable horizontal density

Feifei Zhang Leighton*, Alistair G. L. Borthwick, Paul H. Taylor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

A 1-D numerical model is presented for vertically homogeneous shallow flows with variable horizontal density. The governing equations represent depth-averaged mass and momentum conservation of a liquid species mixture, and mass conservation of the species in the horizontal direction. Here, the term 'species' refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealized simulation of hyper-concentrated sediment-laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to modify the flow structure. A Godunov-type finite volume scheme is implemented to solve the conservation laws written in a deviatoric, hyperbolic form. The model is verified for variable-density flows, where analytical steady-state solutions are derived. The agreement between the numerical predictions and benchmark test solutions illustrates the ability of the model to capture rapidly varying flow features over uniform and non-uniform bed topography. A parameter study examines the effects of varying the initial density and depth in different regions. Copyright (C) 2009 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)1209-1231
Number of pages23
JournalInternational Journal for Numerical Methods in Fluids
Issue number11
Publication statusPublished - 20 Apr 2010

Keywords / Materials (for Non-textual outputs)

  • shallow flow
  • variable density
  • Godunov
  • shock capturing
  • species transport
  • BED


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