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Vorticity preserving finite volume schemes for the shallow water equations

by U. S. Fjordholm and S. Mishra

(Report number 2009-35)

Abstract
We consider the shallow water equations and propose a numerical algorithm that approximates the transport of vorticity accurately. The algorithm is based on a predictor-corrector type projection method. Any consistent finite volume scheme predicts the approximate solution. An elliptic equation is solved and the momentum field is corrected to obtain the correct evolution of vorticity. We describe this projection algorithm for the wave equation and the shallow water equations. The crucial role played by the pseudo-vorticity transport is highlighted. Numerical experiments demonstrating a considerable gain in computational efficiency with the vorticity projection algorithm are presented.

Keywords:

@Techreport{FM09_416,
  author = {U. S. Fjordholm and S. Mishra},
  title = {Vorticity preserving finite volume schemes for the shallow water equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-35},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-35.pdf },
  year = {2009}
}

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