Vorticity Preserving Finite Volume Schemes for the Shallow Water Equations

Authors:
Ulrik S. Fjordholm;Siddhartha Mishra
Affiliations:
ulrikf@sam.math.ethz.ch and smishra@sam.math.ethz.ch;-
Venue:
SIAM Journal on Scientific Computing
Year:
2011

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Abstract

We propose a finite volume method for the shallow water equations that accurately approximates the transport of vorticity. The algorithm is based on a predictor-corrector-type projection method. Any consistent finite volume scheme may be used in the prediction step of the algorithm. 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 pseudovorticity transport is highlighted. Numerical experiments demonstrating a considerable gain in computational efficiency with the vorticity projection algorithm are presented.