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Solution of fully-coupled shallow water equations and contaminant transport using a primitive-variable Riemann method

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Abstract

A Riemann-solver scheme, using primitive variables rather than conserved variables, is configured and tuned for the solution of the fully-coupled two-dimensional shallow water and contaminant transport equations. This scheme is based on the unstructured finite volume discretization using primitive-variable Roe-flux approximation with an entropy fix. The primitive-variable flux associated with the exact source-term balancing is well-behaved and well-balanced for both still-water and dry regions with arbitrary bed topography. Second-order accuracy is used in space and time. The present study uses a nonlinear implicit scheme based on Newton-iterative algorithm for the time integration. In order to show the accuracy of the scheme, numerical results are verified by different test cases for contaminant advection and diffusion. A scenario of contaminant transport in a complex geometry with wet and dry elements is also simulated to demonstrate that the present work can be implemented on practical applications involving flooding and contaminant transport.

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Acknowledgements

This work was supported by the Tennessee Higher Education Commission Center of Excellence for Applied Computational Science and Engineering. This support is greatly appreciated. The authors sincerely appreciate Dr. Bruce Hilbert and Ethan Hereth for their assistance in generating unstructured grids for the test cases.

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Authors and Affiliations

  1. SimCenter: Center of Excellence in Applied Computational Science and Engineering, University of Tennessee at Chattanooga, 701 East M L King Blvd, Chattanooga, TN, 37403, USA

    Faranak Behzadi, Behrouz Shamsaei & James C. Newman III

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  1. Faranak Behzadi
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  2. Behrouz Shamsaei
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  3. James C. Newman III
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Correspondence to Faranak Behzadi.

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Behzadi, F., Shamsaei, B. & Newman, J.C. Solution of fully-coupled shallow water equations and contaminant transport using a primitive-variable Riemann method. Environ Fluid Mech 18, 515–535 (2018). https://doi.org/10.1007/s10652-017-9571-7

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  • DOI: https://doi.org/10.1007/s10652-017-9571-7

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