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A Second-Order Well-Balanced Finite Volume Scheme for the Multilayer Shallow Water Model with Variable Density

Author

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  • Ernesto Guerrero Fernández

    (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos S/N, 29081 Málaga, Spain)

  • Manuel Jesús Castro-Díaz

    (Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos S/N, 29081 Málaga, Spain)

  • Tomás Morales de Luna

    (Departamento de Matemáticas, Universidad de Córdoba, Campus de Rabanales, 14071 Córdoba, Spain)

Abstract

In this work, we consider a multilayer shallow water model with variable density. It consists of a system of hyperbolic equations with non-conservative products that takes into account the pressure variations due to density fluctuations in a stratified fluid. A second-order finite volume method that combines a hydrostatic reconstruction technique with a MUSCL second order reconstruction operator is developed. The scheme is well-balanced for the lake-at-rest steady state solutions. Additionally, hints on how to preserve a general class of stationary solutions corresponding to a stratified density profile are also provided. Some numerical results are presented, including validation with laboratory data that show the efficiency and accuracy of the approach introduced here. Finally, a comparison between two different parallelization strategies on GPU is presented.

Suggested Citation

  • Ernesto Guerrero Fernández & Manuel Jesús Castro-Díaz & Tomás Morales de Luna, 2020. "A Second-Order Well-Balanced Finite Volume Scheme for the Multilayer Shallow Water Model with Variable Density," Mathematics, MDPI, vol. 8(5), pages 1-42, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:848-:d:362041
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    References listed on IDEAS

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    1. Escalante, C. & Morales de Luna, T. & Castro, M.J., 2018. "Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 631-659.
    2. Lastra, Miguel & Mantas, José M. & Ureña, Carlos & Castro, Manuel J. & García-Rodríguez, José A., 2009. "Simulation of shallow-water systems using graphics processing units," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 598-618.
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    Cited by:

    1. Carlino, Michele Giuliano & Gaburro, Elena, 2023. "Well balanced finite volume schemes for shallow water equations on manifolds," Applied Mathematics and Computation, Elsevier, vol. 441(C).

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