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Non-hydrostatic pressure shallow flows: GPU implementation using finite volume and finite difference scheme

Author

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  • Escalante, C.
  • Morales de Luna, T.
  • Castro, M.J.

Abstract

We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step algorithm based on a projection-correction type scheme initially introduced by Chorin–Temam [15]. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix path-conservative finite volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPU-architectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:631-659
    DOI: 10.1016/j.amc.2018.06.035
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    Cited by:

    1. 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.
    2. Echeverribar, I. & Brufau, P. & García-Navarro, P., 2023. "Extension of a Roe-type Riemann solver scheme to model non-hydrostatic pressure shallow flows," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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