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Open AccessFeature PaperArticle

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

1
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos S/N, 29081 Málaga, Spain
2
Departamento de Matemáticas, Universidad de Córdoba, Campus de Rabanales, 14071 Córdoba, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 848; https://doi.org/10.3390/math8050848
Received: 3 May 2020 / Revised: 16 May 2020 / Accepted: 19 May 2020 / Published: 23 May 2020
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment)
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. View Full-Text
Keywords: multilayer shallow-water; variable pressure; density-stratified fluid; hydrostatic reconstruction; GPU parallelization multilayer shallow-water; variable pressure; density-stratified fluid; hydrostatic reconstruction; GPU parallelization
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Guerrero Fernández, E.; Castro-Díaz, M.J.; Morales de Luna, T. A Second-Order Well-Balanced Finite Volume Scheme for the Multilayer Shallow Water Model with Variable Density. Mathematics 2020, 8, 848.

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