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

Ernesto Guerrero Fernández, Manuel Jesús Castro-Díaz and Tomás Morales de Luna
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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

Mathematics, 2020, vol. 8, issue 5, 1-42

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.

Keywords: multilayer shallow-water; variable pressure; density-stratified fluid; hydrostatic reconstruction; GPU parallelization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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