A semi-implicit method for modeling salinity and temperature in variable-density flow

Amine Hanini and Abdelaziz Beljadid

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 222-239

Abstract: In this study, we propose semi-implicit techniques for solving the coupled variable-density model of shallow water flows and transport processes, taking into account temperature and salinity. In the proposed numerical approach, we first compute the water depth and the conservative variables related to temperature and salinity using their governing continuity equations. The obtained values are used in the mixture density source terms which allows us to design semi-implicit discretization techniques for solving the momentum equations. To discretize the flux term, a well-balanced Godunov-type finite volume scheme is used with a suitable linear reconstruction of the system’s variables. The discretization of the mixture density and friction source terms can be used as a stand-alone approach within any other finite volume solver. The performance of the proposed coupled numerical model is tested through a series of numerical examples for modeling flows and transport processes. The developed numerical scheme is positivity-preserving for the computed water depth and salinity. Furthermore, the consistency between the discretizations of the continuity equation and the transport equations of temperature and salinity is satisfied.

Keywords: Shallow water flow; Variable-density; Transport processes; Semi-implicit methods; Well-balanced property; Positivity-preserving scheme (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:222-239

DOI: 10.1016/j.matcom.2025.04.032

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