Abstract
In this article, we consider a time evolution equation for solute transport, coupled with a pressure equation in space dimension 2. For the numerical discretization, we combine the generalized finite volume method SUSHI on adaptive meshes with a time semi-implicit scheme. In the first part of this article, we present numerical simulations for two problems: a rotating interface between fresh and salt water and a well-known test case proposed by Henry. In the second part, we also introduce heat transfer and perform simulations for a system from the documentation of the software SEAWAT.
Highlights
We present numerical simulations for density driven flows involved in the production of lithium batteries
We present the results of numerical simulations for two problems: a problem for a rotating interface and a problem proposed by Henry
HydroExpert, the small hydrology company with whom we used to work, only used square mesh elements for the space discretization; these elements coincided with data coming from physical measurements
Summary
We present numerical simulations for density driven flows involved in the production of lithium batteries. This work was performed in the context of an exploratory CNRS project on the numerical simulation of variable density flows. The objective of the project was related to the exploitation of lithium deposits in salt lakes, known as “salars”. Its production is of great interest to all major groups involved in the automotive industry and to the suppliers of these groups. From a mathematical point of view, we study a system of equations that describes the interaction between flow and transport in a porous medium in which the density ρ increases strictly with respect to the concentration u of the transported species. The equations governing density-dependent transport are Darcy’s law (1), the continuity equation for the fluid (2), and the continuity equation for the solute (3), which are given as k
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