Mixed-finite element and finite volume discretization for heavy brine simulations in groundwater

Recently, a new theory of high-concentration brine transport in groundwater has been developed. This approach is based on two nonlinear mass conservation equations, one for the fluid (flow equation) and one for the salt (transport equation), both having nonlinear diffusion terms. In this paper, we present and analyze a numerical technique for the solution of such a model. The approach is based on the mixed hybrid finite element method for the discretization of the diffusion terms in both the flow and transport equations, and a high-resolution TVD finite volume scheme for the convective term. This latter technique is coupled to the discretized diffusive flux by means of a time-splitting approach. A commonly used benchmark test (Elder problem) is used to verify the robustness and nonoscillatory behavior of the proposed scheme and to test the validity of two different formulations, one based on using pressure head ψ and concentration c as dependent variables, and one using pressure p and mass fraction ω as dependent variables. It is found that the latter formulation gives more accurate and reliable results, in particular, at large times. The numerical model is then compared against a semi-analytical solution and the results of a laboratory test. These tests are used to verify numerically the performance and robustness of the proposed numerical scheme when high-concentration gradients (i.e., the double nonlinearity) are present.