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A SGSP is a basin of water where solar energy is trapped due to an artificially imposed salinity gradient. In a SGSP three zones can be identified: the surface and bottom zones that are both convective and an intermediate zone in between which is intended to be non-convective. This zone acts as a transparent insulation and allows the storage of solar energy at the bottom where it is available for use.A numerical model where the SGSP dynamics is described in terms of velocity , pressure , temperature and salt concentration is presented. It is based on the Navier-Stokes equations for an incompressible fluid coupled to one advection-diffusion equation for and one advection-diffusion equation for . The fluid density is taken to depend on and and the Boussinesq hypothesis is adopted: the fluid density appearing in the LHS of the NavierStokes equation is supposed constant and equal to some reference value whereas it is assumed to be variable in the RHS.The space discretization of the governing equations is based on the respective weak formulations and the discretization employs finite elements with a pressure correction method used to decouple velocity and pressure. Integration in time is accomplished by a BDF (Backward Differentiation Formula) method with the above PDEs treated sequentially within each time step. A computer code was developed employing the finite element class library deal.II.Comparisons with available experimental results are made to validate this numerical model.

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Double-diffusive convection plays an important role in many physical phenomena of practical importance. However, the numerical simulation of these phenomena is challenging since fine meshes are often required to capture the flow physics. Hence, several different numerical methods have been employed in the past. This work reports the development and application of an adaptive finite element method for the simulation of these phenomena, thereby avoiding the need for the use of very fine meshes over the whole domain. The weak formulation of the conservation equations for mass, momentum, energy and species concentration is used. The Boussinesq approximation relates the density of the fluid to the temperature and/or the species concentration. A second-order backward difference method is used for time discretization and the Galerkin method is employed for spatial discretization. Both adaptive time step and grid refinement techniques are employed, and the code is parallelized using MPI. Three different stabilization methods of the convective-diffusion equations are compared; namely, the streamline upwind Petrov–Galerkin (SUPG) method, and two modified methods aimed at diminishing spurious oscillations that include an artificial diffusion term. This diffusion term may be either isotropic or orthogonal to the streamlines. The addition of artificial isotropic diffusion to the SUPG method provides enhanced stability. The method is applied to double-diffusive finger convection in a sucrose-salt aqueous mixture and a stratified salt solution heated from below. The method accurately reproduces the experimentally observed temporal evolution of the salt fingers in the former case and the location of the interfaces between convective and non-convective zones in the latter.

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