A new benchmark semi-analytical solution for density-driven flow in porous media

• We propose a new semi-analytical solution for a density-driven flow problem.
• The problem deals with a square porous cavity salted on one of its vertical wall.
• We develop the semi-analytical solution using the Fourier–Galerkin method.
• The semi-analytical solution is obtained for low diffusion coefficients.
• We show the worthiness of the new semi-analytical solution in codes benchmarking.

A new benchmark semi-analytical solution is proposed for the verification of density-driven flow codes. The problem deals with a synthetic square porous cavity subject to different salt concentrations at its vertical walls. A steady state semi-analytical solution is investigated using the Fourier–Galerkin method. Contrarily to the standard Henry problem, the cavity benchmark allows high truncation orders in the Fourier series and provides semi-analytical solutions for very small diffusion cases. The problem is also investigated numerically to validate the semi-analytical solution. The obtained results represent a set of new test case high quality data that can be effectively used for benchmarking density-driven flow codes.