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

• Published in: Advances in water resources Vol. 70; pp. 24 - 35
• Main Authors: Fahs, Marwan, Younes, Anis, Mara, Thierry Alex
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2014; Elsevier
• Subjects: Benchmark; Benchmarking; Computer Science; density; Density-driven flow; Diffusion; Earth sciences; Earth, ocean, space; equations; Exact sciences and technology; Fourier series; Holes; Hydrogeology; Hydrology. Hydrogeology; Mathematical models; Modeling and Simulation; porous media; Semi-analytical solution; Steady state; Walls; water flow; Water resources; Benchmark; Semi-analytical solution; Density-driven flow; Fourier series; diffusion; salt; density; ground water; concentration; chemically precipitated rocks; evaporites; sedimentary rocks; water resources; water quality; standard samples; Galerkin method; porous media; flow; Spectral method
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2014.04.013

•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.