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Density variations can initiate flow even in a still fluid. In earth systems, density variations can arise from naturally occurring salts, subsurface temperature changes, or migrating pollution. This buoyant or density-driven flow factors into fluid movement in salt-lake systems, saline-disposal basins, dense contaminant and leachate plumes, and geothermal reservoirs, to name just a few.

This example benchmarks a time-dependent buoyant flow in porous media. Known as the Elder problem, it follows a laboratory experiment to study thermal convection. The Elder problem examines the concentrations through the coupling of two physics interfaces: Darcy’s Law and Solute Transport.