Tech Briefs

Multiphysics Flow in Porous Media

Flow and solute transport in porous media is of interest in many practical applications. It can represent the spread of a pollutant (e.g. chemical waste) through ground water flow, salt water incursion in an aquifer, and even the spread of nuclear waste through ground water.

Here we consider a widely used benchmark problem due to Elder [1, 2]. Flow in the porous medium is caused by a density gradient induced by specifying a mass concentration on the boundaries.

The schematic below shows the geometry and boundary conditions for the Elder problem. A constant concentration with a normalized value of 1.0 is specified for a portion of the upper boundary. The concentration for the lower boundary is set to 0.0. Also, a zero pressure head is maintained on the two upper corners of the domain. The simulation with ADINA has been conducted for a time span of 20 years.

Schematic of Elder problem

The first movie on top shows the distribution of solute in the water as a function of time. Diffusion causes the migration of the solute into the fresh water, and then the heavier saline water moves down faster than the surrounding water, setting up a convective pattern.

The second movie shows, by particle tracing, the flow patterns in the medium as a function of time. The vortices in the flow are of interest.

In these types of physical problems the transport equation is strongly coupled to the flow equation through advection. The change of density due to the transport phenomenon is significant and results in a two-way coupling between the transport equation and the flow equation.

This example illustrates the strength of ADINA in modeling strongly coupled density driven flow in porous media, and hence one of the many powerful multiphysics capabilities in ADINA.


  1. Elder, J.W. A Steady Free Convection in a Porous Medium Heated from Below. J. Fluid Mech., 27(1967) 29—50.

  2. Simpson, M.J., Clement T.P. Theoretical Analysis of the Worthiness of Henry and Elder Problems as Benchmarks of Density-dependent Ground Water Flow Models. Advances in Water Resources, 26(2003) 17—31.