This benchmark is one of the classical freeconvection densitydriven flow and mass transport setups. It was originally published by Elder (1965) and has since then been used as a basic test case (Diersch & Kolditz, 1998; Guo & Langevin, 2002), or has been subject to various investigations concerning grid convergence (Graf & Degener, 2011) and numerical stability (Musuuza et al., 2009; Johannsen, 2003).
For the setup and parameterization, see the chapter “Density dependent flow  The Elder Problem” in Kolditz et al. (2012).
The Elder benchmark describes free convection of a dense fluid in mixable, singlephase environment. A highconcentration solute increases fluid density on the upper boundary and perpetrates the domain by evolving concentration fingers. Here, we compare numerical results of OGS6 to those of OGS5. Settings of both simulators were chosen to be as identical as possible. Simulation times were $3300 s$ and $7800 s$ for OGS6 and OGS5, respectively.
A comparison of the numerical data is shown in the figure below. The numerical results of OGS6 coincide with those of OGS5.
Diersch, H.J.G., Kolditz, O., 1998. Coupled groundwater flow and transport: 2. Thermohaline and 3D convection systems. Adv. Water Resour. 21, 401–425. doi:10.1016/S03091708(97)000031.
Elder, J.W., 1965. Numerical experiments with free convection in a vertical slot. J. Fluid Mech. 24, 823. doi:10.1017/S0022112066001022.
Elder, J., Simmons, C., Diersch, H.J., Frolkovič, P., Holzbecher, E., Johannsen, K., 2017. The Elder Problem. Fluids 2, 11. doi:10.3390/fluids2010011.
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Guo, W., Langevin, C.D., 2002. User’s Guide to SEAWAT: A computer program for simulation of threedimensional variabledensity groundwater flow, USGS Techniques of Water Resources Investigations. ISBN: 0607992573.
Johannsen, K., 2003. On the Validity of the Boussinesq Approximation for the Elder Problem. Comput. Geosci. 7, 169–182. doi:10.1023/A:1025515229807.
Kolditz, O., Görke, U.J., Shao, H., Wang, W., 2012. ThermoHydroMechanicalChemical Processes in Porous Media: Benchmarks and Examples, Lecture notes in computational science and engineering. Springer. ISBN: 3642271766.
Musuuza, J.L., Attinger, S., Radu, F.A., 2009. An extended stability criterion for densitydriven flows in homogeneous porous media. Adv. Water Resour. 32, 796–808. doi:10.1016/j.advwatres.2009.01.012.
This article was written by Marc Walther. If you are missing something or you find an error please let us know.
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