On the Validity of the Boussinesq Approximation for the Elder Problem |
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| Authors: | K Johannsen |
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| Institution: | (1) IWR/Simulation in Technology Center, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany |
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| Abstract: | The Elder problem is an example of a density driven flow, motivated by experiments of a thermally driven convection in porous media. It is a mathematical benchmark problem used for code verification of density driven flow simulators and comparison of issues related to its numerical treatment. Its bifurcation diagram with respect to the Rayleigh number is investigated on a hierarchy of uniformly refined grids. Eleven stationary solutions are shown to exist for the Elder problem. Similar solutions can be found using the Boussinesq approximation. Despite this similarity the corresponding bifurcation diagrams are shown to be topologically not equivalent. This gives rise to serious doubts on the validity of Boussinesq approximation for this model problem. Grid convergence is investigated for the numerically obtained solutions. |
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| Keywords: | benchmarking Boussinesq approximation brine transport convection fingering instability numerical simulation porous media variable density |
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