The Elder problem-Bifurcations and steady state solutions

摘要

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. We present a thorough numerical investigation of the problem on the base of the software package d~3f using a hierarchy of uniformly refined, structured grids. The bifurcation diagram with respect to the Rayleigh number is analyzed. The existence of eleven stationary solutions is shown and grid convergence is investigated numerically.