Numerical simulation of convective motion in an anisotropic porous medium and cosymmetry conservation

The onset of convection in a porous anisotropic rectangle occupied by a heat-conducting fluid heated from below is analyzed on the basis of the Darcy–Boussinesq model. It is shown that there are combinations of control parameters for which the system has a nontrivial cosymmetry and a one-parameter family of stationary convective regimes branches off from the mechanical equilibrium. For the two-dimensional convection equations in a porous medium, finite-difference approximations preserving the cosymmetry of the original system are developed. Numerical results are presented that demonstrate the formation of a family of convective regimes and its disappearance when the approximations do not inherit the cosymmetry property.