B. Karasozen, V.G. Tysbulin

We consider finite-difference approximations of the planar Darcy convection problem and study the effect of different
discretizations with respect to preservation of cosymmetry. The important feature of cosymmetrical systems is the existence of the family of stationary regimes with a spectrum that varies over a family,  and an accurate computation of the family of equilibria is the key point of our consideration. Different approximations of Jacobians are compared and we found that the Arakawa scheme provides the most accurate results due to its conservation properties. Some evidence of family degeneration is presented when an inappropriate approximation was used.

 Keywords: Darcy equation, cosymmetry, finite-diferences, Arakawa scheme, family of equilibria