Filtration-Convection Problem: Spectral-Difference Method and Preservation of Cosymmetry

Abstract

For the problem of filtration of viscous fluid in porous medium it was observed that a number of one-parameter families of convective states with the spectrum, which varies along the family. It was shown by V. Yudovich that these families cannot be an orbit of an operation of any symmetry group and as a result the theory of cosymmetry was derived. The combined spectral and finite-difference approach to the planar problem of filtration-convection in porous media with Darcy law is described. The special approximation of nonlinear terms is derived to preserve cosymmetry. The computation of stationary regime transformations is carried out when filtration Rayleigh number varies.