Equivalent initial conditions for compatibility between analytical and computational solutions of convection in porous media

The derivation of a set of compatibility conditions for the equivalence bet ween a weak non-linear analytical solution and any computational or numeric al solution is presented. Both direct and inverse transformations are deriv ed and shown to apply well for arbitrary initial conditions, provided that a validity condition of the asymptotic expansion associated with the weak n on-linear solution is not violated. The results presented by using these co mpatibility conditions for a comparison between computational and analytica l transitional Values of a scaled Rayleigh number, that represents the poin t of transition from steady-to-chaotic solutions, show very good agreement within the validity domain of the asymptotic expansion. (C) 2000 Elsevier S cience Ltd. All rights reserved.