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 between a weak non-linear analytical solution and any computational or numerical solution is presented. Both direct and inverse transformations are derived and shown to apply well for arbitrary initial conditions, provided that a validity condition of the asymptotic expansion associated with the weak non-linear solution is not violated. The results presented by using these compatibility conditions for a comparison between computational and analytical transitional values of a scaled Rayleigh number, that represents the point of transition from steady-to-chaotic solutions, show very good agreement within the validity domain of the asymptotic expansion.