Unconditionally Monotone Schemes for Unsteady Convection-Diffusion Problems.

This paper deals with constructing monotone schemes of the second-order accuracy in space for transient convection-diffusion problems. They are based on a reformulation of the convective and diffusive transport terms using the convective terms in the divergent and nondivergent forms. The stability of the difference schemes is established in the uniform and L-1 norm. For 2D problems, unconditionally monotone schemes of splitting with respect to spatial variables are developed. Unconditionally stable schemes for problems of convection-diffusion-reaction are proposed, too.