Explicit-implicit schemes for convection-diffusion-reaction problems

Boundary value problems for time-dependent convection-diffusion-reaction equations are basic models of problems in continuum mechanics. To study these problems, various numerical methods are used. With a finite difference, finite element, or finite volume approximation in space, we arrive at a Cauchy problem for systems of ordinary differential equations whose operator is asymmetric and indefinite. Explicit-implicit approximations in time are conventionally used to construct splitting schemes in terms of physical processes with separation of convection, diffusion, and reaction processes. In this paper, unconditionally stable schemes for unsteady convection-diffusion-reaction equations are constructed with explicit-implicit approximations used in splitting the operator reaction. The schemes are illustrated by a model 2D problem in a rectangle.