Upwinding finite covolume methods for unsteady convection-diffusion problems

In this paper we present a modified mixed upwinding covolume method for unsteady convection-diffusion equations on two dimensional domain. The equations can be used to model the transport of a contaminant in a porous medium flow. The lowest order Raviart-Thomas mixed element space is used. A new upwinding technique is proposed to treat the convection term. We derive that the method satisfies the conservation of mass and the unconditioned stability. We prove that the concentration flux and the concentration both converge at the first order optimal rate in L-2-norm. Numerical experiments axe given to illustrate the efficiency and accuracy of the method.