Mass conservative characteristic finite difference method for convection-diffusion equations

In the paper, the space second-order conservative characteristic finite difference method for solving convection-diffusion equations is developed and analysed. Applying the directional derivative and mass correction technique, the convection-diffusion equations are changed into the parabolic equations, where the convection term and unsteady term are considered as one term. The splitting implicit solution-flux coupled scheme computes the solutions and fluxes on the staggered meshes. The mass conservation, stability and convergence of our proposed characteristic difference method are analysed theoretically. Numerical experiments are presented to illustrate mass conservation and convergence.