Conservative characteristic finite difference method based on ENO and WENO interpolation for 2D convection-diffusion equations

In the paper, the space second-order conservative characteristic finite difference method based on essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) interpolation for solving two-dimensional conservative convection-diffusion equations in divergence form is developed. Combining the splitting technique, characteristic difference and mass correction method, a two-dimensional convection-diffusion equations are changed into the two-dimensional parabolic equations, where the convection term and unsteady term are considered as one term. The solutions and fluxes on the staggered meshes are computed by the splitting implicit solution-flux coupled scheme. Numerical experiments are presented to illustrate mass conservation and convergence.