In the paper, the space second-order conservative characteristic finite difference method for solving convection-diffusion equations is developed and analyzed. Applying the directional derivative and mass correction technique, the redconvection-diffusion equations are changed into the parabolic equations, where the convection term and unsteady term are considered as one term. redThe 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 analyzed theoretically. Numerical experiments are presented to illustrate mass conservation and convergence.

提出并分析了求解对流扩散方程的空间二阶保守特征有限差分方法。应用方向导数和质量校正技术，将红色对流扩散方程变为抛物线方程，其中对流项和非稳态项被视为一项。红色分裂隐式解-通量耦合方案可计算交错网格上的解和通量。从理论上分析了我们提出的特征差分方法的质量守恒，稳定性和收敛性。数值实验表明了质量守恒和收敛。