Mass conservative characteristic finite difference method for convection–diffusion equations

Abstract

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.

Keywords:

• Mass conservative
• convection–diffusion equations
• characteristic difference
• stability
• convergence

2010 Mathematics Subject Classifications:

• 65M06
• 65M12

Acknowledgments

The authors would thank referees for their comments and suggestions on their manuscript which have helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant No. 61703250), Shandong Agricultural University and Shandong Province College Student Innovation and Entrepreneurship Training Program (Grant No. S202010434064). Shandong Province College Student Innovation and Entrepreneurship Training Program Province College Student Innovation and Entrepreneurship Training Program) has been checked against the Open Funder Registry and we failed to find a match.