Nonlinear Finite Volume Scheme Preserving Positivity for 2D Convection-Diffusion Equations on Polygonal Meshes. (21st August 2020)

• Record Type: Journal Article
• Authors: Lan, Bin; Dong, Jianqiang
• Other Names: Yang Zaoli Guest Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-08-21
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/7343716
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, a nonlinear finite volume scheme preserving positivity for solving 2D steady convection-diffusion equation on arbitrary convex polygonal meshes is proposed. First, the nonlinear positivity-preserving finite volume scheme is developed. Then, in order to avoid the computed solution beyond the upper bound, the cell-centered unknowns and auxiliary unknowns on the cell-edge are corrected. We prove that the present scheme can avoid the numerical solution beyond the upper bound. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results show that our scheme preserves the above conclusion and has second-order accuracy for solution.