Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4629911 | Applied Mathematics and Computation | 2012 | 10 Pages |
Abstract
This paper presents a class of fourth-order compact finite difference technique for solving two-dimensional convection diffusion equation. The equation is recasted as a first-order mixed system, introducing a conservation and flux equations. Since flux appears explicitly in the mixed formulation, we search a fourth-order compact approximation of the primary solution field and flux. Based on Taylor series expansion, the proposed compact mixed formulation generalizes the work of Carey and Spotz [G.F. Carey, W.F. Spotz, Higher-order compact mixed methods, Commun. Numer. Meth. Eng. 13 (1997)]. We show that their fourth-order formulation corresponds to a particular case of our presented scheme, and we extend their work to variable diffusion and convection coefficients. Some numerical experiments are performed to demonstrate the fourth-order effective convergence rate.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Stéphane Abide, Xavier Chesneau, Belkacem Zeghmati,