𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Rotated Monotone Difference Scheme for the Two-Dimensional Anisotropic Drift-Diffusion Equation

✍ Scribed by D. Thangaraj; A. Nathan

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
196 KB
Volume
145
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

A rotated upwind discretization scheme is presented for the discretization of the steady-state two-dimensional anisotropic drift-diffusion equation, taking into account the local characteristic nature of the solution. The notable features of the algorithm lie in the projection of the governing partial differential equation onto two orthogonal axes, to yield a vanishing mixed derivative term, and in the utilization of the upwind flow of information. As a result the limiting behaviour of the elliptic equation is preserved in the discretization. The scheme produces an M-matrix which guarantees an oscillation free solution and which enables the discrete system to be solved using standard iterative solvers. The method is illustrated by numerical examples for which the analytical solutions are known.

📜 SIMILAR VOLUMES

A higher-order predictor–corrector schem
A higher-order predictor–corrector scheme for two-dimensional advection–diffusion equation
✍ Chuanjian Man; Christina W. Tsai 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 367 KB

## Abstract A higher‐order accurate numerical scheme is developed to solve the two‐dimensional advection–diffusion equation in a staggered‐grid system. The first‐order spatial derivatives are approximated by the fourth‐order accurate finite‐difference scheme, thus all truncation errors are kept to

A Comparison of Uniformly Convergent Dif
A Comparison of Uniformly Convergent Difference Schemes for Two-Dimensional Convection—Diffusion Problems
✍ Alan F. Hegarty; Eugene O'Riordan; Martin Stynes 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 372 KB

Galerkin and Petrov Galerkin linite element mellods are used to obtain new linite difference schemes for the solution of linear twodimensional convection difusion problems. Numerical estimates are made of the rates of convergence of these schemes, uniformly with respect to the perturbation parameter