IJPAM: Volume 101, No. 2 (2015)

TOTAL VARIATION DIMINISHING FINITE VOLUME
SCHEMES FOR ONE DIMENSIONAL
ADVECTION-DIFFUSION EQUATION AND
THE RELATIONSHIP BETWEEN FLUX
LIMITER AND MESH PARAMETERS

S. Prabhakaran$^1$, L. Jones Tarcius Doss$^2$
$^{1,2}$Department of Mathematics
College of Engineering Guindy
Anna University
Chennai, 600 025, INDIA


Abstract. Finite volume schemes for one dimensional Advection-Diffusion Equation (ADE) are discussed in this article. As a result, a general explicit difference equation of the form $U^{n+1}_{m}=aU^{n}_{m-1}+bU^{n}_{m}+cU^{n}_{m+1}$ is obtained with general coefficients $a$, $b$, and $c$. Stability condition and local truncation error for this general form of explicit difference equation are derived. Then, total Variation Diminishing (TVD) schemes for general flux limiter $\psi(r)$ are also discussed. Further, a relation between flux limiter and mesh length parameters is also obtained. Numerical justification for order of convergence for upwind, central difference and various TVD schemes are also presented.

Received: October 28, 2014

AMS Subject Classification: 65M08, 65M12, 65M15, 65N08, 65N12

Key Words and Phrases: finite volume method, advection diffusion, truncation error, stability, convergence, total variation diminishing, flux limiter

Download paper from here.




DOI: 10.12732/ijpam.v101i2.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 2
Pages: 233 - 250


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).