IJPAM: Volume 101, No. 2 (2015)
SCHEMES FOR ONE DIMENSIONAL
ADVECTION-DIFFUSION EQUATION AND
THE RELATIONSHIP BETWEEN FLUX
LIMITER AND MESH PARAMETERS
Department of Mathematics
College of Engineering Guindy
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 is obtained with general coefficients , , and . 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 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
Pages: 233 - 250