Title: Investigation of difference schemes on method of lines

Authors: T. Tarhan, N. Selcuk

Addresses: Chemical Engineering Department, Middle East Technical University, 06531 Ankara, Turkey. ' Chemical Engineering Department, Middle East Technical University, 06531 Ankara, Turkey

Abstract: A second-order high-resolution Total Variation Diminishing (TVD) scheme based on Lagrange interpolation polynomial was proposed for the spatial discretisation of convective terms in strongly convected problems with non-uniform grid topologies. Performances of classical and TVD-based Finite Difference (FD) schemes, higher-order Lagrange interpolation polynomial-based schemes and the proposed scheme were investigated on the Method of Lines (MOL) solution of two test problems, a simple one-dimensional convective flow and a two-dimensional unsteady laminar diffusion flame. The proposed scheme produced accurate results without spurious oscillations and numerical diffusion encountered in the classical schemes, and hence, was found to be a successful scheme applicable to strongly convective flow problems with non-uniform grid resolution. The proposed algorithm can be readily incorporated into existing codes based not only on MOL but also on other numerical solution techniques.

Keywords: spatial discretisation; method of lines; MOL; Lagrange interpolation polynomial; total variation diminishing; TVD; unsteady convection; convective flow; unsteady laminar diffusion flame; finite difference; CFD; computational fluid dynamics.

DOI: 10.1504/PCFD.2006.011318

Progress in Computational Fluid Dynamics, An International Journal, 2006 Vol.6 No.8, pp.447 - 458

Published online: 17 Nov 2006 *

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