Investigation of difference schemes on method of lines

Tarhan T., Selcuk N.

PROGRESS IN COMPUTATIONAL FLUID DYNAMICS, vol.6, no.8, pp.447-458, 2006 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 8
  • Publication Date: 2006
  • Doi Number: 10.1504/pcfd.2006.011318
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.447-458


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.