A preliminary investigation on an ELLAM scheme for linear transport equations

Mohamed Al-Lawatia, Hong Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We present an Eulerian-Lagrangian localized adjoint method (ELLAM) for linear advection-reaction partial differential equations in multiple space dimensions. We carry out numerical experiments to investigate the performance of the ELLAM scheme with a range of well-perceived and widely used methods in fluid dynamics including the monotonic upstream-centered scheme for conservation laws (MUSCL), the minmod method, the flux-corrected transport method (FCT), and the essentially non-oscillatory (ENO) schemes and weighted essentially non-oscillatory (WENO) schemes. These experiments show that the ELLAM scheme is very competitive with these methods in the context of linear transport PDEs, and suggest/justify the development of ELLAM-based simulators for subsurface porous medium flows and other applications.

Original languageEnglish
Pages (from-to)22-43
Number of pages22
JournalNumerical Methods for Partial Differential Equations
Issue number1
Publication statusPublished - Jan 2003


  • Advection-reaction equations
  • Characteristic methods
  • Comparison of numerical methods
  • Essentially nonoscillatory schemes
  • Eulerian-Lagrangian methods
  • Transport equations

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'A preliminary investigation on an ELLAM scheme for linear transport equations'. Together they form a unique fingerprint.

Cite this