A preliminary investigation on an ELLAM scheme for linear transport equations

Research output: Contribution to journalArticle

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Abstract

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
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 2003

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Adjoint Method
Transport Equation
Linear equation
Advection
Fluid dynamics
Partial differential equations
Porous materials
Conservation
Simulators
Experiments
Fluxes
Porous Media Flow
Fluid Dynamics
Monotonic
Justify
Conservation Laws
Simulator
Partial differential equation
Numerical Experiment
Range of data

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

A preliminary investigation on an ELLAM scheme for linear transport equations. / Al-Lawatia, Mohamed; Wang, Hong.

In: Numerical Methods for Partial Differential Equations, Vol. 19, No. 1, 01.2003, p. 22-43.

Research output: Contribution to journalArticle

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