ADAPTIVE EULERIAN-LAGRANGIAN FINITE ELEMENT METHOD FOR ADVECTION-DISPERSION.

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Abstract

A new adaptive finite element method is proposed for the advection-dispersion equation using an Eulerian-Lagrangian formulation. The method is based on a decomposition of the concentration field in two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single-step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices.

Original languageEnglish (US)
Pages (from-to)321-337
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Volume20
Issue number2
StatePublished - Feb 1984

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Eulerian-Lagrangian Methods
Advection
Finite Element Method
Finite element method
Decomposition
Adaptive Finite Element Method
Dissipate
Particle Tracking
Method of Characteristics
Formulation
Diagonal matrix
Symmetric matrix
Reverse
Finite Element
Grid
Decompose

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

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abstract = "A new adaptive finite element method is proposed for the advection-dispersion equation using an Eulerian-Lagrangian formulation. The method is based on a decomposition of the concentration field in two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single-step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices.",
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