Efficiency of the Eulerian-Lagrangian localized adjoint method for solving advection-dispersion equations on highly heterogeneous media

Fanilo Ramasomanana, Anis Younes

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The Eulerian-Lagrangian Localized Adjoint Method (ELLAM) is well adapted for advection-dominated transport problems. The method can use large time steps because the advection term is accurately approximated without any CFL restriction. A new formulation of ELLAM was developed by Younes et al. (Adv. Water Resour. 2006; 29:1056-1074) for unstructured triangular meshes. This formulation uses only strategic numerical integration points and thus requires a very limited number of integration points (usually 1 per element). To avoid numerical dispersion due to interpolation when several time steps are used, the method continuously tracks characteristics, and only changes due to dispersion are interpolated at each time step. In this work, we study the applicability and efficiency of this formulation for highly heterogeneous domains. The results show that (i) this formulation remains efficient even for highly heterogeneous domains, (ii) special care must be taken for the approximation of the dispersive term when large time steps are used, (iii) interpolation at intermediate times can be used to reduce memory requirement for problems with a large number of elements and small time steps, and (iv) the method can be used successfully for heterogeneous problems including injection and pumping wells, and remains much more efficient than the discontinuous Galerkin finite element method even when small time steps are required.

Original languageEnglish
Pages (from-to)639-652
Number of pages14
JournalInternational Journal for Numerical Methods in Fluids
Volume69
Issue number3
DOIs
Publication statusPublished - 30 May 2012
Externally publishedYes

Fingerprint

Adjoint Method
Heterogeneous Media
Advection
Interpolation
Formulation
Finite element method
Data storage equipment
Water
Interpolate
Numerical Dispersion
Discontinuous Galerkin Finite Element Method
Triangular Mesh
Unstructured Mesh
Term
Numerical integration
Injection
Restriction
Requirements
Approximation

Keywords

  • ELLAM
  • Heterogeneous media
  • Unphysical oscillations
  • Unstructured triangular meshes

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Applied Mathematics
  • Mechanical Engineering
  • Mechanics of Materials

Cite this

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abstract = "The Eulerian-Lagrangian Localized Adjoint Method (ELLAM) is well adapted for advection-dominated transport problems. The method can use large time steps because the advection term is accurately approximated without any CFL restriction. A new formulation of ELLAM was developed by Younes et al. (Adv. Water Resour. 2006; 29:1056-1074) for unstructured triangular meshes. This formulation uses only strategic numerical integration points and thus requires a very limited number of integration points (usually 1 per element). To avoid numerical dispersion due to interpolation when several time steps are used, the method continuously tracks characteristics, and only changes due to dispersion are interpolated at each time step. In this work, we study the applicability and efficiency of this formulation for highly heterogeneous domains. The results show that (i) this formulation remains efficient even for highly heterogeneous domains, (ii) special care must be taken for the approximation of the dispersive term when large time steps are used, (iii) interpolation at intermediate times can be used to reduce memory requirement for problems with a large number of elements and small time steps, and (iv) the method can be used successfully for heterogeneous problems including injection and pumping wells, and remains much more efficient than the discontinuous Galerkin finite element method even when small time steps are required.",
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AB - The Eulerian-Lagrangian Localized Adjoint Method (ELLAM) is well adapted for advection-dominated transport problems. The method can use large time steps because the advection term is accurately approximated without any CFL restriction. A new formulation of ELLAM was developed by Younes et al. (Adv. Water Resour. 2006; 29:1056-1074) for unstructured triangular meshes. This formulation uses only strategic numerical integration points and thus requires a very limited number of integration points (usually 1 per element). To avoid numerical dispersion due to interpolation when several time steps are used, the method continuously tracks characteristics, and only changes due to dispersion are interpolated at each time step. In this work, we study the applicability and efficiency of this formulation for highly heterogeneous domains. The results show that (i) this formulation remains efficient even for highly heterogeneous domains, (ii) special care must be taken for the approximation of the dispersive term when large time steps are used, (iii) interpolation at intermediate times can be used to reduce memory requirement for problems with a large number of elements and small time steps, and (iv) the method can be used successfully for heterogeneous problems including injection and pumping wells, and remains much more efficient than the discontinuous Galerkin finite element method even when small time steps are required.

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