Efficient water table evolution discretization using domain transformation

W. M. Boon, Nicola Balbarini, Philip John Binning, J. M. Nordbotten

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem is greatly simplified by using a mapping from the physical domain to a reference domain and is then further reduced to a single, (nonlinear) partial differential equation. We show well-posedness of the approach and propose a stable and convergent discretization scheme. Numerical results are presented supporting the theory.
Original languageEnglish
JournalComputational Geosciences
Volume21
Issue number1
Pages (from-to)3-11
Number of pages9
ISSN1420-0597
DOIs
Publication statusPublished - 2017

Keywords

  • Domain tranformation
  • Water table evolution
  • Finite element method

Cite this

Boon, W. M. ; Balbarini, Nicola ; Binning, Philip John ; Nordbotten, J. M. / Efficient water table evolution discretization using domain transformation. In: Computational Geosciences. 2017 ; Vol. 21, No. 1. pp. 3-11.
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Efficient water table evolution discretization using domain transformation. / Boon, W. M.; Balbarini, Nicola; Binning, Philip John; Nordbotten, J. M.

In: Computational Geosciences, Vol. 21, No. 1, 2017, p. 3-11.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Efficient water table evolution discretization using domain transformation

AU - Boon, W. M.

AU - Balbarini, Nicola

AU - Binning, Philip John

AU - Nordbotten, J. M.

PY - 2017

Y1 - 2017

N2 - Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem is greatly simplified by using a mapping from the physical domain to a reference domain and is then further reduced to a single, (nonlinear) partial differential equation. We show well-posedness of the approach and propose a stable and convergent discretization scheme. Numerical results are presented supporting the theory.

AB - Domain transformation methods are useful techniques for solving problems on non-stationary domains. In this work, we consider the evolution of the water table in an unconfined aquifer. This nonlinear, time-dependent problem is greatly simplified by using a mapping from the physical domain to a reference domain and is then further reduced to a single, (nonlinear) partial differential equation. We show well-posedness of the approach and propose a stable and convergent discretization scheme. Numerical results are presented supporting the theory.

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KW - Water table evolution

KW - Finite element method

U2 - 10.1007/s10596-016-9597-9

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JF - Computational Geosciences

SN - 1420-0597

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