Efficient water table evolution discretization using domain transformation

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

doi:10.1007/s10596-016-9597-9

Efficient water table evolution discretization using domain transformation

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

University of Bergen

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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 language	English
Journal	Computational Geosciences
Volume	21
Issue number	1
Pages (from-to)	3-11
Number of pages	9
ISSN	1420-0597
DOIs	https://doi.org/10.1007/s10596-016-9597-9
Publication status	Published - 2017

Keywords

Domain tranformation
Water table evolution
Finite element method

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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 - Finite element method

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Efficient water table evolution discretization using domain transformation

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