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.
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This work was supported in part by Norwegian Research Council grants 233736 and 228832 and the research project GEOCON, Advancing GEOlogical, geophysical and CONtaminant monitoring technologies for contaminated site investigation (contract 1305-00004B). The funding for GEOCON is provided by Innovation Fund Denmark.
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Boon, W.M., Balbarini, N., Binning, P.J. et al. Efficient water table evolution discretization using domain transformation. Comput Geosci 21, 3–11 (2017). https://doi.org/10.1007/s10596-016-9597-9
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DOI: https://doi.org/10.1007/s10596-016-9597-9