Downscaling: a complement to homogenization
Anna Trykozko 1, Geert Brouwer 2, Wouter Zijl 31 ICM Interdisciplinary Centre of Mathematical and Computational Modelling, University of Warsaw, Pawinskiego 5a, PL-02-106 Warsaw, Poland
2 TNO Construction and Built Environment, P.O. Box 80015, NL-3508 TA Utrecht, The Netherlands
3 Z-consult, c/o Laboratory of Hydrology, Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
A groundwater flow model based on a specified hydraulic conductivity field in the modeling domain has a unique solution only if either the head or the normal flux component is specified on the boundary. On the other hand, specification of both head and flux as boundary conditions may be used to determine the conductivity field, or at least improve an initial estimate of it. The specified head and flux data may be obtained from measurements on the boundary, including the wells. We have presented a relatively simple, but instructive approach: the Double Constraint (DC) method. The method is exemplified in the context of upscaling and its inverse: downscaling. The DC method is not only instructive, but also easy to implement because it is based on existing groundwater modeling software. The exemplifications shown in this paper related to downscaling and demonstrate that the DC method has practical relevance.
AMS subject classifications: 31B20, 35J25, 65C20
Key words: Double Constraint method; Dowscaling; Inverse problems; Conductivity
Email: A.Trykozko@icm.edu.pl (A. Trykozko), firstname.lastname@example.org (G. Brouwer), email@example.com (W. Zijl)