{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:26:38Z","timestamp":1760243198588,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,12,29]],"date-time":"2015-12-29T00:00:00Z","timestamp":1451347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Modeling flow and transport in porous media requires the management of complexities related both to physical processes and to subsurface heterogeneity. A thorough approach needs a great number of spatially-distributed phenomenological parameters, which are seldom measured in the field. For instance, modeling a phreatic aquifer under high water extraction rates is very challenging, because it requires the simulation of variably-saturated flow. 3D steady groundwater flow is modeled with YAGMod (yet another groundwater flow model), a model based on a finite-difference conservative scheme and implemented in a computer code developed in Fortran90. YAGMod simulates also the presence of partially-saturated or dry cells. The proposed algorithm and other alternative methods developed to manage dry cells in the case of depleted aquifers are analyzed and compared to a simple test. Different approaches yield different solutions, among which, it is not possible to select the best one on the basis of physical arguments. A possible advantage of YAGMod is that no additional non-physical parameter is needed to overcome the numerical difficulties arising to handle drained cells. YAGMod also includes a module that allows one to identify the conductivity field for a phreatic aquifer by solving an inverse problem with the comparison model method.<\/jats:p>","DOI":"10.3390\/computation4010002","type":"journal-article","created":{"date-parts":[[2015,12,29]],"date-time":"2015-12-29T10:00:08Z","timestamp":1451383208000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Modeling Groundwater Flow in Heterogeneous Porous Media with YAGMod"],"prefix":"10.3390","volume":"4","author":[{"given":"Laura","family":"Cattaneo","sequence":"first","affiliation":[{"name":"Universit\u00e0 degli Studi di Milano, Dipartimento di Scienze della Terra \u201cA. Desio\u201d, via Cicognara 7, I-20129 Milano, Italy"},{"name":"CNR-IDPA (Consiglio Nazionale delle Ricerche, Istituto per la Dinamica dei Processi Ambientali), via Mario Bianco 9, I-20131 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Comunian","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Milano, Dipartimento di Scienze della Terra \u201cA. Desio\u201d, via Cicognara 7, I-20129 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovanna","family":"De Filippis","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Milano, Dipartimento di Scienze della Terra \u201cA. Desio\u201d, via Cicognara 7, I-20129 Milano, Italy"},{"name":"CINFAI, Consorzio Interuniversitario Nazionale per la Fisica delle Atmosfere e delle Idrosfere, Piazza Niccol\u00f2 Mauruzi 17, I-62029 Tolentino (MC), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6703-5748","authenticated-orcid":false,"given":"Mauro","family":"Giudici","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Milano, Dipartimento di Scienze della Terra \u201cA. Desio\u201d, via Cicognara 7, I-20129 Milano, Italy"},{"name":"CNR-IDPA (Consiglio Nazionale delle Ricerche, Istituto per la Dinamica dei Processi Ambientali), via Mario Bianco 9, I-20131 Milano, Italy"},{"name":"CINFAI, Consorzio Interuniversitario Nazionale per la Fisica delle Atmosfere e delle Idrosfere, Piazza Niccol\u00f2 Mauruzi 17, I-62029 Tolentino (MC), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chiara","family":"Vassena","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Milano, Dipartimento di Scienze della Terra \u201cA. Desio\u201d, via Cicognara 7, I-20129 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,29]]},"reference":[{"key":"ref_1","unstructured":"Bear, J. (1979). Hydraulics of Groundwater, Springer-Verlag."},{"key":"ref_2","unstructured":"De Marsily, G. (1986). Quantitative Hydrogeology\u2014Groundwater Hydrology for Engineers, Academic Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1111\/j.1745-6584.2001.tb02474.x","article-title":"Improved calculations for dewatered cells in MODFLOW","volume":"39","author":"Doherty","year":"2001","journal-title":"Groundwater"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1111\/j.1745-6584.2009.00555.x","article-title":"A stable and efficient numerical algorithm for unconfined aquifer analysis","volume":"47","author":"Keating","year":"2009","journal-title":"Groundwater"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.1745-6584.2011.00829.x","article-title":"Approaches to the simulation of unconfined flow and perched groundwater flow in MODFLOW","volume":"50","author":"Bedekar","year":"2012","journal-title":"Groundwater"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Niswonger, R.G., Panday, S., and Ibaraki, M. (2011). MODFLOW-NWT, a Newton Formulation for MODFLOW-2005, US Geological Survey Techniques and Methods.","DOI":"10.3133\/tm6A37"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1289\/ehp.898377","article-title":"The hydrogeological role of an aquitard in preventing drinkable water well contamination: A case study","volume":"83","author":"Ponzini","year":"1989","journal-title":"Environ. Health Perspect."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S0037-0738(98)00145-6","article-title":"Effects of sedimentary heterogeneity on groundwater flow in a quaternary pro-glacial delta environment: Joining facies analysis and numerical modelling","volume":"129","author":"Bersezio","year":"1999","journal-title":"Sediment. Geol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113","DOI":"10.5194\/hess-4-113-2000","article-title":"A quasi three dimensional model of water flow in the subsurface of Milano (Italy): The stationary flow","volume":"4","author":"Giudici","year":"2000","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1111\/j.1745-6584.2002.tb02534.x","article-title":"Is the forward problem of ground water hydrology always well posed?","volume":"40","author":"Valota","year":"2002","journal-title":"Ground Water"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jhydrol.2005.10.016","article-title":"Modeling heterogeneity of gravel-sand, braided stream, alluvial aquifers at the facies scale","volume":"325","author":"Zappa","year":"2006","journal-title":"J. Hydrol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.2110\/jsr.2006.091","article-title":"Geostatistical simulation and numerical upscaling, to model ground water flow in a sandy-gravel, braided river, aquifer analogue","volume":"76","author":"Felletti","year":"2006","journal-title":"J. Sediment. Res."},{"key":"ref_13","first-page":"207","article-title":"Some lessons from modelling ground water flow in the metropolitan area of Milano (Italy) at different scales","volume":"76","author":"Giudici","year":"2007","journal-title":"Mem. Descr. Della Carta Geol. d\u2019Italia"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1016\/j.pce.2008.01.004","article-title":"The importance of observations on fluxes to constrain ground water model calibration","volume":"33","author":"Vassena","year":"2008","journal-title":"Phys. Chem. Earth A B C"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1007\/s10040-009-0523-2","article-title":"Assessment of the role of facies heterogeneity at the fine scale by numerical transport experiments and connectivity indicators","volume":"18","author":"Vassena","year":"2010","journal-title":"Hydrogeol. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/s10040-011-0822-2","article-title":"Modeling water resources of an highly irrigated alluvial plain: Coupling and calibrating soil and ground water models","volume":"20","author":"Vassena","year":"2011","journal-title":"Hydrogeol. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1007\/s12665-012-1631-1","article-title":"Modeling hydrostratigraphy and groundwater flow of a fractured and karst aquifer in a Mediterranean basin (Salento peninsula, southeastern Italy)","volume":"67","author":"Giudici","year":"2012","journal-title":"Environ. Earth Sci."},{"key":"ref_18","first-page":"518","article-title":"An approximate solution for the inverse problem in hydraulics","volume":"49","author":"Scarascia","year":"1972","journal-title":"L\u2019Energia Elettr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1029\/WR018i003p00597","article-title":"Identification of aquifer transmissivities: The comparison model method","volume":"18","author":"Ponzini","year":"1982","journal-title":"Water Resour. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/BF00233178","article-title":"The comparison model method: A new arithmetic approach to the discrete inverse problem of groundwater hydrology, 1, One-dimensional flow","volume":"3","author":"Ponzini","year":"1988","journal-title":"Transp. Porous Media"},{"key":"ref_21","unstructured":"Associazione Irrigazione Est Sesia (1979). Le Acque Sotterranee Della Pianura Irrigua Novarese-Lomellina. Studi e Ricerche Per La Realizzazione di un Modello Gestionale (Subsurface Water of Irrigated Novara-Lomellina Plain. Study and Research for a Managing Model Realization.), Associazione Irrigazione Est Sesia. (In Italian)."},{"key":"ref_22","first-page":"469","article-title":"Optimierung der Ben\u00f6tigten daten f\u00fcr ein numerisches Modell der Grundwasserbewirtschaftung im Lockergestein (Optimization of the required data for a numerical model of groundwater management in soil)","volume":"63","author":"Beatrizotti","year":"1983","journal-title":"Gas Wasser Abwasser"},{"key":"ref_23","unstructured":"Benoit, N., Pasquier, P., Marcotte, D., and Nastev, M. (2005, January 6\u20139). Conditional stochastic inverse modelling of the Ch\u00e2teauguay river aquifers. Proceedings of the ModelCARE 2005, The Hague (Scheveningen), The Netherlands."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Hill, M.C., Kavetski, D., Clark, M., Ye, M., Arabi, M., Lu, D., Foglia, L., and Mehl, S. (2015). Practical Use of Computationally Frugal Model Analysis Methods. Groundwater.","DOI":"10.1111\/gwat.12330"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Harbaugh, A.W. (2005). MODFLOW-2005, the US Geological Survey Modular Ground-Water Model: The Ground-Water Flow Process.","DOI":"10.3133\/tm6A16"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1190\/1.1442691","article-title":"Identification of thermal conductivities by temperature gradient profiles: One-dimensional steady state flow","volume":"54","author":"Ponzini","year":"1989","journal-title":"Geophysics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1934","DOI":"10.1016\/j.advwatres.2006.02.001","article-title":"Steady- and transient-state inversion in hydrogeology by successive flux estimation","volume":"29","author":"Pasquier","year":"2006","journal-title":"Adv. Water Resour."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1016\/j.advwatres.2007.03.002","article-title":"Comment to \u201cSteady- and transient-state inversion in hydrogeology by successive flux estimation\u201d by P. Pasquier and D. Marcotte","volume":"30","author":"Ponzini","year":"2007","journal-title":"Adv. Water Resour."},{"key":"ref_29","unstructured":"Pasquier, P. (2005). R\u00e9solution du probl\u00e9me inverse en hydrog\u00e9ologie par une estimation successive des flux (Solving hydrogeological inverse problem by successive flux estimation). [Ph.D. Thesis, \u00c9cole Polytechnique de Montr\u00e9al]."},{"key":"ref_30","unstructured":"Renard, P., and Demougeot-Renard, H.F.R. Solving the Groundwater Inverse Problem by Successive Flux Estimation. Proceedings of the Fifth European Conference on Geostatistics for Environmental Applications."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"De Filippis, G., Giudici, M., Negri, S., and Margiotta, S. (2015). Conceptualization and preliminary characterization of a karst, coastal aquifer in the Mediterranean area of the Taranto gulf (southern Italy). Environ. Earth Sci., submitted.","DOI":"10.1007\/s12665-016-5507-7"},{"key":"ref_32","first-page":"240","article-title":"A critical review of the properties of forward and inverse problems in groundwater hydrology","volume":"Volume 320","author":"Refsgaard","year":"2008","journal-title":"Calibration and Reliability in Groundwater Modelling: Credibility of Modelling"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s11242-007-9142-3","article-title":"Spectral analysis of the balance equation of ground water hydrology","volume":"72","author":"Giudici","year":"2008","journal-title":"Transp. Porous Media"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1029\/WR012i001p00057","article-title":"An integrated finite difference method for analyzing fluid flow in porous media","volume":"12","author":"Narasimhan","year":"1976","journal-title":"Water Resour. Res."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:55:00Z","timestamp":1760216100000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,29]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["computation4010002"],"URL":"https:\/\/doi.org\/10.3390\/computation4010002","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2015,12,29]]}}}