dc.contributor.author | Chapuis R.P | |
dc.contributor.author | Duhaime F | |
dc.contributor.author | Weber S | |
dc.contributor.author | Marefat V | |
dc.contributor.author | Zhang L | |
dc.contributor.author | Blessent D | |
dc.contributor.author | Bouaanani N | |
dc.contributor.author | Pelletier D. | |
dc.date.accessioned | 2023-10-24T19:24:23Z | |
dc.date.available | 2023-10-24T19:24:23Z | |
dc.date.created | 2023 | |
dc.identifier.issn | 0266352X | |
dc.identifier.uri | http://hdl.handle.net/11407/7943 | |
dc.description.abstract | Groundwater numerical studies do not include H-convergence tests, contrarily to computational fluid dynamics (CFD) studies. In regional groundwater studies with pumping wells, the grids may exceed 106 nodes. The authors examine whether H-convergence tests can help to calculate the numerical errors made by using large grids with element sizes in the 10–500 m range. First, the differences between numerical and mathematical convergences are explained. Then, a method is proposed that most users may easily implement for their groundwater studies to assess the numerical error linked to the element size, ES, and the aspect ratio, AR. A single problem, forming a simple part of a regional groundwater study, was examined and solved by using many uniform grids. The results show that most regional groundwater studies make errors in the 50–500% range, considering their usual values for ES and AR. The numerical convergence domain, NCD, is shown to be larger than the mathematical convergence domain, MCD. This means that the codes can provide a numerical solution for a large range of ES values, even for many values outside the MCD, which is a risky situation for designers who are unaware of the difference between NCD and MCD and ignore the H-convergence tests. © 2023 Elsevier Ltd | eng |
dc.language.iso | eng | |
dc.publisher | Elsevier Ltd | |
dc.relation.isversionof | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85164226524&doi=10.1016%2fj.compgeo.2023.105615&partnerID=40&md5=1bcce6252f005edb7eb50af6ba230043 | |
dc.source | Comput. Geotech. | |
dc.source | Computers and Geotechnics | eng |
dc.subject | Groundwater | eng |
dc.subject | Mathematical convergence | eng |
dc.subject | Numerical analysis | eng |
dc.subject | Numerical convergence | eng |
dc.subject | Pumping | eng |
dc.title | Numerical convergence does not mean mathematical convergence: Examples of simple saturated steady-state groundwater models with pumping wells | eng |
dc.type | Article | |
dc.rights.accessrights | info:eu-repo/semantics/restrictedAccess | |
dc.publisher.program | Ingeniería Ambiental | spa |
dc.type.spa | Artículo | |
dc.identifier.doi | 10.1016/j.compgeo.2023.105615 | |
dc.relation.citationvolume | 162 | |
dc.publisher.faculty | Facultad de Ingenierías | spa |
dc.affiliation | Chapuis, R.P., Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, P.O. Box 6079, Sta. CV, Montreal (Quebec), H3C 3A7, Canada | |
dc.affiliation | Duhaime, F., Department of Construction Engineering, École de Technologie Supérieure, 1100 Notre-Dame west, Montreal (Quebec), H3C 1K3, Canada | |
dc.affiliation | Weber, S., Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, P.O. Box 6079, Sta. CV, Montreal (Quebec), H3C 3A7, Canada, Department of Construction Engineering, École de Technologie Supérieure, 1100 Notre-Dame west, Montreal (Quebec), H3C 1K3, Canada | |
dc.affiliation | Marefat, V., Geotechnical Engineering Team Leader, BBA, 2200 Boul. Robert-Bourassa, Suite 300, Montreal, QC H3A 2A5, Canada | |
dc.affiliation | Zhang, L., College of Construction Engineering, Jilin University, 938 Ximinzhu St., Changchun, 130021, China | |
dc.affiliation | Blessent, D., University of Medellin, Environmental Engineering Program, Medellin, 050026, Colombia | |
dc.affiliation | Bouaanani, N., Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, P.O. Box 6079, Sta. CV, Montreal (Quebec), H3C 3A7, Canada | |
dc.affiliation | Pelletier, D., Department of Mechanical Engineering, Polytechnique Montréal, P.O. Box 6079, Sta. CV, Montreal (Quebec), H3C 3A7, Canada | |
dc.relation.references | Baliga, B.R., Lokhmanets, I., Generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions (2016) Int. J. Num. Methods Heat & Fluid Flow, 26 (3-4), pp. 1121-1144 | |
dc.relation.references | Banks, J.W., Aslam, T., Rider, W.J., On sub-linear convergence for linearly degenerate waves in capturing schemes (2008) J. Comput. Phys., 227 (14), pp. 6985-7002 | |
dc.relation.references | Baptiste, N., Chapuis, R.P., What maximum permeability can be measured with a monitoring well? (2015) Eng. Geol., 184, pp. 111-118 | |
dc.relation.references | Bear, J., Jacobs, M., On the movement of water bodies injected into aquifers (1965) J. Hydrol., 3, pp. 37-57 | |
dc.relation.references | Brock, J.S., Bounded numerical error estimates for oscillatory convergence of simulation data (2007) AIAA Paper, pp. 2007-4091 | |
dc.relation.references | Brunner, P., Simmons, C.T., Hydrogeosphere: A fully integrated, physically based hydrological model (2012) Ground Water, 50 (2), pp. 170-176 | |
dc.relation.references | Celik, I., Li, J., Hu, G., Shaffer, C., Limitations of Richardson extrapolation and some possible remedies (2005) J. Fluids Eng., 127 (4), pp. 795-805 | |
dc.relation.references | Chapuis, R.P., Controlling the quality of ground water parameters: some examples (1995) Can. Geotech. J., 32 (1), pp. 172-177 | |
dc.relation.references | Chapuis, R.P., Numerical modeling of reservoirs or pipes in groundwater seepage (2009) Comp. Geotech., 36 (5), pp. 895-901 | |
dc.relation.references | Chapuis, R.P., Proof of multiplicity of solutions for groundwater seepage in recharged heterogeneous unconfined aquifers (2016) Int. J. Num. Anal. Methods Geomech., 40 (14), pp. 1988-2002 | |
dc.relation.references | Chapuis, R.P., A simple reason explains why it is so difficult to assess groundwater ages and contamination ages (2017) Sci. Total Envir., 593, pp. 109-115 | |
dc.relation.references | Chapuis, R.P., Tracer tests in stratified alluvial aquifers: predictions of effective porosity and longitudinal dispersivity versus field values (2019) Geotech. Test. J., 42 (2), pp. 407-432 | |
dc.relation.references | Chapuis, R.P., Evaluating at three scales the hydraulic conductivity in an unconfined and stratified alluvial aquifer (2021) Geotech. Test. J., 44 (4), pp. 948-970 | |
dc.relation.references | Chapuis, R.P., The physical reasons to have underdamped or oscillating variable-head (slug) tests: A review and a clarification (2022) Geotech. Testing J., 45 (1), pp. 244-279 | |
dc.relation.references | Chapuis, R.P., Aubertin, M., A simplified method to estimate saturated and unsaturated seepage through dikes under steady-state conditions (2001) Can. Geotech. J., 38 (6), pp. 1321-1328 | |
dc.relation.references | Chapuis, R.P., Saucier, A., A leaky aquifer below Champlain Sea clay: Closed–form solutions for natural seepage (2013) Ground Water, 51 (6), pp. 960-967 | |
dc.relation.references | Chapuis, R.P., Chenaf, D., Bussière, B., Aubertin, M., Crespo, R., A user's approach to assess numerical codes for saturated and unsaturated seepage conditions (2001) Can. Geotech. J., 38 (5), pp. 1113-1126 | |
dc.relation.references | Chapuis, R.P., Chenaf, D., Acevedo, N., Marcotte, D., Chouteau, M., Unusual drawdown curves for a pumping test in an unconfined aquifer at Lachenaie, Quebec: Field data and numerical modeling (2005) Can. Geotech. J., 42 (4), pp. 1133-1144 | |
dc.relation.references | Chenaf, D., Chapuis, R.P., Seepage face height, water table position, and well efficiency for steady state (2007) Ground Water, 45 (2), pp. 168-177 | |
dc.relation.references | Chesnaux, R., Molson, J., Chapuis, R.P., An analytical solution for ground water transit time through unconfined aquifers (2005) Ground Water, 43 (4), pp. 511-517 | |
dc.relation.references | Coleman, H.W., Stern, F., Di Mascio, A., Campana, E., The problem with oscillatory behavior in grid convergence studies (2001) J. Fluids Eng., 123 (2), pp. 438-439 | |
dc.relation.references | Delbar, A., Chapuis, R.P., Tracer tests in a straight uniform flow: New equations considering the distortion of flow lines around the well (2021) J. Cont. Hydrol., 239 | |
dc.relation.references | Duhaime, F., Chapuis, R.P., A joint analysis of cavity and pore volume changes for pulse tests conducted in soft clay deposits (2014) Int. J. Num. Anal. Meth. Geomech., 38 (9), pp. 903-924 | |
dc.relation.references | Duhaime, F., Chapuis, R.P., Marefat, V., Benabdallah, E.M., Influence of seasonal hydraulic head changes on slug tests conducted in shallow low-permeability soils (2017) Eng. Geol., 228, pp. 385-394 | |
dc.relation.references | Fala, O., Molson, J., Aubertin, M., Dawood, I., Bussière, B., Chapuis, R.P., A numerical modelling approach to assess long–term unsaturated flow and geochemical transport in a waste rock pile (2013) Int. J. Mining Reclam. Envir., 27 (1), pp. 38-55 | |
dc.relation.references | Ferrandon, J., (1948), Les lois d’écoulement de filtration [The seepage filtration laws]. Le Génie Civil 125 (2), 24–28 (in French). No doi | |
dc.relation.references | Goderniaux, P., Brouyère, S., Fowler, H.J., Blenkinsop, S., Therrien, R., Orban, P., Dassargues, A., Large scale surface-subsurface hydrological model to assess climate change impacts on groundwater reserves (2009) J. Hydrol., 373 (1-2), pp. 122-138 | |
dc.relation.references | Hvilshøj, S., Jensen, K.H., Barlebo, H.C., Madsen, B., Analysis of pumping tests of partially penetrating wells in an unconfined aquifer using inverse numerical optimization (1999) Hydrogeo. J., 7, pp. 365-379 | |
dc.relation.references | Jimenez, M., Velasquez, N., Jimenez, J.E., Barco, J., Blessent, D., Lopez-Sanchez, J., Cordoba Castrillon, S., Múnera, J.C., Sequential surface and subsurface flow modeling in a tropical aquifer under different rainfall scenarios (2022) Environ. Model. Software, 149 | |
dc.relation.references | Mao, D., Yeh, T.C.J., Wan, L., Hsu, K.C., Lee, C.H., Wen, J.C., Necessary conditions for inverse modeling of flow through variably saturated porous media (2013) Adv. Water Res., 52, pp. 50-61 | |
dc.relation.references | Marefat, V., Chapuis, R.P., Duhaime, F., Le Borgne, V., Fully grouted piezometers under transient flow conditions: Field performance and numerical studies (2019) Geotech. Test. J., 42 (2), pp. 433-456 | |
dc.relation.references | Morin, P., Nochetto, R.H., Siebert, K.G., Convergence of adaptive finite element methods (2002) SIAM Rev., 44 (4), pp. 631-658. , No doi | |
dc.relation.references | Piggott, A.R., Bobba, A.G., (1996), https://doi.org/10.1061/(ASCE)0733-9496122:1(1), Novakowski, K.S. 1996. Regression and inverse analysis in regional ground-water modelling. J. Water Res. Planning Manag.-ASCE 122(1), 1–10 | |
dc.relation.references | Richards, L.A., Capillary conduction of liquids through porous medium (1931) Physics, 1 (5), pp. 318-333 | |
dc.relation.references | Richardson, L.F., Gaunt, J.A., The deferred approach to the limit. Part I. Single lattice. Part II. Interpenetrating lattices (1937) Philos. Trans. Royal Soc. London, Ser. A, 226, pp. 299-361 | |
dc.relation.references | Roache, P.J., Perspective: A method for uniform reporting of grid refinement studies (1994) ASME J. Fluids Eng., 116 (3), pp. 405-413 | |
dc.relation.references | Roache, P.J., Verification and Validation in Computational Science and Engineering (1998), Hermosa Publishers New Mexico | |
dc.relation.references | Roache, P.J., Fundamentals of verification and validation (2009), Hermosa Publishers Socorro, NM | |
dc.relation.references | Roache, P.J., Knupp, P.M., Completed Richardson extrapolation (1993) Comm. Num. Methods Eng., 9 (5), pp. 365-374 | |
dc.relation.references | Roy, C.J., Oberkampf, W.L., A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing (2011) Comp. Methods Applied Mech. Eng., 200 (25-28), pp. 2131-2144 | |
dc.relation.references | (2010), Roy, C.J. Review of discretization error estimators in scientific computing. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4–7 Jan. 2010, Orlando, Florida, 29 p | |
dc.relation.references | Stern, F., Wilson, R.V., Coleman, H.W., (1999), Paterson, E.G. Verification and Validation of CFD Simulations. IIHR Report No. 407, Iowa Institute of Hydraulic Research, College of Engineering, The University of Iowa, Iowa City, IA 52242 | |
dc.relation.references | Stern, F., Wilson, R.V., Coleman, H.W., Paterson, E.G., Comprehensive approach to verification and validation of CFD simulations Part 1: Methodology and procedures (2001) J. Fluids Eng., 123 (4), pp. 793-802 | |
dc.relation.references | Thiem, G., Hydrologische methoden (1906), Gebhardt Leipzig, Germany | |
dc.relation.references | Thwaites, B., Approximate calculation of the laminar boundary layer (1949) Aeronaut. Quart., 1 (3), pp. 245-280 | |
dc.relation.references | Zhang, Y., Nonlinear inversion of an unconfined aquifer: simultaneous estimation of heterogeneous hydraulic conductivities, recharge rates, and boundary conditions (2014) Transp. Porous Media, 102 (2), pp. 275-299 | |
dc.relation.references | Zhang, L., Chapuis, R.P., Recovery test after a constant-head test in a monitoring well: interpretation methods and new findings (2019) Eng. Geol., 259 | |
dc.relation.references | Zhang, L., Chapuis, R.P., Marefat, V., Numerical values of shape factors for field permea-bility tests in unconfined aquifers (2020) Acta Geotech., 15 (5), pp. 1243-1257 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | |
dc.identifier.reponame | reponame:Repositorio Institucional Universidad de Medellín | |
dc.identifier.repourl | repourl:https://repository.udem.edu.co/ | |
dc.identifier.instname | instname:Universidad de Medellín | |