Modeling of Hydrological Processes Using Unstructured and Irregular Grids: 2D Groundwater Application
Publication: Journal of Hydrologic Engineering
Volume 16, Issue 2
Abstract
To better handle landscape heterogeneities in distributed hydrological modeling, an earlier work proposed a discretization based on nested levels, which leads to fully unstructured modeling meshes. Upon such a discretization, traditional numerical solutions must be adapted, especially to describe lateral flow between the unstructured mesh elements. In this paper, we illustrated the feasibility of the numeric solution of the diffusion equation, representing groundwater flow, using unstructured meshes. Thus, a two-dimensional (2D) groundwater model (BOUSS2D), adapted to convex unstructured and irregular meshes was developed. It is based on the approximation of the 2D Boussinesq equation using numeric techniques suitable for nonorthogonal grids. The handling of vertical and horizontal aquifer heterogeneities is also addressed. The fluxes through the interfaces among joined mesh elements are estimated by the finite volume method and the gradient approximation method. Comparisons between the BOUSS2D predictions and analytical solutions or predictions from existing codes suggest the acceptable performance of the BOUSS2D model. These results therefore encourage the further development of hydrological models using unstructured meshes that are capable of better representing the landscape heterogeneities.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Special thanks go to the International Service of CEMAGREF for funding the stay of the second writer at CEMAGREF-Lyon.
References
Aavatsmark, I. (2002). “An introduction to multipoint flux approximations for quadrilateral grids.” Computat. Geosci., 6(3), 405–432.
Aavatsmark, I., Barkve, T., Bøe, Ø., and Mannseth, T. (1994). “Discretisation on non-orthogonal, curvilinear grids for multiphase flow.” Proc., 4th European Conf. on the Mathematics of Oil Recovery, Røros, Norway.
Abbott, M. B., Bathurst, J. C., Cunge, J. A., O’Connell, P. E., and Rasmussen, J. (1986a). “An introduction to the European Hydrological System—Systeme Hydrologique Europeen, ‘SHE’, 1: History and philosophy of a physically-based, distributed modeling system.” J. Hydrol., 87, 45–59.
Abbott, M. B., Bathurst, J. C., Cunge, J. A., O’Connell, P. E., and Rasmussen, J. (1986b). “An introduction to the European Hydrological System—Systeme Hydrologique Europeen, ‘SHE’, 2: Structure of a physically-based, distributed modeling system.” J. Hydrol., 87, 61–77.
Anderson, M., and Woessner, W. W. (1992). Applied groundwater modeling: Simulation of flow and advective transport, Academic, San Diego.
Barth, T. (1994). “Aspects of unstructured grids and finite volume solvers for the Euler and Navier-Stockes equation.” Proc., VKI Lectures Series, Van Kareman Institue, INIST-CNRS BELGIQUE.
Barth, T., and Ohlberger, M. (2004). “Finite volume methods: Foundation and analysis.” Encyclopedia of computational mechanics, 57, John Wiley & Sons, Ltd.
Branger, F., Braud, I., Viallet, P., and Debionne, S. (2008). “Modeling the influence of landscape management practices on the hydrology of a small agricultural catchment.” Proc., 8th Int. Conf. on Hydro-Sciences and Engineering (ICHE-2008), ICHE, Japan.
Cai, Z. (1990). “On the finite volume element method.” Numerische Mathematik, 58(1), 713–735.
Castany, G. (1966). Prospection et exploitation des eaux souterraines, Dunod, Paris.
Coudière, Y., Vila, J. P., and Villedieu, P. (1996). “Convergence of a finite volume scheme for a diffusion problem.” Finite volumes for complex applications: Problems and perspectives, F. Benkhaldoun and R. Vilsmeier, eds., Hermes, Paris, 161–168.
de Marsily, G. (1981). Quantitative hydrogeology: Groundwater hydrology for engineers, Ed Masson, Paris.
Dehotin, J. (2007). “Prise en compte de l’hétérogénéité spatiale des surfaces continentales dans la modélisation hydrologique spatialisée. Application au Haut-bassin de la Saône.” Ph.D. thesis, Université Joseph Fourier, Grenoble, France, ⟨http://cemadoc.cemagref.fr/exl-php/cadcgp.php?MODELE=vues/p_recherche_publication/home.html&VUES=p_recherche_publication⟩ (France).
Dehotin, J., and Braud, I. (2008). “Which spatial discretisation for distributed hydrological models? Proposition of a methodology and illustration for medium to large-scale catchments.” Hydrology Earth Syst. Sci., 12, 769–796.
Edwards, M. G. (2002). “Unstructured, control-volume distributed, full-tensor finite-volume schemes with flow based grids.” Comput. Geosci., 6(3–4), 433–452.
Edwards, M. G., and Rogers, C. (1994). “A flux continuous scheme for the full tensor pressure equation.” Proc., 4th European Conf. on the Mathematics of Oil Recovery, Røros, Norway.
Edwards, M. G., and Rogers, C. (1998). “Finite volume discretization with imposed flux continuity for general tensor pressure equation.” Comput. Geosci., 2, 259–290.
Eymard, R., Gallouet, T., and Herbin, R. (1997). “Finite volumes method.” Handbook of numerical analysis, P. Ciarlet and J. L. Lyons, eds., Vol. 7, 713–1020.
Eymard, R., Gutnic, M. l., and Hilhorst, D. (1999). “The finite volume method for Richards equation.” Comput. Geosci., 3(3/4), 259–294.
Ivanov, V. Y., Vivoni, E. R., Bras, R. L., and Entekhabi, D. (2004). “Catchment hydrologic response with a fully distributed triangulated irregular network model.” Water Resour. Res., 40(11), 23 p.
Jayantha, A. (2005). “A second order control-volume finite element least-squares strategy for simulating diffusion in strongly anisotropic media.” J. Comput. Math., 23, 1–16.
Jayantha, A., and Turner, I. (2001). “A comparison of gradient approximations for use in finite-volume computational models for two-dimensional diffusion equations.” Numer. Heat Transfer, Part B, 40, 367–390.
Jayantha, A., and Turner, I. (2003a). “Generalised finite volume strategies for simulating transport in strongly orthotropic porous media.” ANZIAM J., 44, C443–C463.
Jayantha, A., and Turner, I. (2003b). “On the use of surface interpolation techniques in generalised finite volume strategies for simulating transport in highly anisotropic porous media.” J. Comput. Appl. Math., 152, 199–216.
Loudyi, D., Falconer, R. A., and Lin, B. (2007). “Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications.” Adv. Water Resour., 30, 29–42.
McDonald, M. G., and Harbaugh, A. W. (1988). “A modular three-dimensional finite difference ground-water flow model.” U.S. Geology Survey techniques of water—Resources investigations, book 6, Department of the Interior, Reston, Va.
Murthy, J. Y., and Mathur, S. R. (1998). “Computation of anisotropic conduction using unstructured meshes.” Numer. Heat Transfer, Part B, 31, 195–215.
Pal, M., Edwards, M. G., and Lamb, A. L. (2006). “Convergence study of a family of flux-continuous, finite-volume schemes for the general tensor pressure equation.” Int. J. Numer. Methods Fluids, 51(9–10), 1177–1203.
Schlumberger Water Services (SWS). (2007). Visual MODFLOW premium demo tutorial, Waterloo, Canada.
Siek, J. G., and Lumsdaine, A. (1998a). “The matrix template library: A generic programming approach to high performance numerical linear algebra.” Proc., ECOOP Workshops, Springer (LNCS), Belgium.
Siek, J. G., and Lumsdaine, A. (1998b). “The matrix template library: A unifying framework for numerical linear algebra.” Proc., ECOOP Workshops, Springer (LNCS), Belgium.
Siek, J. G., Lumsdaine, A., and Lee, L. Q. (1998). “Generic programming for high performance numerical linear algebra.” Proc., SIAM Workshop on Object Oriented Methods for Inter-operable Scientic and Engineering Computing (OO’98), SIAM Press, United States.
Theis, C. V. (1935). “The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage.” Trans., Am. Geophys. Union, 16, 519–524.
Tison, L. J. (1953). “Theory of rivers in permanent movement, filtration phenomena.” Hydraul. Corses, 2, 265–430.
Turkel, E. (1985). “Accuracy of schemes with nonuniform meshes for compressible fluid flows.” ICASE Rep., NASA, United States, Virginia, 43–85.
Turner, I. W., and Ferguson, W. J. (1995). “An unstructured mesh cell-centered control volume method for simulating heat and mass transfert in porous media: Application to soft wood drying, part I: The isotropic model.” Appl. Math. Model., 19, 654–667.
van der Vorst, H. A. (1992). “A fast and smoothly converging variant of bi-CGSTAB for the solution of nonsymmetric linear systems.” SIAM J. Sci. Stat. Comput., 13, 631–644.
Verma, S., and Aziz, K. (1997). “A control volume scheme for flexible grids in reservoir simulation, SPE 37999.” Proc., 14th SPE Reservoir Simulation, Symp., SPE, Dallas, Tex., 215–227.
Viallet, P., et al. (2006). “Towards multi-scale integrated hydrological models using the LIQUID framework.” Proc., 7th Int. Conf. on Hydroinformatics, SHF, Nice, France, 542–549, ⟨http://www.hydrowide.com/liquid/⟩ (March 27, 2010).
Vivoni, E. R., Ivanov, V. Y., Bras, R. L., and Entekhabi, D. (2004). “Generation of triangulated irregular networks based on hydrologic similarity.” J. Hydrol. Eng., 9, 288–302.
Information & Authors
Information
Published In
Copyright
© 2011 ASCE.
History
Received: Mar 18, 2009
Accepted: Jul 13, 2010
Published online: Jul 19, 2010
Published in print: Feb 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.