The velocity oriented approach revisited

• Autorzy: Nawalany M. , Zijl W.
• Konferencja: Groundwater quality sustainability : XXXVIII IAH Congress in Kraków
• Języki publikacji: EN

Abstrakty

EN

A great deal of hydrogeological situations requires an extremely accurate calculation of the 3-dimensional groundwater discharge rates in the subsoil. Examples are: hydrology of wetlands, water balances of aquatic ecosystems depending on groundwater recharge, river-groundwater interaction, advective transport of pollution underneath waste disposal sites, particle trajectories in aquifer-aquitard systems with contrasting heterogeneities and many others. Numerical determination of the vertical groundwater velocity is a notoriously difficult problem. In nature this component may be two or three orders of magnitude smaller than the horizontal velocity components. In such cases application of Darcy’s law to the numerically calculated hydraulic heads obtained from a finite difference or finite element model may lead to relatively inaccurate vertical velocities. More specifically, when estimating vertical velocity components in cases where the Dupuit approximation – negligible vertical head gradient – holds, numerical differentiation of hydraulic heads yields zero vertical velocity. In the 1980s of the last century Zijl and Nawalany proposed to invert the order of calculating the velocity field by eliminating the head from Darcy’s law and to consider the Darcy velocity as the primary variable. For 2-dimensional flow this was already common practice and the challenge was a 3-dimensional extension, which was called the Velocity Oriented Approach (VOA). In two dimensions such methods were conventionally based on a stream function as primary variable. However, at that time application of a 3D stream function was not feasible and, therefore, the Darcy velocity itself was considered as the primary variable. This approach has been proven to yield a high accuracy for all three components of the specific discharge, including the relatively small vertical component, especially in cases where the subsoil is smoothly heterogeneous in the horizontal directions. In the 1990s the mixed-hybrid finite element method was developed. The physical interpretation of this method shows the way how to liberate the VOA from its smoothness requirement by introduction of a practical applicable 3D stream function. In conclusion, the velocity oriented approach indicates a change in paradigm regarding the accurate calculation of specific discharge in groundwater flow.

Słowa kluczowe

EN

velocity oriented approach; continuity of water flux; groundwater flow modeling

• Wydawca: Państwowy Instytut Geologiczny - Państwowy Instytut Badawczy
• Czasopismo: Biuletyn Państwowego Instytutu Geologicznego
• Rocznik: 2010
• Tom: nr 441 Hydrogeologia z. 10
• Strony: 113--121
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Nawalany M.

• Warsaw University of Technology, Faculty of Environmental Engineering, Nowowiejska 20, 00-653 Warszawa, Poland

autor

Zijl W.

• Vrije Universiteit Brussel, Departament of Hydrology and Hydraulic Engineering, Pleinlaan 2, 1050 Brussels, Belgium

Bibliografia

• 1. KAASSCHIETER E.F., 1988 — Preconditioned conjugate gradients for solving singular systems. J. Comput. Appl. Math., 24: 265–275.
• 2. KAASSCHIETER E.F., 1990 — Preconditioned Conjugate Gradients and Mixed-Hybrid Finite Elements for the Solution of Potential Flow Problems. [PhD thesis] Delft University of Technology, Delft.
• 3. KAASSCHIETER E.F., HUIJBEN A.J.M., 1992 — Mixed-hybrid finite elements and streamline computations for the potential flow problem. Numer. Meth. Part. D. E., 8, 221–226.
• 4. MOHAMMED G.A., 2009 — Modeling Groundwater-Surface Water Interaction and Development of an Inverse Groundwater Modeling Methodology. [PhD thesis] Vrije Universiteit Brussel (VUB), Brussels.
• 5. MOHAMMED G.A., ZIJL W., BATELAAN O., DE SMEDT F., 2009 — Comparison of two mathematical models for 3D groundwater flow: block-centered heads and edge-based stream functions. Transp. Porous Media, 79: 469–485.
• 6. NAWALANY M., 1986a — Numerical model for the transport velocity representation of groundwater flow. In: VIth Int. Conf. on Finite Elements in Water Resources, Lisbon.
• 7. NAWALANY M., 1986b — Environmental applications of the transport velocity representation for groundwater flow. In: Envirosoft’86, Los Angeles.
• 8. NAWALANY M., 1990 — Regional vs. local computations of groundwater flow. In: VIIIth Int. Conf. on Computational Methods in Water Resources, Venice.
• 9. NAWALANY M., 1992 — Decoupling the velocity oriented groundwater flow equations for the third type boundary conditions In: IXth Int. Conf. on Computational Methods in Water Resources, Denver.
• 10. TÓTH J., 2009 — Gravitational systems of groundwater flow: theory, evaluation, utilization. Cambridge University Press, Cambridge.
• 11. TRYKOZKO A., 1997 — A Numerical Model for Hydraulic Isolation of Waste Disposal. [PhD thesis] Warsaw Politechnics, Warsaw [in Polish].
• 12. TRYKOZKO A., ZIJL W., BOSSAVIT A., 2004 — Nodal and mixed finite elements for the numerical homogenization of 3D permeability. Computat. Geosci., 5: 61–84.
• 13. WEISER A.,WHEELER M.F., 1988 — On convergence of block-centered finite differences for elliptic problems. SIAM J. Numer. Anal., 25: 351–357.
• 14. ZIJL W., 2005 — Face-centered and volume-centered discrete analogs of the exterior differential equations governing porous medium flow. Transp. Porous Media, 60: 109–133.
• 15. ZIJL W., NAWALANY M., 1993 — Natural groundwater flow. Lewis Publishers/CRC Press, Boca Raton.
• 16. ZIJL W., NAWALANY M., 2004 — The edge-based face element method for 3D-stream function and flux calculations in porous media flow. Transp. Porous Media, 55: 361–382.
• 17. ZIJL W., NAWALANY M., PASVEER F., 1987 — Numerical simulation of fluid flow in porous media using the Cyber 205 and the Delft Parallel Processor. In: Algorithms and Applications on Vector and Parallel Computers (ed. H.J.J. te Riele et al.). Elsevier Science Publisher (North Holland).