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| Titel |
A novel numerical technique for the high-precision simulation of flow processes related to artificial recharge |
| VerfasserIn |
David Stevens, Paolo Orsini, Henry Power, Herve Morvan, Jacob Bensabat |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250041699
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| Zusammenfassung |
| This paper presents a novel numerical technique for large-scale groundwater flow simulations, in the frame of artificial recharge planning. The implementation is demonstrated using two test-sites from the EU funded GABARDINE project (FP6): The Sindos test site, near Thessaloniki, Greece, examines the infiltration of water towards the water table, through several unsaturated soil layers. The test site at Campina de Faro, Portugal, investigates phreatic surface movement around a large-diameter well. For both test cases a numerical simulation is constructed, and the local subsurface flow regime is investigated.
Numerical methods for solving PDEs using interpolation with radial basis functions (RBFs) will typically provide high accuracy solutions, achieve excellent convergence rates, and offer great flexibility with regards to the enforcement of arbitrary boundary conditions. However, RBF methods have traditionally been limited to the solution of small academic problems, due to issues of computational cost and numerical conditioning. Recent developments in locally supported RBF methods have led to techniques which can be scaled to the largest problem sizes, while maintaining many of the flexibilities of traditional RBF methods. As a contribution to the GABARDINE project, two such numerical techniques have been developed; the meshless LHI method and the control-volume based CV-RBF method. These numerical techniques are capable of modelling flow and transport in heterogeneous porous media, and are of order-N computational complexity, allowing problems to be solved on large and irregular datasets.
For both numerical techniques, the RBF Hermitian collocation method is utilised to perform interpolation at the local level, allowing the simultaneous imposition of pressure and mass-flux matching conditions at soil-layer interfaces. The non-overlapping stencil configuration then allows the accurate capture of non-smooth solution profiles across layer interfaces, to a high degree of accuracy [4,10]. Previous publications have verified the LHI and CV-RBF methods against analytical solutions obtained from several benchmark test-cases (see [1-10]), demonstrating highly accurate solutions in most cases. Procedures have also been demonstrated for the modelling of pumping and injection wells [8], infiltration ponds [2,6], and dynamic phreatic surfaces [8].
References
[1] Stevens, D.; Power, H. & Morvan, H. “An order-N complexity meshless algorithm for transport-type PDEs, based on local Hermitian interpolation”, Engineering Analysis with Boundary Elements, 2009, 33, 425-441
[2] Stevens, D.; Power, H.; Lees, M. & Morvan, H., “A Meshless Solution Technique for the Solution of 3D Unsaturated Zone Problems, Based on Local Hermitian Interpolation with Radial Basis Functions”, Transport in Porous Media, 2009, 79, 149-169
[3] Stevens, D.; Power, H.; Lees, M. & Morvan, H., “The use of PDE centres in the local RBF Hermitian method for 3D Convective-Diffusion problems” J. Comput. Phys., 2009, 228, 4606-4624
[4] Stevens, D.; Power, H.; Lees, M. & Morvan, H., “A local Hermitian RBF meshless numerical method for the solution of multi-zone problems”, Numerical Methods for Partial Differential Equations, 2009, (to appear)
[5] Stevens, D. & Power, H., “A scalable meshless formulation based on RBF Hermitian interpolation for 3D nonlinear heat conduction problems”, Computer modelling in engineering and sciences, 2009, (to appear), -
[6] Stevens, D. & Power, H., “A scalable and implicit meshless RBF method for the 3D unsteady nonlinear Richards equation, with single and multi-zone domains”, International Journal for Numerical Methods in Engineering, 2009, (submitted)
[7] Orsini P.; Power H.; Morvan H., ”Improving Volume Element Method by Meshless Radial Basis Function”, CMES: Computer Modeling in Engineering and Sciences, 2008, 23(3), 187-207
[8] Orsini P.; Power H.; Lees M.; Morvan H., “A Control Volume Radial Basis Function Techniques for the Numerical Simulation of Saturated Flows in Semi-confined Aquifer”, Transport in Porous Media, 2009, 79(2), 171-196.
[9] Orsini P.; Power H.; Morvan H.; Lees M., “An implicit upwinding volume element method based on meshless radial basis function techniques for modelling transport phenomena”, International Journal for Numerical Methods in Engineering, 2009, (in press)
[10] Orsini P.; Power H.; Morvan H.; Lees M. “Non-overlapping domain decomposition algorithm for the Hermite Radial Basis Function Control Volume method”, Computer Methods in Applied Mechanics and Engineering, 2009, (submitted). |
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