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  • 1
    Electronic Resource
    Electronic Resource
    Transport parameters identification: application of the Sentinel method (2000)
    Springer
    Computational geosciences 4 (2000), S. 251-273 
    Details
    ISSN: 1573-1499
    Keywords: groundwater pollution modeling ; inverse problem ; Sentinel method ; pollution parameters ; pollutant source localization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract In this paper, the Sentinel method is applied to groundwater pollution parameter identification. First, the inverse problem is solved in the linear case to estimate pollutant mass flow rates. Then, the non-linear case, which is the determination of the pollutant source coordinates, is developed. Finally, numerical tests, conducted on the Rhenan aquifer, south of Strasbourg, are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011516101288
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  • 2
    Electronic Resource
    Electronic Resource
    Modeling Variable Density Flow and Solute Transport in Porous Medium: 1. Numerical Model and Verification (1999)
    Springer
    Transport in porous media 35 (1999), S. 345-373 
    Details
    ISSN: 1573-1634
    Keywords: groundwater ; density driven flow ; numerical simulation ; mixed finite elements ; discontinuous finite elements ; Elder problem.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A new numerical model for the resolution of density coupled flow and transport in porous media is presented. The model is based on the mixed hybrid finite elements (MHFE) and discontinuous finite elements (DFE) methods. MHFE is used to solve the flow equation and the dispersive part of the transport equation. This method is more accurate in the calculation of velocities and ensures continuity of fluxes from one element to the adjacent one. DFE is used to solve the convective part of the transport equation. Combined with a slope limiting procedure, it avoids numerical instabilities and creates a very limited numerical dispersion, even for high grid Peclet number. Flow and transport equations are coupled by a standard iterative scheme. Residual based criterion is used to stop the iterations. Simulations of an unstable equilibrium show the effects of the criteria used to stop the iterations and the stopping criterion in the solver. The effects are more important for finer grids than for coarser grids. The numerical model is verified by the simulation of standard benchmarks: the Henry and the Elder test cases. A good agreement is found between the revised semi‐analytical Henry solution and the numerical solution. The Elder test case was also studied. The simulations were similar to those presented in previous works but with significantly less unknowns (i.e. coarser grids). These results show the efficiency of the used numerical schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006564309167
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  • 3
    Electronic Resource
    Electronic Resource
    Modeling Variable Density Flow and Solute Transport in Porous Medium: 2. Re‐Evaluation of the Salt Dome Flow Problem (1999)
    Springer
    Transport in porous media 35 (1999), S. 375-394 
    Details
    ISSN: 1573-1634
    Keywords: groundwater ; density driven flow ; numerical simulation ; salt dome.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Case 5, Level 1 of the international HYDROCOIN groundwater flow modeling project is an example of idealized flow over a salt dome. The groundwater flow is strongly coupled to solute transport since density variations in this example are large (20%). Several independent teams simulated this problem using different models. Results obtained by different codes can be contradictory. We develop a new numerical model based on the mixed hybrid finite elements approximation for flow, which provides a good approximation of the velocity, and the discontinuous finite elements approximation to solve the advection equation, which gives a good approximation of concentration even when the dispersion tensor is very small. We use the new numerical model to simulate the salt dome flow problem. In this paper we study the effect of molecular diffusion and we compare linear and non‐linear dispersion equations. We show the importance of the discretization of the boundary condition on the extent of recirculation and the final salt distribution. We study also the salt dome flow problem with a more realistic dispersion (very small dispersion tensor). Our results are different to prior works with regard to the magnitude of recirculation and the final concentration distribution. In all cases, we obtain recirculation in the lower part of the domain, even for only dispersive fluxes at the boundary. When the dispersion tensor becomes very small, the magnitude of recirculation is small. Swept forward displacement could be reproduced by using finite difference method to compute the dispersive fluxes instead of mixed hybrid finite elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006504326005
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  • 4
    Electronic Resource
    Electronic Resource
    SOLUTION OF THE ADVECTION-DIFFUSION EQUATION USING A COMBINATION OF DISCONTINUOUS AND MIXED FINITE ELEMENTS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 595-613 
    Details
    ISSN: 0271-2091
    Keywords: advection-diffusion equation ; discontinuous finite element method ; mixed finite element method ; solute transport in porous media ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: When transport is advection-dominated, classical numerical methods introduce excessive artificial diffusion and spurious oscillations. Special methods are required to overcome these phenomena. To solve the advection-diffusion equation, a numerical method is developed using a discontinuous finite element method for the discretization of the advective terms. At the discontinuities of the approximate solution, numerical advective fluxes are calculated using one-dimensional approximate Riemann solvers. The method is stabilized with a multidimensional slope limiter which introduces small amounts of numerical diffusion when sharp concentration fronts occur. In addition, the diffusive term is discretized using a mixed hybrid finite element method. With this approach, numerical oscillations are completely avoided for a full range of cell Peclet numbers. The combination of discontinuous and mixed finite elements can be easily applied to 2D and 3D models using various types of elements in regular and irregular meshes. Numerical tests show good agreement with 1D and 2D analytical solutions. This approach is compared at the same time with two different numerical methods, a standard mixed finite method and a finite volume approach with high-resolution upwind terms. Regular and irregular meshes are used for the numerical tests to study the mesh effects on the numerical results. Our data show that in all cases this approach performs well. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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