Global random walk stochastic simulations for the assessment of the contamination risk in groundwater systems

• Applicant: Dr. Nicolae Suciu
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2005 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5455052

• Final Report Year: 2008

Final Report Abstract

The predictability ofthe contamination in groundwater systems was investigaled via stochastic simulations using the "global random walk" (GRW) method. Ergodicity ranges, estimated by root mean square deviations of actual observables from predictions provided by stochastic advection-dispersion models, were obtained from statistical ensembles of GRW transport simulations carried out on high performance parallel computers. The GRW simulations provided a numerical evidence for the mean square convergence of transport realizations to the upscaled macrodispersion process of transport in velocity fields with finile correlation range; that is the theoretically challenging issue of asymptotic ergodicity. Another new result was the discovery of the memory effects that manifest in the pre-asymptotic transport regime by a strong dependence of ergodicity ranges on the shape, orientation, and dimensions of the initial solute plumes. This surprising behavior invalidates the common thinking that large transverse dimensions of the source ensure ergodicity and has serious consequences for practical applications, such as the calibration of the model parameters, forecasting, and identification of the contaminant sources.

Publications

• Biased global random walk, a cellular automaton for diffusion, in Simulationstechnique, I^^ Symposium in Erlangen, September 2005, edited by P. Husemann, M. Kowarschik, and, U. Rüde, pp. 562--567, SCS Publishing House e. v., Erlangen.
  Suciu N.. C. Vamos. P. Knabner. and U. Rüde (2005).
  
• Ergodicity in the large sense and stochastic modeling of transport in heterogeneous aquifers, paper presented at EGU General Assembly 2006, Geophysical Research Abstracts, Vol. 8, EGU06-A-03627.
  Suciu. N.. C. Vamos. H. Vereecken (2006c).
  
• Evaluation of overshooting errors in particle methods for diffusion by biased global random walk, Rev. Anal. Num. Th. Approx. (Romanian Academy Publishing House) Tome 35, pp. 119-126, 2006.
  Suciu N.. and C. Vamos (2006).
  
• Evaluation ofthe first-order approximations for transport in heterogeneous media. Water Resour. Res. 42, W11504
  Suciu, N.; Vamoş, C. & Eberhard, J.
  
• Numerical investigations on ergodicity of solute transport in heterogeneous aquifers, Water Resour. Res., 42, W04409
  Suciu, N.; Vamoş, C.; Vanderborght, J.; Hardelauf, H. & Vereecken, H.
  
• Comment on "Nonstationary flow and nonergodic transport in random porous media" by G. Darvini and P. Salandin, Water Resour. Res., 43, W12601.
  Suciu, N. & Vamoş, C.
  
• Ergodic simulations of diffusion in random velocity field, pp. 659-668 in Monte Carlo and Quasi-Monte Carlo Methods 2006, Ed. A. Keller, S. Heinrich, and H. Niederreiter, Springer Verlag, Heidelberg.
  Suciu N.. C. Vamos. and K. Sabelfeld (2007).
  
• Global random walk modeling of transport in complex systems, Computing and Visualization in Science
  Suciu, N.; Vamoş, C.; Turcu, I.; Pop, C. V. L. & Ciortea, L. I.
  
• Memory effects and ergodicity for diffusion in spatially correlated velocity fields, Proc. Appl. Math. Mech., 7, 2010015-2010016.
  Suciu, Nicolae; Sabelfeld, Karl; Vamoş, Călin & Andronache, Constantin
  
• Multiple meanings of ergodicity in real life problems, pp. 196-211 in Proceedings ofthe 5th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, Ed. G. Marinoschi, S. Ion and C. Popa, Rom. Acad. Publishing House, Bucharest.
  Suciu N.. C. Vamos. and H. Vereecken (2007)
  
• Non-ergodic behavior of "ergodic plumes", paper presented at EGU General Assembly 2007, Geophysical Research Abstracts, Vol. 9, EGU2007-A-09861.
  Suciu. N.. Vamos. C. Vereecken. H.. K. Sabelfeld. and P. Knabner (2007e).
  
• On the self-averaging of dispersion for transport in periodic random media, J. Phys. A: Math. Theor., 40, 597-610
  Eberhard, J. P.; Suciu, N. & Vamoş, C.
  
• P., Memory effects induced by dependence on initial conditions of transport in heterogeneous media, paper presented at EGU General Assembly 2007, Geophysical Research Abstracts, Vol. 9, EGU2007- A-09800.
  Suciu. N.. C. Vamos. H. Vereecken. K. Sabelfeld. and P. Knabner (2007d).
  
• Fast computation of macrodispersion coefficients for transport in ergodic velocity fields, paper presented at EGU General Assembly 2008, Geophysical Research Abstracts, Vol. 10, EGU2008-A-06154.
  Suciu. N.. and C. Vamos (2008).
  
• Lagrangian stationarity and memory effects for dispersion in ergodic velocity fields, paper presented at EGU General Assembly 2008, Geophysical Research Abstracts, Vol. 10, EGU2008-A-06i 17.
  Suciu N.. C. Vamos. H. Vereecken. K. Sabelfeld. and P. Knabner (2008).
  
• Lagrangian-Eulerian statistics and numerical modeling of transport in homogeneous random media, in Proceedings ofthe 6th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems, Ed. G. Marinoschi, S. Ion, and C. Popa, Rom. Acad. Publishing House, Bucharest.
  Suciu N.. F. A. Radu. and C. Vamos (2008).
  
• Memory Effects Induced by Dependence on Initial Conditions and Ergodicity of Transport in Heterogeneous Media, Water Resour.
  Suciu, N.; Vamoş, C.; Vereecken, H.; Sabelfeld, K. & Knabner, P.