Numerical simulations of solute transport in highly heterogeneous formations: A comparison of alternative numerical schemes

Advances in Water Resources

Volumn 52, Issue , 2013, Pages 178-189

  Boso, Francesca ^a   Bellin, Alberto ^a   Dumbser, Michael ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

High heterogeneity; Local dispersion model; Numerical diffusion; Numerical schemes; Reactive transport

Indexed keywords

HIGH HETEROGENEITY; LOCAL DISPERSION; NUMERICAL DIFFUSION; NUMERICAL SCHEME; REACTIVE TRANSPORT;

DIFFUSION; DISPERSIONS; HYDRODYNAMICS; LAGRANGE MULTIPLIERS; SOLUTE TRANSPORT;

NUMERICAL METHODS;

DIFFUSION; EULERIAN ANALYSIS; NUMERICAL MODEL; POROUS MEDIUM; REACTIVE TRANSPORT; SOLUTE TRANSPORT;

EID: 84870179558     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2012.08.006     Document Type: Article

References (47)

1. Ottino J. The kinematics of mixing: stretching, chaos, and transport 1989, Cambridge University Press.
2. Bellin A., Rubin Y. HYDRO GEN: a spatially distributed random field generator for correlated properties. Stoch Hydrol Hydraul 1996, 10(4):2913-2924.
3. Dentz M., Le Borgne T., Englert A., Bijeljic B. Mixing, spreading and reaction in heterogeneous media: a brief review. J Contam Hydrol 2011, 120-121. 017107.
4. Toro E. Riemann solvers and numerical methods for fluid dynamics - A practical introduction 1999, Springer.
5. Quarteroni A., Valli A. Numerical approximation of partial differential equations 1994, Springer.
6. Cirpka O., Helmig R., Frind E. Numerical methods for reactive transport on rectangular and streamline-oriented grids. Adv Water Res 1999, 22(7):711-728.
7. Harten A., Engquist B., Osher S., Chakravarthy S. Uniformly high order essentially non-oscillatory schemes III. J Comput Phys 1987, 71:231-303.
8. Jiang G., Shu C. Efficient implementation of weighted ENO schemes. J Comput Phys 1996, 126:202-228.
9. Hu C., Shu C. Weighted essentially non-oscillatory schemes on triangular meshes. J Comput Phys 1999, 150:97-127.
10. Dumbser M., Käser M. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J Comput Phys 2007, 221:693-723.
11. Dumbser M., Käser M., Titarev V., Toro E. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J Comput Phys 2007, 226:204-243.
12. LaBolle E., Fogg G., Tompson A. Random-walk simulation of transport in heterogeneous porous media: local Mass-conservation problem and implementation methods. Water Resour Res 1996, 32(3):583-593.
13. Monaghan J. Smoothed particle hydrodynamics. Rep Progress Phys 2005, 68:1703-1759.
14. Zheng C., Wang P. MT3DMS, A modular three-dimensional multi-species transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems; documentation and user's guide. U.S. Army Engineer Research and Development Center Contract Report SERDP-99-1. U.S. Army Engineer Research and Development Center, Vicksburg, Mississippi. 1999.
15. Herrera P., Massabó M., Beckie R. A meshless method to simulate solute transport in heterogeneous porous media. Adv Water Res 2009, 32:413-429.
16. Frind E. The principal direction technique: a new approach to groundwater contaminant transport modelling. Proceedings of the fourth international conference on finite elements in water resources 1982, 13-25. Springer. K. Holz, U. Meissner, W. Zielke, C. Brebia, G. Pinder, W. Gray (Eds.).
17. Obi E., Blunt M. Streamline-based simulation of advective-dispersive solute transport. Adv Water Res 2004, 27:913-924.
18. Herrera P., Valocchi A., Beckie R. A multidimensional streamline-based method to simulate reactive solute transport in heterogeneous porous media. Adv Water Res 2010, 33:711-727.
19. Ruan F., McLaughlin D. An investigation of Eulerian-Lagrangian methods for solving heterogeneous advection-dominated transport problems. Water Resour Res 1999, 35(8). 10.1029/1999WR90004.
20. Bear J. Dynamics of fluids in porous materials 1972, American Elsevier.
21. Scheidegger A.E. On the theory of flow of miscible phases in porous media 1957, 236-242. University of Toronto Press.
22. Chiogna G., Cirpka O., Grathwohl P., Rolle M. Relevance of local compound-specific transverse dispersion for conservative and reactive mixing in heterogeneous porous media. Water Resour Res 2011, 47(W07540).
23. Rubin J. Transport of reacting solutes in porous media: relation between mathematical nature of problem formulation and chemical nature of reactions. Water Resour Res 1983, 19(5):1231-1252.
24. De Simoni M., Carrera J., Sánchez-Vila S., Guadagnini A. A procedure for the solution of multicomponent reactive transport problems. Water Resour Res 2005, 41(W11410). d10.1029/2005WR00405.
25. Hellferich F., Klein G. Multicomponent chromatography theory of interference 1970, Marcel Dekker.
26. Valocchi A., Street R., Roberts P. Transport of ion-exchanging solutes in groundwater. Chromatographic theory and field simulation. Water Resour Res 1981, 15(5):1517-1527.
27. Saaltink M., Ayora C., Carrera J. A mathematical formulation for reactive transport that eliminates mineral concentrations. Water Resour Res 1998, 34(7):1649-1656.
28. Harbaugh A., Banta ER, Hill M, McDonald M. MODFLOW-2000, The U.S. Geological survey modular ground-water model - user guide to modularization concepts and the ground-water flow process: U.S. Geological Survey Open-File Report 00-92, 121, p. 2000.
29. Salamon P., Fernández-Garcia D., Jaime Gómez-Hernandez J. A review and numerical assessment of the random walk particle tracking method. J Contam Hydrol 2006, 87:277-305.
30. Tonina D., Bellin A. The influence of pore scale dispersion, formation heterogeneity, source size and sampling volume on the concentration of conservative tracers. Adv Water Resour 2008, 31(2):339-354.
31. Kinzelbach W. The random walk method in pollutant transport simulation. Advances in analytical and numerical groundwater flow and quality modelling. NATO ASI Series C 1987, vol. 224:227-246. E. Custodio (Ed.).
32. Brookshaw L. A method of calculating radiative heat diffusion in particle simulations. Proc Astron Soc Australia 1985, 6(2):207-210.
33. Cleary P., Monaghan J. Conduction modelling using smoothed particle hydrodynamics. J Comput Phys 1999, 148:227-264.
34. Tartakovsky A., Meakin P., Scheibe T., Wood B. A smoothed particle hydrodynamics model for reactive transport and mineral precipitation in porous and fractured porous media. Water Resour Res 2007, 43(W05437).
35. Hammersley J., Handscomb D. Monte Carlo methods 1964, Chapman and Hall, London (UK).
36. Tartakovsky A., Tartakovsky G., Scheibe T. Effects of incomplete mixing on multicomponent reactive transport. Adv Water Resour 2009, 32:1674-1679.
37. Ferrari A., Dumbser M., Toro E., Armanini A. A new 3D parallel scheme for free surface flows. Comput Fluids 2009, 38(6):1203-1217.
38. Gelhar L., Collins M. General analysis of longitudinal dispersion in nonuniform flow. Water Resour Res 1971, 7(6):1511-1521.
39. LeVeque R. Finite-volume methods for hyperbolic problems 2004, Cambridge University Press.
40. Caflish R. Monte Carlo and quasi-Monte Carlo methods. Acta Numer 1998, 1-49.
41. Gómez-Hernandez J., Srivastava R. ISIM3D: an ANSI-C-three-dimensional multiple indicator conditional simulation program. Comput Geosci 1990, 16(4):395-440.
42. Cainelli O., Bellin A., Putti M. On the accuracy of finite element schemes for computing the flow field in heterogeneous formations. Adv Water Resour 2012, 47:43-55.
43. Dagan G. Flow and transport in porous formations 1989, Springer.
44. Rubin Y. Applied stochastic hydrogeology 2003, Oxford University Press.
45. Cabezon R., Garcia-Senz D., Relano A. A one-parameter family of interpolation kernels for SPH studies. J Comput Phys 2008, 227:8523-8540.
46. Kitanidis P. The concept of dilution index. Water Resour Res 1994, 30(7):2011-2026.
47. Chilakapati A., Yabusaki S. Nonlinear reactions and nonuniform flows. Water Resour Res 1999, 35(8):2427-2438.