A meshless method to simulate solute transport in heterogeneous porous media

Advances in Water Resources

Volumn 32, Issue 3, 2009, Pages 413-429

  Herrera, Paulo A ^a   Massabó, Marco ^b   Beckie, Roger D ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b CIMA   (Italy)

Author keywords

Advection; Dispersion; Lagrangian numerical methods; Meshless numerical methods; Numerical dispersion; Porous media; Solute transport

Indexed keywords

ADVECTION; DISPERSION (WAVES); DISPERSIONS; FLUID DYNAMICS; LAGRANGE MULTIPLIERS; NUMBER THEORY; POROUS MATERIALS; SOLUTE TRANSPORT; TWO DIMENSIONAL;

GEOLOGICAL FORMATIONS; HETEROGENEOUS POROUS MEDIAS; LAGRANGIAN NUMERICAL METHODS; MESH-LESS METHODS; MESHLESS NUMERICAL METHODS; NUMERICAL DISPERSION; NUMERICAL SOLUTIONS; POROUS MEDIA; SMOOTHED PARTICLE HYDRODYNAMICS; STANDARD METHODS;

NUMERICAL METHODS;

ADVECTION; BENCHMARKING; COMPUTER SIMULATION; DISPERSION; HETEROGENEOUS MEDIUM; HYDRODYNAMICS; LAGRANGIAN ANALYSIS; NUMERICAL METHOD; NUMERICAL MODEL; POROUS MEDIUM; SMOOTHING; SOLUTE TRANSPORT;

EID: 61349104288     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2008.12.005     Document Type: Article

References (54)

1. Ahlstrom S, Foote H, Arnett R, Cole C, Serne R. Multicomponent mass transport model: theory and numerical implementation (discrete-parcel-random-walk version). Tech. rep., BNWL-2127, Battelle Pacific Northwest Labs., Richland, Wash.(USA), 1977.
2. Bagtzoglou A., Tompson A., and Dougherty D. Projection functions for particle-grid methods. Numer Meth Part Diff Eq 8 4 (1992) 325-340
3. Barnes J., and Hut P. A hierarchical O (Nlog N) force-calculation algorithm. Nature 324 6096 (1986) 446-449
4. Brackbill J. Particle methods. Int J Numer Meth Fluids 47 8-9 (2005) 693-705
5. Brookshaw L. A method of calculating radiative heat diffusion in particle simulations. Proc Astron Soc Aust, 0066-9997 6 2 (1985) 207-210
6. Celia M., Russell T., Herrera I., and Ewing R. An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Water Resour 13 4 (1990) 187
7. Chaniotis A., Poulikakos D., and Koumoutsakos P. Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. J Comput Phys 182 (2002) 67-90
8. Chaniotis A.K., Frouzakis C.E., Lee J.C., Tomboulides A.G., Poulikakos D., and Boulouchos K. Remeshed smoothed particle hydrodynamics for the simulation of laminar chemically reactive flows. J Comput Phys 191 1 (2003) 1-17
9. Cirpka O., Frind E., and Helmig R. Numerical simulation of biodegradation controlled by transverse mixing. J Contam Hydrol 40 2 (1999) 159-182
10. Cleary P.W., and Monaghan J.J. Conduction modelling using smoothed particle hydrodynamics. J Comput Phys 148 1 (1999) 227-264
11. Cottet G., and Koumoutsakos P. Vortex methods: theory and practice (2000), Cambridge University Press
12. Degond P., and Mas-Gallic S. The weighted particle method for convection-diffusion equations. Part 1: The case of an isotropic viscosity. Math Comput 53 188 (1989) 485-507
13. Delay F., Ackerer P., and Danquigny C. Simulating solute transport in porous or fractured formations using random walk particle tracking: a review. Vadose Zone J 4 2 (2005) 360-379
14. Dilts G. Moving-least-squares-particle hydrodynamics I. Consistency and stability. Int J Numer Meth Eng 44 (1999) 1115-1155
15. Español P., and Revenga M. Smoothed dissipative particle dynamics. Phys Rev E 67 2 (2003) 026705-026712
16. Gardiner C. Handbook of stochastic methods for physics. Chemistry and the natural sciences, 1990.
17. Gingold R., and Monaghan J. Kernel estimates as a basis for general particle methods in hydrodynamics. J Comput Phys 46 June (1982) 429-453
18. Gingold R.A., and Monaghan J.J. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not Roy Astron Soc 181 (1977) 375-389
19. Greengard L. Fast algorithms for classical physics. Science 265 5174 (1994) 909-914
20. Harbaugh A. MODFLOW-2000, the US Geological Survey Modular Ground-water Model: User Guide to Modularization Concepts and the Ground-water Flow Process. US Geological Survey, 2000.
21. Herrera P., and Valocchi A. Positive solution of two-dimensional solute transport in heterogeneous aquifers. Ground Water 44 6 (2006) 803-813
22. Jubelgas M., Springel V., and Dolag K. Thermal conduction in cosmological SPH simulations. Mon Not Roy Astron Soc 351 (2004) 423-435
23. Konikow L, Goode D, Hornberger G, Survey G. A three-dimensional method-of-characteristics solute-transport model (MOC3D). US Geological Survey, 1996.
24. Kuzmin D., and Turek S. Flux correction tools for finite elements. J Comput Phys 175 (2002) 525-558
25. LaBolle E.M., Fogg G.E., and Tompson A.F.B. Random-walk simulation of transport in heterogeneous porous media: local mass-conservation problem and implementation methods. Water Resour Res 32 3 (1996) 583-594
26. Labolle E.M., Quastel J., Fogg G.E., and Gravner J. Diffusion processes in composite porous media and their numerical integration by random walks: generalized stochastic differential equations with discontinuous coefficients. Water Resour Res 36 3 (2000) 651
27. Lichtner P., Kelkar S., and Robinson B. New form of dispersion tensor for axisymmetric porous media with implementation in particle tracking. Water Resour Res 38 8 (2002) 1146
28. Lucy L. A numerical approach to the testing of the fission hypothesis. Astron J 82 (1977) 1013-1024
29. Monaghan J. Smoothed particle hydrodynamics. Rep Prog Phys 68 8 (2005) 1703-1759
30. Monaghan J.J. Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30 (1992) 543-574
31. Morris J., Fox P., and Zhu Y. Modeling low Reynolds number incompressible flows using SPH. J Comput Phys 136 1 (1997) 214-226
32. Neuman S. A Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids. J Comput Phys 41 2 (1981)
33. Neuman S. Adaptive Eulerian-Lagrangian finite element method for advection-dispersion. Int J Numer Meth Eng 20 (1984) 321-337
34. Obi E., and Blunt M. Streamline-based simulation of advective-dispersive solute transport. Adv Water Resour 27 9 (2004) 913-924
35. Pickens J., and Grisak G. Scale-dependent dispersion in stratified granular aquifer. Water Resour Res 17 4 (1981) 1191-1211
36. Pollock D. Semianalytical computation of path lines for finite-difference models. Ground Water 26 6 (1988) 743-750
37. Press W., Teukolsky S., Vetterling W., and Flannery B. Numerical recipes in C: the art of scientific computing (1992), Cambridge University Press, New York (NY), USA
38. Price DJ. Magnetic fields in astrophysics. PhD thesis, Institute of Astronomy, University of Cambridge, 2004.
39. Quinlan N.J., Basa M., and Lastiwka M. Truncation error in mesh-free particle methods. Int J Numer Meth Eng 66 (2006) 2064-2085
40. Russell T., and Celia M. An overview of research on Eulerian-Lagrangian localized adjoint methods (ELLAM). Adv Water Resour 25 8 (2002) 1215-1231
41. Salamon P., Fernàndez-Garcia D., and Gòmez-Hernàndez J. A review and numerical assessment of the random walk particle tracking method. J Contam Hydrol 87 3-4 (2006) 277-305
42. Schaback R., and Wendland H. Kernel techniques: from machine learning to meshless methods. Acta Numer (2006) 1-97
43. Shepard D. A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 23rd ACM national conference, 1968. p. 517-24.
44. Smith L., and Schwartz F.W. Mass transport. 1. A stochastic analysis of macroscopic dispersion. Water Resour Res 16 2 (1980) 303-313
45. Tartakovsky A., and Meakin P. A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and two-dimensional Rayleigh-Taylor instability. J Comput Phys 207 (2005) 610-624
46. Tompson A. Numerical simulation of chemical migration in physically and chemically heterogeneous porous media. Water Resour Res 29 11 (1993) 3709-3726
47. Tompson A., and Dougherty D. Particle-grid methods for reacting flows in porous media with applications to Fisher's equation. Appl Math Model 16 (1992) 374-383
48. Valocchi A, Quinodoz A. Application of the random walk method to simulate the transport of kinetically sorbing solutes. Groundwater Contamination. IAHS Publ, 1989. p. 35-42.
49. Viccione G., Bovolin V., and Pugliese E. Defining and optimizing algorithms for neighbouring particle identification in SPH fluid simulations. Int J Numer Meth Fluids 58 6 (2008) 625-638
50. Waltz J., Page G.L., Milder S.D., Wallin J., and Antunes A. A performance comparison of tree data structures for N-body simulation. J Comput Phys 178 1 (2002) 1-14
51. Zheng C, Wang P. MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems; documentation and user's guide. Contract Report SERDP-99-1, US Army Engineer Research and Development Center, Vicksburg, MS, 1999.
52. Zhu Y., and Fox P. Simulation of pore-scale dispersion in periodic porous media using smoothed particle hydrodynamics. J Comput Phys 182 2 (2002) 622-645
53. Zhu Y., Fox P., and Morris J. A pore-scale numerical model for flow through porous media. Int J Numer Anal Meth Geomech 23 (1999) 881-904
54. Zimmermann S., Koumoutsakos P., and Kinzelbach W. Simulation of pollutant transport using a particle method. J Comput Phys 173 (2001) 322-347