Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM

Environmental Earth Sciences

Volumn 61, Issue 2, 2010, Pages 341-353

  Kumar, R Praveen ^a   Dodagoudar, G R ^b  

^a UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

^b INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Contaminant transport; Landfill liners; Meshfree method; Radial point interpolation method; Thin plate spline radial basis functions

Indexed keywords

CONTAMINANT TRANSPORT; LANDFILL LINER; MESH-FREE METHOD; RADIAL BASIS FUNCTIONS; RADIAL POINT INTERPOLATION METHOD; THIN PLATE SPLINE;

COMPUTATIONAL MECHANICS; CONTAMINATION; FUNCTION EVALUATION; INTERPOLATION; LAND FILL; POROUS MATERIALS; RADIAL BASIS FUNCTION NETWORKS; SORPTION; SPLINES; TWO DIMENSIONAL; WASTE DISPOSAL;

FINITE ELEMENT METHOD;

ADVECTION-DIFFUSION EQUATION; FINITE ELEMENT METHOD; INTERPOLATION; LANDFILL LINER; POLLUTANT TRANSPORT; POROUS MEDIUM; SATURATED MEDIUM; SORPTION; TWO-DIMENSIONAL MODELING;

EID: 77954018404     PISSN: 18666280     EISSN: 18666299     Source Type: Journal    
DOI: 10.1007/s12665-009-0346-4     Document Type: Article

References (42)

1. Atluri SN, Zhu T (1998) A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 22: 117-127.
2. Bear J (1979) Hydraulics of groundwater. McGraw-Hill, New York.
3. Beuth L, Benz T, Vermeer PA, Coetzee CJ, Bonnier P, van Den Berg P (2007) Formulation and validation of a quasi-static material point method. In: Proceedings of the 10th international symposium on numerical methods in Geomechanics (NUMOG), Rhodes, Greece, pp 189-195.
4. Boztosun I, Charafi A (2002) An analysis of the linear advection-diffusion equation using mesh-free and mesh-dependent methods. Eng Anal Bound Elem 26: 889-895.
5. Boztosun I, Charafi A, Zerroukat M, Djidjeli K (2002) Thin-plate spline radial basis function scheme for advection-diffusion problems. Electron J Bound Elem BETEQ 2001: 267-282.
6. Boztosun I, Charafi A, Boztosun D (2003) On the numerical solution of linear advection-diffusion equation using compactly supported radial basis functions, vol 26. In: Griebel M, Alexander Schweitzer M (eds) Lecture notes in Comput Sci Eng Meshfree Methods for Partial Diff Eq. Springer, pp 63-73.
7. Chinchapatnam PP, Djidjeli K, Nair PB (2006) Unsymmetric and symmetric meshless schemes for the unsteady convection-diffusion equation. Comp Meth Appl Mech Eng 195: 2432-2453.
8. Coetzee CJ (2004) The modelling of granular flow using the particle-in-cell method. PhD Thesis, University of Stellenbosch, South Africa.
9. Coetzee CJ, Vermeer PA, Basson AH (2005) The modelling of anchors using the material point method. Int J Numer Anal Methods Geomech 29: 879-895.
10. Craig JR, Rabideau AJ (2006) Finite difference modelling of contaminant transport using analytic element flow solutions. Adv Water Resour 29: 1075-1087.
11. Crank J (1956) The mathematics of diffusion. Oxford Press, London.
12. Dolbow J, Belytschko T (1998) An introduction to programming the meshless element-free Galerkin method. Arch Comput Methods Eng 5: 207-241.
13. Domenico P (1987) An analytical model for multidimensional transport of a decaying contaminant species. J Hydrol 91: 49-58.
14. Durner W, Schultze B, Zurmühl T (1999) State-of-the-art in inverse modeling of inflow/outflow experiments. In: van Genuchten MTh, Leij FJ, Wu L (eds) Proceedings of international workshop on characterisation and measurement of the hydraulic properties of unsaturated porous media, University of California, Riverside, CA, pp 661-681.
15. Eldho TI, Rao BV (1997) Simulation of two-dimensional contaminant transport with dual reciprocity boundary elements. Eng Anal Bound Elem 20: 213-228.
16. Finsterle S (2004) Multiphase inverse modelling: review and iTOUGH2 applications. Vadose Zone J 3: 747-762.
17. Freiboth S, Class H, Helmig R (2007) Numerical simulation of multiphase multicomponent processes considering structural alterations of porous media-a phenomenological model. In: Schanz T (ed) Theoretical and numerical unsaturated soil mechanics. Springer, Berlin, pp 127-134.
18. Freiboth S, Class H, Helmig R, Graf T, Ehlers W, Schwarz V, Vrettos C (2009) A model for multi-phase flow and transport in porous media including a phenomenological approach to account for deformation-a model concept and its validation within a code intercomparison study. Comput Geosci 13: 281-300.
19. Frind EO (1988) Solution of the advection-dispersion equation with free exit boundary. Numer Methods Partial Differ Equ 4: 301-313.
20. GeoSlope International Ltd (2007) Transport modelling with CTRAN/W 2007: an engineering methodology, student version 7. 02, Alberta, Canada.
21. Golberg MA, Chen CS, Bowman H (1999) Some recent results and proposals for the use of radial basis functions in the BEM. Eng Anal Bound Elem 23: 285-296.
22. King KS, Quigley RM, Fernandez F, Reades DW, Bacopoulos A (1993) Hydraulic conductivity and diffusion monitoring of the Keele Valley Landfill liner, Maple, Ontario. Can Geotech J 30: 124-134.
23. Li J, Chen Y, Pepper D (2003) Radial basis function method for 1-d and 2-d groundwater contaminant transport modelling. Comput Mech 32: 10-15.
24. Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Eng 20: 1081-1106.
25. Liu GR, Zhang GY, Gu YT, Wang YY (2005) A meshfree radial point interpolation method (RPIM) for three-dimensional solids. Comput Mech 36: 421-430.
26. Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30: 543-574.
27. Ogata A, Banks RB (1961) A solution of the differential equation of longitudinal dispersion in porous media. USGS, Professional paper: 411-A, Reston, VA.
28. Praveen Kumar R (2008) Modelling of 1d, 2d and 3d contaminant transport through saturated and unsaturated porous media using meshfree techniques. PhD Thesis, Indian Institute of Technology Madras, India.
29. Praveen Kumar R, Dodagoudar GR (2008) Two-dimensional modelling of contaminant transport through saturated porous media using the radial point interpolation method (RPIM). Hydrogeol J 16: 1497-1505.
30. Praveen Kumar R, Dodagoudar GR, Rao BN (2007) Meshfree modelling of one-dimensional contaminant transport in unsaturated porous media. Geomech Geoeng An Int J 2: 129-136.
31. Priesack E, Durner W (2006) Closed-form expression for the multi-modal unsaturated conductivity function. Vadose Zone J 5: 121-124.
32. Quigley RM, Rowe RK (1986) Leachate migration through clay below a domestic waste landfill, Sarnia, Ontario, Canada: chemical interpretation and modelling philosophies. In: Lorenzen D, Conway RA, Jackson LP, Hamza A, Perket CL, Lacy WJ (eds) Hazardous and industrial solid waste testing and disposal, vol 6, ASTM STP 933. American Society for Testing and Materials, Philadelphia, pp 93-103.
33. Quigley RM, Fernandez F, Yanful E, Helgason T, Margaritis A, Whitby JL (1987) Hydraulic conductivity of contaminated natural clay directly beneath a domestic landfill. Can Geotech J 24: 377-383.
34. Rowe RK, Booker JR (1985) 1-D pollutant migration in soils of finite depth. J Geotech Eng ASCE 111: 479-499.
35. Rowe RK, Quigley RM, Brachman RWI, Booker JR (2004) Barrier systems for waste disposal. E & FN Spon Press, London.
36. Sheu WHT, Chen YH (2002) Finite element analysis of contaminant transport in groundwater. Appl Math Comput 127: 23-43.
37. Sukumar N, Moran B, Semenov AY, Belikov VV (2001) Natural neighbour Galerkin methods. Int J Numer Methods Eng 50: 1-27.
38. Sulsky D, Chen Z, Schreyer HL (1994) A particle method for history-dependent materials. Comput Methods Appl Mech Eng 118: 179-196.
39. van Genuchten MTh (1981) Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay. J Hydrol 49: 213-233.
40. Vermeer PA, Beuth L, Benz T (2008) A quasi-static method for large deformation problems in geomechanics. In: Proceedings of the 12th international conference of international association for computer methods and advances in geomechanics (IACMAG), Goa, India, pp 55-63.
41. Wang JG, Liu GR (2002) A point interpolation meshless method based on radial basis functions. Int J Numer Methods Eng 54: 1623-1648.
42. Zimmermann S, Koumoutsakos P, Kinzelbach W (2001) Simulation of pollutant transport using a particle method. J Comput Physics 173: 322-347.