Solution of contaminant transport with adsorption in porous media by the method of characteristics
- Volume: 35, Issue: 5, page 981-1006
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topKacur, Jozef, and Keer, Roger Van. "Solution of contaminant transport with adsorption in porous media by the method of characteristics." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.5 (2001): 981-1006. <http://eudml.org/doc/194084>.
@article{Kacur2001,
abstract = {A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.},
author = {Kacur, Jozef, Keer, Roger Van},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {relaxation method; method of characteristics; contaminant transport; convection-diffusion with adsorption; convection-diffusion; adsorption; convergence; porous media},
language = {eng},
number = {5},
pages = {981-1006},
publisher = {EDP-Sciences},
title = {Solution of contaminant transport with adsorption in porous media by the method of characteristics},
url = {http://eudml.org/doc/194084},
volume = {35},
year = {2001},
}
TY - JOUR
AU - Kacur, Jozef
AU - Keer, Roger Van
TI - Solution of contaminant transport with adsorption in porous media by the method of characteristics
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 5
SP - 981
EP - 1006
AB - A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
LA - eng
KW - relaxation method; method of characteristics; contaminant transport; convection-diffusion with adsorption; convection-diffusion; adsorption; convergence; porous media
UR - http://eudml.org/doc/194084
ER -
References
top- [1] H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983) 311–341. Zbl0497.35049
- [2] J.W. Barrett and P. Knabner, Finite element approximation of transport of reactive solutes in porous media. Part i: error estimates for nonequilibrium adsorption processes. SIAM J. Numer. Anal. 34 (1997) 201–227. Zbl0870.76039
- [3] J.W. Barrett and P. Knabner, Finite element approximation of transport of reactive solutes in porous media. Part ii: error estimates for equilibrium adsorption processes. SIAM J. Numer. Anal. 34 (1997) 455–479. Zbl0904.76039
- [4] J.W Barrett and P. Knabner, An improved error bound for a Lagrange-Galerkin method for contaminant transport with non-Lipschitzian adsorption kinetics. SIAM J. Numer. Anal. 35 (1998) 1862–1882. Zbl0911.65078
- [5] J. Bear, Dynamics of Fluids in Porous Media. Elsevier, New York (1972). Zbl1191.76001
- [6] R. Bermejo, Analysis of an algorithm for the Galerkin-characteristics method. Numer. Math. 60 (1991) 163–194. Zbl0723.65073
- [7] R. Bermejo, A Galerkin-characteristics algorithm for transport-diffusion equation. SIAM J. Numer. Anal. 32 (1995) 425–455. Zbl0854.65083
- [8] C.N. Dawson, Godunov-mixed methods for advection diffusion equations in multidimensions. SIAM J. Numer. Anal. 30 (1993) 1315–1332. Zbl0791.65062
- [9] C.N. Dawson, Analysis of an upwind-mixed finite element method for nonlinear contaminant transport equations. SIAM J. Numer. Anal. 35 (1998) 1709–1724. Zbl0954.76043
- [10] C.N. Dawson, C.J. van Duijn, and R.E. Grundy, Large time asymptotics in contaminant transport in porous media. SIAM J. Appl. Math. 56 (1996) 965–993. Zbl0862.35012
- [11] C.N. Dawson, C.J. van Duijn, and M.F. Wheeler, Characteristic-Galerkin methods for contaminant transport with non-equilibrium adsorption kinetics. SIAM J. Numer. Anal. 31 (1994) 982–999. Zbl0808.76046
- [12] R Douglas and T.F. Russel, Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19 (1982) 871–885. Zbl0492.65051
- [13] N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory. John Wiley & Sons Ltd., New York (1959). Zbl0635.47001MR1009162
- [14] R.E. Grundy, C.J. van Duijn, and C.N. Dawson, Asymptotic profiles with finite mass in one-dimensional contaminant transport through porous media. Quart. J. Mech. Appl. Math. 1 (1994) 69–106. Zbl0821.76076
- [15] W. Jäger and J. Kačur, Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. RAIRO Modél. Math. Anal. Numér. 29 (1995) 605–627. Zbl0837.65103
- [16] J. Kačur, Solution of some free boundary problems by relaxation schemes. SIAM J. Numer. Anal. 36 (1999) 290–316. Zbl0924.65090
- [17] J. Kačur, Solution to strongly nonlinear parabolic problems by a linear approximation scheme. IMA J. Numer. Anal. 19 (1999) 119–154. Zbl0946.65145
- [18] J. Kačur and S. Luckhaus, Approximation of degenerate parabolic systems by nondegenerate elliptic and parabolic systems. Appl. Numer. Math. 25 (1997) 1–21. Zbl0894.65043
- [19] J. Kačur, Solution of convection-diffusion problems with the memory terms, in Applied Mathematical Analysis, A. Sequiera, H. Beirao de Veiga, and J.H. Videman, Eds., Kluwer Academic, Plenum Publ., New York (1999) 199–212. Zbl0953.65098
- [20] P. Knabner, Mathematische Modelle für den Transport gelöstes Stoffe in sorbierenden Porösen Medien. Habilitationschrift, University of Augsburg, Germany (1989). Zbl0704.35072
- [21] P. Knabner and F. Otto, Solute transport in porous media with equilibrium and nonequilibrium multiple site adsorption: uniqueness. To appear. Zbl0958.35074
- [22] A. Kufner, O. John, and S. Fučík, Function Spaces. Noordhoff International Publishing, Leyden; Publishing House of the Czechoslovak Academy of Sciences, Prague (1977). Zbl0364.46022MR482102
- [23] K.W. Morton, A. Priestly, and E. Suli, Stability of the Lagrange-Galerkin method with non-exact integration. RAIRO Modél. Math. Anal. Numér. 4 (1988) 225–250. Zbl0661.65114
- [24] J. Nečas, Les méthodes directes en théorie des équations elliptiques. Academia, Prague (1967). MR227584
- [25] F. Otto, L1-contraction and uniqueness for quasilinear elliptic-parabolic equations. C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 105–110. Zbl0845.35056
- [26] P. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38 (1982) 309–332. Zbl0505.76100
- [27] C.J. van Duijn and P. Knabner, Solute transport in porous media with equilibrium and nonequilibrium multiple site adsorption: Traveling waves. J. Reine Angew. Math. 415 (1991) 1–49. Zbl0716.73076
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.