Geodesic
Solution of inverse problems in contaminant transport with adsorption
Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 1 
J. Kacur; M. Remesikova; B. Malengier. Solution of inverse problems in contaminant transport with adsorption. Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2007_76_1_a4/
@article{AMUC_2007_76_1_a4,
     author = {J. Kacur and M. Remesikova and B. Malengier},
     title = {Solution of inverse problems in contaminant transport with adsorption},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2007},
     volume = {76},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2007_76_1_a4/}
}
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In this paper, solution of inverse contaminant transport problems is studied, including nonlinear sorption in equilibrium and non-equilibrium mode. A precise numerical solver for the direct problem is discussed. The method is based on time stepping and operator splitting with respect to the nonlinear transport, diffusion and adsorption. The nonlinear transport problem corresponds to a multiple Riemann problem and is solved by modified front tracking method. The diffusion problem is solved by a finite volume scheme and the sorption part is solved by an implicit numerical scheme. The solution of the inverse problem is based on an iterative approach. The gradient of the cost functional with respect to the determined parameters is constructed by means of solution of the corresponding adjoint system. Numerical examples are presented for a 1D situation and for a dual-well setting with steady-state flow between injection and extraction wells.