Contaminant transport with adsorption in dual-well flow.

*(English)*Zbl 1099.76064The paper is concerned with practically important and mathematically very complex problem of steady-state contaminant transport with adsorption and diffusion in dual-well flow. The porous medium is assumed to be homogeneous. The problem is strongly nonlinear. The goal is not only to compute the solution, but also to compare the solution obtained with real measured data (i.e. calibration).

The authors use the Dupuit-Forchheimer approximation for negligible vertical flow and obtain thus a nonlinear \(2\)D problem. The first step in the treatment of the problem is a conformal mapping of the domain considered into a rectangle. The resulting equation and corresponding boundary and initial value conditions are split into two nonlinear problems: the transport problem and the diffusion problem treated on time levels. The transport problem is solved by the Godunov finite difference scheme while the diffusion problem by the finite volume method. Numerical results are presented in the conclusion.

The paper contributes to the present state of the art as it splits the original flow problem into two and solves then by two different methods. Better figure captions would help reader to an easier orientation in the numerical results shown.

The authors use the Dupuit-Forchheimer approximation for negligible vertical flow and obtain thus a nonlinear \(2\)D problem. The first step in the treatment of the problem is a conformal mapping of the domain considered into a rectangle. The resulting equation and corresponding boundary and initial value conditions are split into two nonlinear problems: the transport problem and the diffusion problem treated on time levels. The transport problem is solved by the Godunov finite difference scheme while the diffusion problem by the finite volume method. Numerical results are presented in the conclusion.

The paper contributes to the present state of the art as it splits the original flow problem into two and solves then by two different methods. Better figure captions would help reader to an easier orientation in the numerical results shown.

Reviewer: Karel Segeth (Praha)

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76R50 | Diffusion |

76M12 | Finite volume methods applied to problems in fluid mechanics |

76M20 | Finite difference methods applied to problems in fluid mechanics |

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\textit{J. Kačur} and \textit{R. Van Keer}, Appl. Math., Praha 48, No. 6, 525--536 (2003; Zbl 1099.76064)

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