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Article

Keywords:
porous media equation; inverse problems; Richard’s equation
Summary:
In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA. Several numerical experiments are included.
References:
[1] D. G. Aronson: Regularity properties of flows through porous media: The interface. Arch. Rational Mech. Anal. 37 (1970), 1–10. MR 0255996 | Zbl 0202.37901
[2] L. A. Caffarelli, A. Friedman: Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Amer. J. Math. 101 (1979), 1193–1218. MR 0548877
[3] J. Chen, J. W. Hopmans, M. E. Grisnier: Parameter estimation of two-fluid capillary pressure-saturation and permeability functions. Advances in Water Resources 22 (1999), 479–493.
[4] D. Constales: Automatic differentiation in LSODA. In preparation.
[5] D. Constales, J. Kačur: Inverse problems in porous media flow. Submitted to Computational Geosciences.
[6] S. O. Eching, J. W. Hopmans: Optimization of hydraulic functions from transient outflow and soil water data. Soil Sci. Soc. Am. J. 57 (1993), 1167–1175.
[7] S. O. Eching, J. W. Hopmans, O. Wendroth: Unsaturated hydraulic conductivity from transient multistep outflow and soil water pressure. Soil Sci. Soc. Am. J. 58 (1994), 687–695.
[8] B. H. Gilding: Flow and Transport in Porous Media. World Scientific, Singapore, 1992.
[9] A. S. Kalašnikov: Formation of singularities in solutions of the equation of nonstationary filtration. Ž. Vyčisl. Mat. i Mat. Fiz. 7 (1967), 440–444. MR 0211058
[10] O. A. Olejnik, A. S. Kalašnikov, Chzhou Jui-Lin: Cauchy problems and boundary-value problems for equations of type of infiltration. Izv. AN SSSR Ser. Mat. 5 (1958), 667–704. (Russian)
[11] L. R. Petzold: Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J. Sci. Stat. Comput. 4 (1983), 136–148. MR 0689694 | Zbl 0518.65051
[12] D. Russo, E. Bresler, U. Shani, J. C. Parker: Analysis of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology. Water Resources Research 27 (1991), 1361–1373.
[13] C. J. van Duijn, L. A. Peletier: Nonstationary filtration in partially saturated porous media. Arch. Rational Mech. Anal. 78 (1982), 173–198. MR 0648943
[14] M. Th. van Genuchten: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44 (1980), 892–898.
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