Identification of the Exchange Coefficient from Indirect Data for a Coupled Continuum Pipe-Flow Model

Calibration and identification of the exchange effect between the karst aquifers and the underlying conduit network are important issues in order to gain a better understanding of these hydraulic systems. Based on a coupled continuum pipe-flow (CCPF for short) model describing flows in karst aquifers, this paper is devoted to the identification of an exchange rate function, which models the hydraulic interaction between the fissured volume (matrix) and the conduit, from the Neumann boundary data, i.e., matrix/conduit seepage velocity. The authors formulate this parameter identification problem as a nonlinear operator equation and prove the compactness of the forward mapping. The stable approximate solution is obtained by two classic iterative regularization methods, namely, the Landweber iteration and Levenberg-Marquardt method. Numerical examples on noisefree and noisy data shed light on the appropriateness of the proposed approaches.