Leak identification in saturated unsteady flow via a Cauchy problem

A. Ben Abda, B.T. Johansson, S. Khalfallah

Research output: Contribution to journalArticle


This work is an initial study of a numerical method for identifying multiple leak zones in saturated unsteady flow. Using the conventional saturated groundwater flow equation, the leak identification problem is modelled as a Cauchy problem for the heat equation and the aim is to find the regions on the boundary of the solution domain where the solution vanishes, since leak zones correspond to null pressure values. This problem is ill-posed and to reconstruct the solution in a stable way, we therefore modify and employ an iterative regularizing method proposed in [1] and [2]. In this method, mixed well-posed problems obtained by changing the boundary conditions are solved for the heat operator as well as for its adjoint, to get a sequence of approximations to the original Cauchy problem. The mixed problems are solved using a Finite element method (FEM), and the numerical results indicate that the leak zones can be identified with the proposed method.
Original languageEnglish
JournalApplied Mathematical Modelling
VolumeIn press
Early online date23 Mar 2016
Publication statusE-pub ahead of print - 23 Mar 2016

Bibliographical note

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/


  • Cauchy problem
  • heat equation
  • iterative regularization method
  • leak identification
  • mixed problem

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