A Gradient Scheme for the Discretization of Richards Equation

  • Konstantin Brenner
  • Danielle HilhorstEmail author
  • Huy Cuong Vu Do
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)


We propose a finite volume method on general meshes for the discretization of Richards equation, an elliptic—parabolic equation modeling groundwater flow. The diffusion term, which can be anisotropic and heterogeneous, is discretized in a gradient scheme framework, which can be applied to a wide range of unstructured possibly non-matching polyhedral meshes in arbitrary space dimension. More precisely, we implement the SUSHI scheme which is also locally conservative. As is needed for Richards equation, the time discretization is fully implicit. We obtain a convergence result based upon energy-type estimates and the application of the Fréchet-Kolmogorov compactness theorem. We implement the scheme and present the results of a number of numerical tests.


Relative Permeability Dirichlet Boundary Condition Adaptive Mesh Absolute Permeability Richards Equation 
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D. Hilhorst and H.C. Vu Do acknowledge the support of the ITN Marie Curie Project FIRST and of the Fondation Jacques Hadamard


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Konstantin Brenner
    • 1
    • 2
  • Danielle Hilhorst
    • 3
    Email author
  • Huy Cuong Vu Do
    • 4
  1. 1.LJADUniversity Nice Sophia-AntipolisNiceFrance
  2. 2.Coffee Team Inria Sophia-Antipolis-MéditerranéeValbonneFrance
  3. 3.Laboratoire de MathématiquesCNRS et Université de Paris-SudOrsayFrance
  4. 4.Laboratoire de MathématiquesUniversité de Paris-SudOrsayFrance

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