Computational Geosciences

, Volume 2, Issue 4, pp 291–309 | Cite as

Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions

  • Michael D. Tocci
  • C.T. Kelley
  • Cass T. Miller
  • Christopher E. Kees

Abstract

Richards' equation (RE) is often used to model flow in unsaturated porous media. This model captures physical effects, such as sharp fronts in fluid pressures and saturations, which are present in more complex models of multiphase flow. The numerical solution of RE is difficult not only because of these physical effects but also because of the mathematical problems that arise in dealing with the nonlinearities. The method of lines has been shown to be very effective for solving RE in one space dimension. When solving RE in two space dimensions, direct methods for solving the linearized problem for the Newton step are impractical. In this work, we show how the method of lines and Newton-iterative methods, which solve linear equations with iterative methods, can be applied to RE in two space dimensions. We present theoretical results on convergence and use that theory to design an adaptive method for computation of the linear tolerance. Numerical results show the method to be effective and robust compared with an existing approach.

Richards' equation method of lines inexact Newton methods 65F10 65H10 65M06 65M20 76S05 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Michael D. Tocci
    • 1
  • C.T. Kelley
    • 2
  • Cass T. Miller
    • 2
  • Christopher E. Kees
    • 2
  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Center for Research in Scientific Computation, Department of MathematicsNorth Carolina State UniversityRaleighUSA

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