A Nested Newton-Type Algorithm for Finite Volume Methods Solving Richards' Equation in Mixed Form

Authors:
Vincenzo Casulli;Paola Zanolli
Affiliations:
vincenzo.casulli@unitn.it;paola.zanolli@unitn.it
Venue:
SIAM Journal on Scientific Computing
Year:
2010

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Abstract

A finite volume discretization of the mixed form of Richards' equation leads to a nonlinear numerical model which yields exact local and global mass conservation. The resulting nonlinear system requires sophisticated numerical strategies, especially in a variable saturated flow regime. In this paper a nested, Newton-type algorithm for the discretized Richards' equation is proposed and analyzed. With a judicious choice of the initial guess, the quadratic convergence rate is obtained for any time step size and for all flow regimes.