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.

A Nested Newton Type Algorithm for Finite Volume Methods Solving Richards Equation in Mixed Form / Casulli, Vincenzo; Zanolli, Paola. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - STAMPA. - 32:4(2010), pp. 2255-2273. [10.1137/100786320]

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

Casulli, Vincenzo;Zanolli, Paola
2010-01-01

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.
2010
4
Casulli, Vincenzo; Zanolli, Paola
A Nested Newton Type Algorithm for Finite Volume Methods Solving Richards Equation in Mixed Form / Casulli, Vincenzo; Zanolli, Paola. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - STAMPA. - 32:4(2010), pp. 2255-2273. [10.1137/100786320]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/84109
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