A NESTED NEWTON-TYPE ALGORITHM FOR FINITE VOLUME METHODS SOLVING RICHARDS' EQUATION IN MIXED FORM

被引：74

作者：

Casulli, Vincenzo ^{[1
]}

Zanolli, Paola ^{[2
]}

机构：

[1] Univ Trent, Dept Civil & Environm Engn, Lab Appl Math, I-38050 Trento, Italy

[2] Univ Trent, Dept Math, I-38050 Trento, Italy

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2010年 / 32卷 / 04期

关键词：

Richards' equation; variably saturated flow; finite volume; mildly nonlinear systems; Jordan decomposition; nested iterations; VARIABLY SATURATED FLOW; CONSERVATIVE NUMERICAL-SOLUTION; POROUS-MEDIA; UNSATURATED FLOW; SOILS;

D O I：

10.1137/100786320

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2255 / 2273

页数：19

共 11 条

[1] Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
Bergamaschi, L
Putti, M
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1999, 45 (08) : 1025 - 1046
[2] Ross scheme, Newton-Raphson iterative methods and time-stepping strategies for solving the mixed form of Richards' equation
Maina, Fadji Hassane
Ackerer, Philippe
HYDROLOGY AND EARTH SYSTEM SCIENCES, 2017, 21 (06) : 2667 - 2683
[3] Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions
Tocci, MD
Kelley, CT
Miller, CT
Kees, CE
COMPUTATIONAL GEOSCIENCES, 1998, 2 (04) : 291 - 309
[4] 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
Computational Geosciences, 1998, 2 : 291 - 309
[5] Finite analytic method based on mixed-form Richards' equation for simulating water flow in vadose zone
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Wang, Wenke
Yeh, Tian-chyi Jim
Chen, Li
Wang, Zhoufeng
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[6] A mass-conservative control volume-finite element method for solving Richards' equation in heterogeneous porous media
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Moroney, Tim
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BIT NUMERICAL MATHEMATICS, 2011, 51 (04) : 845 - 864
[7] Mass-conservative finite volume methods on 2-D unstructured grids for the Richards' equation
Manzini, G
Ferraris, S
ADVANCES IN WATER RESOURCES, 2004, 27 (12) : 1199 - 1215
[8] A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media
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Tim Moroney
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[9] Second-order accurate finite volume schemes with the discrete maximum principle for solving Richards' equation on unstructured meshes
Svyatskiy, D.
Lipnikov, K.
ADVANCES IN WATER RESOURCES, 2017, 104 : 114 - 126
[10] A novel vertex-centered finite volume method for solving Richards' equation and its adaptation to local mesh refinement
Qian, Yingzhi
Zhang, Xiaoping
Zhu, Yan
Ju, Lili
Guadagnini, Alberto
Huang, Jiesheng
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