New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation
Abstract
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Environmental Management (EM)
- OSTI Identifier:
- 1256101
- Alternate Identifier(s):
- OSTI ID: 1325352
- Report Number(s):
- LA-UR-15-27929
Journal ID: ISSN 0309-1708
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Advances in Water Resources
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: C; Journal ID: ISSN 0309-1708
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Mathematics; Planetary Sciences; Richards' equation, variable saturated flow, nonlinear solver, Picard method
Citation Formats
Lipnikov, Konstantin, Moulton, David, and Svyatskiy, Daniil. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation. United States: N. p., 2016.
Web. doi:10.1016/j.advwatres.2016.04.016.
Lipnikov, Konstantin, Moulton, David, & Svyatskiy, Daniil. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation. United States. https://doi.org/10.1016/j.advwatres.2016.04.016
Lipnikov, Konstantin, Moulton, David, and Svyatskiy, Daniil. Fri .
"New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation". United States. https://doi.org/10.1016/j.advwatres.2016.04.016. https://www.osti.gov/servlets/purl/1256101.
@article{osti_1256101,
title = {New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation},
author = {Lipnikov, Konstantin and Moulton, David and Svyatskiy, Daniil},
abstractNote = {We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.},
doi = {10.1016/j.advwatres.2016.04.016},
journal = {Advances in Water Resources},
number = C,
volume = 94,
place = {United States},
year = {Fri Apr 29 00:00:00 EDT 2016},
month = {Fri Apr 29 00:00:00 EDT 2016}
}
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Works referencing / citing this record:
Numerical Solution of Richards' Equation: A Review of Advances and Challenges
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- Soil Science Society of America Journal, Vol. 81, Issue 6