A Comparison of Iterative Methods as Applied to the Solution of the Nonlinear Three-Dimensional Groundwater Flow Equation

Kuiper, Logan K.

doi:10.1137/0908049

Cited by 18 publications

(24 citation statements)

References 9 publications

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“…Relative efficiency of the Newton and Picard methods seems to be problem specific (Kuiper, 1987;Mehl, 2006). There is evidence that the Newton method performs better for highly nonlinear problems when combined with relaxation schemes and residual control (Cooley, 1983;Jacobs, 1988;Press, 2007).…”

Section: Newton Linearization Methodsmentioning

confidence: 99%

MODFLOW-NWT, a Newton formulation for MODFLOW-2005

Niswonger¹,

Panday²,

Ibaraki³

2011

Techniques and Methods

323

257

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For more information on the USGS-the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS.For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprodTo order this and other USGS information products, visit http://store.usgs.gov Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.Although this report is in the public domain, permission must be secured from the individual copyright owners to reproduce any copyrighted materials contained within this report. Altitude, as used in this report, refers to distance above the vertical datum.*Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times foot of aquifer thickness [(ft 3 /d)/ft 2 ]ft. In this report, the mathematically reduced form, foot squared per day (ft 2 /d), is used for convenience. The UPW Package treats nonlinearities of cell drying and rewetting by use of a continuous function of groundwater head, rather than the discrete approach of drying and rewetting that is used by the BCF, LPF, and HUF Packages. This further enables application of the Newton formulation for unconfined groundwater-flow problems because conductance derivatives required by the Newton method are smooth over the full range of head for a model cell. TablesThe NWT linearization approach generates an asymmetric matrix, which is different from the standard MODFLOW formulation that generates a symmetric matrix. Because all linear solvers presently available for use with MODFLOW-2005 solve only symmetric matrices, MODFLOW-NWT includes two previously developed asymmetric matrix-solver options. The matrix-solver options include a generalized-minimum-residual (GMRES) Solver and an Orthomin / stabilized conjugate-gradient (CGSTAB) Solver. The GMRES Solver is documented in a previously published report, such that only a brief description and input instructions are provided in this report. However, the CGSTAB Solver (called χMD) is documented in this report.Flow-property input for the UPW Package is designed based on the LPF Package and material-property input is identical to that for the LPF Package except that the rewetting and vertical-conductance correction options of the LPF Package are not available with the UPW Package. Input files constructed for the LPF Package can be used with slight modification as input for the UPW Package. This report presents the theory and methods used by MODFLOW-NWT, including the UPW Package. Additionally, this report provides comparisons of the new methodology to analytical solutions of groundwater flow and to standard MODFLOW-2005 results by use of an unconfined aquifer MODFLOW example problem. The standard MODFLOW-2005 simulation uses the LPF Package with the wet/dry option active. A new example problem also is presented to demonstrate MODFLOW-NWT's ability to provide a sol...

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Section: Newton Linearization Methodsmentioning

confidence: 99%

MODFLOW-NWT, a Newton formulation for MODFLOW-2005

Niswonger¹,

Panday²,

Ibaraki³

2011

Techniques and Methods

323

257

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“…Complex DNAPL distribution patterns have been observed in case studies (see e.g. Feenstra and Cherry , 1988; Cherry , 1987), laboratory experiments ( Kueper et al , 1989; Schwille , 1988) and through detailed numerical simulations of DNAPL migration in random spatially correlated permeability fields ( Kueper and Frind , 1990). An erratic, imperfectly known source location combined with poorly defined dissolution kinetics that further depend on local groundwater velocities affected by heterogeneity is likely to lead to pump‐and‐treat remediation uncertainties far greater than those predicted by current groundwater quality optimization models.…”

Section: Uncertainty and Risk Associated With Plume Prediction And Aqmentioning

confidence: 98%

Contaminant Migration in Imperfectly Known Heterogeneous Groundwater Systems

Sudicky

Huyakorn²

1991

Reviews of Geophysics

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Recent studies dealing with methodologies for describing contaminant migration in complex groundwater flow systems are summarized. Emphasis is placed on the role played by heterogeneity in the flow and transport properties of geologic media because it is one of the largest sources of uncertainty for making reliable predictions of contaminant plume evolution and remediation. Advancements made in stochastic subsurface transport theories are highlighted with a complementary discussion of findings based on recent detailed field experiments and progress in numerical modelling techniques.

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“…The iteration methods that are generally used are the Picard and Newton algorithms. Theoretically, Newton's method converges one order of magnitude faster than the Picard scheme [19], but several studies have shown that this method is inferior to the Picard method [44,65,66]. Newton's method converges quadratically only in the vicinity of the solution.…”

Section: Iterative Procedures and Adaptive Time-steppingmentioning

confidence: 99%

Parameter estimation in flow through partially saturated porous materials

Zadeh

2008

Journal of Computational Physics

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A Comparison of Iterative Methods as Applied to the Solution of the Nonlinear Three-Dimensional Groundwater Flow Equation

Cited by 18 publications

References 9 publications

MODFLOW-NWT, a Newton formulation for MODFLOW-2005

MODFLOW-NWT, a Newton formulation for MODFLOW-2005

Contaminant Migration in Imperfectly Known Heterogeneous Groundwater Systems

Parameter estimation in flow through partially saturated porous materials

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