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Assessment of initial solution estimates and adaptive vs. heuristic time stepping for variably saturated flow

Christophe D'haese, M Putti, Claudio Paniconi, Niko Verhoest UGent and François De Troch UGent (2004) DEVELOPMENTS IN WATER SCIENCE. 55. p.545-556
abstract
The performance of improved (higher order extrapolation) initial estimates and a poste(heuristic) and a priori(adaptive) techniques for time step adaptation in the solution of the nonlinear Richards ' equation governing flow in unsaturated porous media is evaluated. The so-called heuristic technique uses the convergence behavior of the iterative scheme (Picard linearization in this case) to estimate the next time step (e.g., increase the step size if convergence was fast, decrease it if convergence was slow). The a priori technique adapts the time step on the basis of an approximation of the local time truncation error obtained from finite difference estimates of the first and second order time derivatives. The local error estimate is used to predict the largest step size that satisfies a preset error tolerance. The sample problem used to assess these various schemes is characterized by non-uniform (in time) boundary conditions and sharp gradients in the soil hydraulic properties and is thus a challenging test case for numerical simulators. The influence of chord slope approximations to the derivatives of the hydraulic functions in the presence of steep gradients is also included in the assessment of the time stepping techniques. It is found that higher order initial solution estimates improve the convergence of the Picard linearization scheme when using the a posteriori technique. When simulating strong nonlinearities. the a priori technique diminishes computational performance the a posteriori technique seems to be more appropriate to guide the simulation under such circumstances.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
TRUNCATION ERROR CONTROL, RICHARDS EQUATION, POROUS-MEDIA, FORM, NUMERICAL-SOLUTION
in
DEVELOPMENTS IN WATER SCIENCE
Dev. Water Sci.
editor
CT Miller, MW Farthing, WG Gray and GF Pinder
volume
55
issue title
Computational Methods in Water Resources, Vols 1 and 2
pages
545 - 556
publisher
Elsevier Science bv
place of publication
Amsterdam, The Netherlands
conference name
15th International Conference on Computational Methods in Water Resources
conference location
Chapel Hill, NC, USA
conference start
2004-06-13
conference end
2004-06-17
Web of Science type
Article
Web of Science id
000228987900049
ISSN
7108-8070
ISBN
0-444-51839-8
0-444-51769-3
language
English
UGent publication?
yes
classification
P1
id
405050
handle
http://hdl.handle.net/1854/LU-405050
date created
2008-05-14 16:22:00
date last changed
2010-01-12 10:15:27
@inproceedings{405050,
  abstract     = {The performance of improved (higher order extrapolation) initial estimates and a poste(heuristic) and a priori(adaptive) techniques for time step adaptation in the solution of the nonlinear Richards ' equation governing flow in unsaturated porous media is evaluated. The so-called heuristic technique uses the convergence behavior of the iterative scheme (Picard linearization in this case) to estimate the next time step (e.g., increase the step size if convergence was fast, decrease it if convergence was slow). The a priori technique adapts the time step on the basis of an approximation of the local time truncation error obtained from finite difference estimates of the first and second order time derivatives. The local error estimate is used to predict the largest step size that satisfies a preset error tolerance. The sample problem used to assess these various schemes is characterized by non-uniform (in time) boundary conditions and sharp gradients in the soil hydraulic properties and is thus a challenging test case for numerical simulators. The influence of chord slope approximations to the derivatives of the hydraulic functions in the presence of steep gradients is also included in the assessment of the time stepping techniques. It is found that higher order initial solution estimates improve the convergence of the Picard linearization scheme when using the a posteriori technique. When simulating strong nonlinearities. the a priori technique diminishes computational performance the a posteriori technique seems to be more appropriate to guide the simulation under such circumstances.},
  author       = {D'haese, Christophe and Putti, M and Paniconi, Claudio and Verhoest, Niko and De Troch, Fran\c{c}ois},
  booktitle    = {DEVELOPMENTS IN WATER SCIENCE},
  editor       = {Miller, CT and Farthing, MW and Gray, WG and Pinder, GF},
  isbn         = {0-444-51839-8},
  issn         = {7108-8070},
  keyword      = {TRUNCATION ERROR CONTROL,RICHARDS EQUATION,POROUS-MEDIA,FORM,NUMERICAL-SOLUTION},
  language     = {eng},
  location     = {Chapel Hill, NC, USA},
  pages        = {545--556},
  publisher    = {Elsevier Science bv},
  title        = {Assessment of initial solution estimates and adaptive vs. heuristic time stepping for variably saturated flow},
  volume       = {55},
  year         = {2004},
}

Chicago
D’haese, Christophe, M Putti, Claudio Paniconi, Niko Verhoest, and François De Troch. 2004. “Assessment of Initial Solution Estimates and Adaptive Vs. Heuristic Time Stepping for Variably Saturated Flow.” In Developments in Water Science, ed. CT Miller, MW Farthing, WG Gray, and GF Pinder, 55:545–556. Amsterdam, The Netherlands: Elsevier Science bv.
APA
D’haese, C., Putti, M., Paniconi, C., Verhoest, N., & De Troch, F. (2004). Assessment of initial solution estimates and adaptive vs. heuristic time stepping for variably saturated flow. In C. Miller, M. Farthing, W. Gray, & G. Pinder (Eds.), DEVELOPMENTS IN WATER SCIENCE (Vol. 55, pp. 545–556). Presented at the 15th International Conference on Computational Methods in Water Resources, Amsterdam, The Netherlands: Elsevier Science bv.
Vancouver
1.
D’haese C, Putti M, Paniconi C, Verhoest N, De Troch F. Assessment of initial solution estimates and adaptive vs. heuristic time stepping for variably saturated flow. In: Miller C, Farthing M, Gray W, Pinder G, editors. DEVELOPMENTS IN WATER SCIENCE. Amsterdam, The Netherlands: Elsevier Science bv; 2004. p. 545–56.
MLA
D’haese, Christophe, M Putti, Claudio Paniconi, et al. “Assessment of Initial Solution Estimates and Adaptive Vs. Heuristic Time Stepping for Variably Saturated Flow.” Developments in Water Science. Ed. CT Miller et al. Vol. 55. Amsterdam, The Netherlands: Elsevier Science bv, 2004. 545–556. Print.