Adaptive time integration for the convection-dispersion equation

Guoping Tang; Akram N. Alshawabkeh; Melanie A. Mayes; Jack C. Parker

doi:10.1061/40972(311)83

Adaptive time integration for the convection-dispersion equation

Guoping Tang
, Akram N. Alshawabkeh
, Melanie A. Mayes
, Jack C. Parker

Ecosystem Processes

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We applied two schemes that automatically select the time-step to control the temporal approximation error and reduce the computational cost for numerical solution of the convection-dispersion equation. The first scheme is based on control of the truncation error difference between the second order Crank-Nicolson method and the first order backward Euler method. The second scheme is based on an a posteriori global error estimate. Results from the two numerical tests show that the first scheme is more efficient but may fail due to numerical oscillation of the Crank-Nicolson method when the specified tolerance is large; the second scheme explicitly controls global error, but may require more time steps and computational efforts when the specified error tolerance is small. Copyright ASCE 2008.

Original language	English
Title of host publication	Proceedings of Sessions of GeoCongress 2008 - GeoCongress 2008
Subtitle of host publication	Characterization, Monitoring, and Modeling of GeoSystems, GSP 179
Pages	670-677
Number of pages	8
Edition	179
DOIs	https://doi.org/10.1061/40972(311)83
State	Published - 2008
Event	GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems - New Orleans, LA, United States Duration: Mar 9 2008 → Mar 12 2008

Publication series

Name	Geotechnical Special Publication
Number	179
ISSN (Print)	0895-0563

Conference

Conference	GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems
Country/Territory	United States
City	New Orleans, LA
Period	03/9/08 → 03/12/08

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10.1061/40972(311)83

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Tang, G., Alshawabkeh, A. N., Mayes, M. A., & Parker, J. C. (2008). Adaptive time integration for the convection-dispersion equation. In Proceedings of Sessions of GeoCongress 2008 - GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems, GSP 179 (179 ed., pp. 670-677). (Geotechnical Special Publication; No. 179). https://doi.org/10.1061/40972(311)83

@inproceedings{8594b55216ba4f6e87f23b16c18d8623,

title = "Adaptive time integration for the convection-dispersion equation",

abstract = "We applied two schemes that automatically select the time-step to control the temporal approximation error and reduce the computational cost for numerical solution of the convection-dispersion equation. The first scheme is based on control of the truncation error difference between the second order Crank-Nicolson method and the first order backward Euler method. The second scheme is based on an a posteriori global error estimate. Results from the two numerical tests show that the first scheme is more efficient but may fail due to numerical oscillation of the Crank-Nicolson method when the specified tolerance is large; the second scheme explicitly controls global error, but may require more time steps and computational efforts when the specified error tolerance is small. Copyright ASCE 2008.",

author = "Guoping Tang and Alshawabkeh, \{Akram N.\} and Mayes, \{Melanie A.\} and Parker, \{Jack C.\}",

year = "2008",

doi = "10.1061/40972(311)83",

language = "English",

isbn = "9780784409725",

series = "Geotechnical Special Publication",

number = "179",

pages = "670--677",

booktitle = "Proceedings of Sessions of GeoCongress 2008 - GeoCongress 2008",

edition = "179",

note = "GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems ; Conference date: 09-03-2008 Through 12-03-2008",

}

Tang, G, Alshawabkeh, AN, Mayes, MA & Parker, JC 2008, Adaptive time integration for the convection-dispersion equation. in Proceedings of Sessions of GeoCongress 2008 - GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems, GSP 179. 179 edn, Geotechnical Special Publication, no. 179, pp. 670-677, GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems, New Orleans, LA, United States, 03/9/08. https://doi.org/10.1061/40972(311)83

Adaptive time integration for the convection-dispersion equation. / Tang, Guoping; Alshawabkeh, Akram N.; Mayes, Melanie A. et al.
Proceedings of Sessions of GeoCongress 2008 - GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems, GSP 179. 179. ed. 2008. p. 670-677 (Geotechnical Special Publication; No. 179).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Adaptive time integration for the convection-dispersion equation

AU - Tang, Guoping

AU - Alshawabkeh, Akram N.

AU - Mayes, Melanie A.

AU - Parker, Jack C.

PY - 2008

Y1 - 2008

N2 - We applied two schemes that automatically select the time-step to control the temporal approximation error and reduce the computational cost for numerical solution of the convection-dispersion equation. The first scheme is based on control of the truncation error difference between the second order Crank-Nicolson method and the first order backward Euler method. The second scheme is based on an a posteriori global error estimate. Results from the two numerical tests show that the first scheme is more efficient but may fail due to numerical oscillation of the Crank-Nicolson method when the specified tolerance is large; the second scheme explicitly controls global error, but may require more time steps and computational efforts when the specified error tolerance is small. Copyright ASCE 2008.

AB - We applied two schemes that automatically select the time-step to control the temporal approximation error and reduce the computational cost for numerical solution of the convection-dispersion equation. The first scheme is based on control of the truncation error difference between the second order Crank-Nicolson method and the first order backward Euler method. The second scheme is based on an a posteriori global error estimate. Results from the two numerical tests show that the first scheme is more efficient but may fail due to numerical oscillation of the Crank-Nicolson method when the specified tolerance is large; the second scheme explicitly controls global error, but may require more time steps and computational efforts when the specified error tolerance is small. Copyright ASCE 2008.

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U2 - 10.1061/40972(311)83

DO - 10.1061/40972(311)83

M3 - Conference contribution

AN - SCOPUS:66449130450

SN - 9780784409725

T3 - Geotechnical Special Publication

SP - 670

EP - 677

BT - Proceedings of Sessions of GeoCongress 2008 - GeoCongress 2008

T2 - GeoCongress 2008: Characterization, Monitoring, and Modeling of GeoSystems

Y2 - 9 March 2008 through 12 March 2008

ER -

Adaptive time integration for the convection-dispersion equation

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