Error driven node placement as applied to one dimensional shallow water equations

Zhenquan Li; Peter Crowhurst; Robert Wood

doi:10.1109/UKSim.2015.31

Error driven node placement as applied to one dimensional shallow water equations

Zhenquan Li, Peter Crowhurst, Robert Wood

Research output: Book chapter/Published conference paper › Conference paper › peer-review

Abstract

This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. © 2015 IEEE.

Original language	English
Title of host publication	UKSim 2015
Subtitle of host publication	UKSim-AMSS 17th International conference on omputer modelling and simulation, Cambridge, United Kingdom 25-27 March 2015
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	31-38
Number of pages	8
ISBN (Electronic)	9781479987139
ISBN (Print)	9781479987146
DOIs	https://doi.org/10.1109/UKSim.2015.31
Publication status	Published - 2016
Event	2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim) - Cambridge University, Cambridge, United Kingdom Duration: 25 Mar 2015 → 27 Mar 2015 Conference number: 123957

Publication series

Name	IEEE Computer Society Conference Publishing Services (CPS)
Publisher	IEEE Computer Society

Conference

Conference	2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim)
Country/Territory	United Kingdom
City	Cambridge
Period	25/03/15 → 27/03/15

Access to Document

10.1109/UKSim.2015.31

1 Peer review responsibility, including review panel or committee

International Journal for Numerical Methods in Fluids (Journal)
Li, Z. (Reviewer)
01 Nov 2023 → 31 Dec 2023
Activity: Publication peer-review and editorial work › Peer review responsibility, including review panel or committee

Cite this

Li, Z., Crowhurst, P., & Wood, R. (2016). Error driven node placement as applied to one dimensional shallow water equations. In UKSim 2015: UKSim-AMSS 17th International conference on omputer modelling and simulation, Cambridge, United Kingdom 25-27 March 2015 (pp. 31-38). Article 7576517 (IEEE Computer Society Conference Publishing Services (CPS) ). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/UKSim.2015.31

Li, Zhenquan ; Crowhurst, Peter ; Wood, Robert. / Error driven node placement as applied to one dimensional shallow water equations. UKSim 2015: UKSim-AMSS 17th International conference on omputer modelling and simulation, Cambridge, United Kingdom 25-27 March 2015. IEEE, Institute of Electrical and Electronics Engineers, 2016. pp. 31-38 (IEEE Computer Society Conference Publishing Services (CPS) ).

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title = "Error driven node placement as applied to one dimensional shallow water equations",

abstract = "This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. {\textcopyright} 2015 IEEE.",

keywords = "Finite difference methods, Nonlinear difference equations, Fluid flow",

author = "Zhenquan Li and Peter Crowhurst and Robert Wood",

note = "Includes bibliographical references.; 2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim) ; Conference date: 25-03-2015 Through 27-03-2015",

year = "2016",

doi = "10.1109/UKSim.2015.31",

language = "English",

isbn = "9781479987146",

series = "IEEE Computer Society Conference Publishing Services (CPS) ",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

pages = "31--38",

booktitle = "UKSim 2015",

address = "United States",

}

Li, Z, Crowhurst, P & Wood, R 2016, Error driven node placement as applied to one dimensional shallow water equations. in UKSim 2015: UKSim-AMSS 17th International conference on omputer modelling and simulation, Cambridge, United Kingdom 25-27 March 2015., 7576517, IEEE Computer Society Conference Publishing Services (CPS) , IEEE, Institute of Electrical and Electronics Engineers, pp. 31-38, 2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim), Cambridge, United Kingdom, 25/03/15. https://doi.org/10.1109/UKSim.2015.31

Error driven node placement as applied to one dimensional shallow water equations. / Li, Zhenquan; Crowhurst, Peter; Wood, Robert.
UKSim 2015: UKSim-AMSS 17th International conference on omputer modelling and simulation, Cambridge, United Kingdom 25-27 March 2015. IEEE, Institute of Electrical and Electronics Engineers, 2016. p. 31-38 7576517 (IEEE Computer Society Conference Publishing Services (CPS) ).

Research output: Book chapter/Published conference paper › Conference paper › peer-review

TY - GEN

T1 - Error driven node placement as applied to one dimensional shallow water equations

AU - Li, Zhenquan

AU - Crowhurst, Peter

AU - Wood, Robert

N1 - Conference code: 123957

PY - 2016

Y1 - 2016

N2 - This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. © 2015 IEEE.

AB - This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. © 2015 IEEE.

KW - Finite difference methods

KW - Nonlinear difference equations

KW - Fluid flow

U2 - 10.1109/UKSim.2015.31

DO - 10.1109/UKSim.2015.31

M3 - Conference paper

SN - 9781479987146

T3 - IEEE Computer Society Conference Publishing Services (CPS)

SP - 31

EP - 38

BT - UKSim 2015

PB - IEEE, Institute of Electrical and Electronics Engineers

T2 - 2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim)

Y2 - 25 March 2015 through 27 March 2015

ER -

Li Z, Crowhurst P, Wood R. Error driven node placement as applied to one dimensional shallow water equations. In UKSim 2015: UKSim-AMSS 17th International conference on omputer modelling and simulation, Cambridge, United Kingdom 25-27 March 2015. IEEE, Institute of Electrical and Electronics Engineers. 2016. p. 31-38. 7576517. (IEEE Computer Society Conference Publishing Services (CPS) ). doi: 10.1109/UKSim.2015.31

Error driven node placement as applied to one dimensional shallow water equations

Abstract

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Conference

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Activities

International Journal for Numerical Methods in Fluids (Journal)

Cite this