Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

doi:10.1016/j.anucene.2015.04.016

Title: Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

Authors:: Zou, Ling; Zhao, Haihua; Zhang, Hongbin

Publication Date:: Tue Sep 01 00:00:00 EDT 2015

Sponsoring Org.:: USDOE

OSTI Identifier:: 1247857

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Annals of Nuclear Energy

Additional Journal Information:: Journal Name: Annals of Nuclear Energy Journal Volume: 83 Journal Issue: C; Journal ID: ISSN 0306-4549

Publisher:: Elsevier

Country of Publication:: United Kingdom

Language:: English

Citation Formats


                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems.  United Kingdom: N. p., 2015. 
Web.  doi:10.1016/j.anucene.2015.04.016.

Copy to clipboard


                    Zou, Ling, Zhao, Haihua, & Zhang, Hongbin. Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems.  United Kingdom.  https://doi.org/10.1016/j.anucene.2015.04.016

Copy to clipboard


                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Tue .  
"Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems".  United Kingdom.  https://doi.org/10.1016/j.anucene.2015.04.016.

Copy to clipboard


                    
@article{osti_1247857,

  title        = {Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems},

  author       = {Zou, Ling and Zhao, Haihua and Zhang, Hongbin},

  abstractNote = {},

  doi          = {10.1016/j.anucene.2015.04.016},

  journal      = {Annals of Nuclear Energy},

  number       = C,

  volume       = 83,

  place        = {United Kingdom},

  year         = {Tue Sep 01 00:00:00 EDT 2015},

  month        = {Tue Sep 01 00:00:00 EDT 2015}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Publisher's Version of Record
https://doi.org/10.1016/j.anucene.2015.04.016

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 24 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Numerical calculation of almost incompressible flow
journal, August 1968

Harlow, Francis H.; Amsden, Anthony A.
Journal of Computational Physics, Vol. 3, Issue 1
DOI: 10.1016/0021-9991(68)90007-7

A Fully Implicit, Second Order in Time, Simulation of a Nuclear Reactor Core
conference, January 2006

Mousseau, Vincent A.
Volume 4: Computational Fluid Dynamics, Neutronics Methods and Coupled Codes; Student Paper Competition
DOI: 10.1115/ICONE14-89737

Improvement of the one-dimensional dissolved-solute convection equation using the QUICKEST–ULTIMATE algorithm
journal, January 2011

Bertolotto, D.; Manera, A.; Macián-Juan, R.
Nuclear Engineering and Design, Vol. 241, Issue 1
DOI: 10.1016/j.nucengdes.2010.10.021

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows
journal, January 2003

Stelling, G. S.; Duinmeijer, S. P. A.
International Journal for Numerical Methods in Fluids, Vol. 43, Issue 12
DOI: 10.1002/fld.537

Accurate Solution of the Nonlinear Partial Differential Equations from Thermal Hydraulics: Thermal Hydraulics
journal, April 2007

Mousseau, Vincent A.
Nuclear Technology, Vol. 158, Issue 1
DOI: 10.13182/NT07-A3822

Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004

Knoll, D. A.; Keyes, D. E.
Journal of Computational Physics, Vol. 193, Issue 2
DOI: 10.1016/j.jcp.2003.08.010

Implementation and assessment of high-resolution numerical methods in TRACE
journal, October 2013

Wang, Dean; Mahaffy, John H.; Staudenmeier, Joseph
Nuclear Engineering and Design, Vol. 263
DOI: 10.1016/j.nucengdes.2013.05.015

Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
journal, October 2004

Mousseau, V. A.
Journal of Computational Physics, Vol. 200, Issue 1
DOI: 10.1016/j.jcp.2004.03.009

A numerical fluid dynamics calculation method for all flow speeds
journal, October 1971

Harlow, Francis H.; Amsden, Anthony A.
Journal of Computational Physics, Vol. 8, Issue 2
DOI: 10.1016/0021-9991(71)90002-7

The physical closure laws in the CATHARE code
journal, December 1990

Bestion, D.
Nuclear Engineering and Design, Vol. 124, Issue 3
DOI: 10.1016/0029-5493(90)90294-8

A Jacobian-free Newton-Krylov method for thermalhydraulics simulations: A JFNK METHOD FOR THERMALHYDRAULICS SIMULATIONS
journal, January 2015

Ashrafizadeh, A.; Devaud, C. B.; Aydemir, N. U.
International Journal for Numerical Methods in Fluids, Vol. 77, Issue 10
DOI: 10.1002/fld.3999

Modelling of Two-Phase Flow with Second-Order Accurate Scheme
journal, September 1997

Tiselj, Iztok; Petelin, Stojan
Journal of Computational Physics, Vol. 136, Issue 2
DOI: 10.1006/jcph.1997.5778

A Numerical Method Using Upwind Schemes for the Resolution of Two-Phase Flows
journal, September 1997

Coquel, F.; El Amine, K.; Godlewski, E.
Journal of Computational Physics, Vol. 136, Issue 2
DOI: 10.1006/jcph.1997.5730

Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model
journal, November 2003

Frepoli, Cesare; Mahaffy, John H.; Ohkawa, Katsuhiro
Nuclear Engineering and Design, Vol. 225, Issue 2-3
DOI: 10.1016/S0029-5493(03)00159-6

Similar Records in DOE PAGES and OSTI.GOV collections:

Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

Journal Article Zou, Ling ; Zhao, Haihua ; Zhang, Hongbin - Annals of Nuclear Energy (Oxford)

The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system hasmore »« less
https://doi.org/10.1016/j.anucene.2015.04.016
Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

Journal Article Zou, Ling ; Zhao, Haihua ; Zhang, Hongbin - Computers and Fluids

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore »« less
https://doi.org/10.1016/j.compfluid.2016.02.008
Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

Journal Article Zou, Ling ; Zhao, Haihua ; Zhang, Hongbin - Computers and Fluids
Cited by 16
https://doi.org/10.1016/j.compfluid.2016.02.008
Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

Journal Article Zou, Ling ; Zhao, Haihua ; Zhang, Hongbin - Nuclear Engineering and Design

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore »« less
Cited by 24
https://doi.org/10.1016/j.nucengdes.2016.01.033

Full Text Available
Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

Journal Article Zou, Ling ; Zhao, Haihua ; Zhang, Hongbin - Annals of Nuclear Energy (Oxford)

This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. Themore »« less
Cited by 25
https://doi.org/10.1016/j.anucene.2015.07.033

Full Text Available

Similar Records

Title: Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

Citation Formats

Numerical calculation of almost incompressible flow journal, August 1968

A Fully Implicit, Second Order in Time, Simulation of a Nuclear Reactor Core conference, January 2006

Improvement of the one-dimensional dissolved-solute convection equation using the QUICKEST–ULTIMATE algorithm journal, January 2011

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows journal, January 2003

Accurate Solution of the Nonlinear Partial Differential Equations from Thermal Hydraulics: Thermal Hydraulics journal, April 2007

Jacobian-free Newton–Krylov methods: a survey of approaches and applications journal, January 2004

Implementation and assessment of high-resolution numerical methods in TRACE journal, October 2013

Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction journal, October 2004

A numerical fluid dynamics calculation method for all flow speeds journal, October 1971

The physical closure laws in the CATHARE code journal, December 1990

A Jacobian-free Newton-Krylov method for thermalhydraulics simulations: A JFNK METHOD FOR THERMALHYDRAULICS SIMULATIONS journal, January 2015

Modelling of Two-Phase Flow with Second-Order Accurate Scheme journal, September 1997

A Numerical Method Using Upwind Schemes for the Resolution of Two-Phase Flows journal, September 1997

Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model journal, November 2003

Numerical calculation of almost incompressible flow
journal, August 1968

A Fully Implicit, Second Order in Time, Simulation of a Nuclear Reactor Core
conference, January 2006

Improvement of the one-dimensional dissolved-solute convection equation using the QUICKEST–ULTIMATE algorithm
journal, January 2011

A staggered conservative scheme for every Froude number in rapidly varied shallow water flows
journal, January 2003

Accurate Solution of the Nonlinear Partial Differential Equations from Thermal Hydraulics: Thermal Hydraulics
journal, April 2007

Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004

Implementation and assessment of high-resolution numerical methods in TRACE
journal, October 2013

Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
journal, October 2004

A numerical fluid dynamics calculation method for all flow speeds
journal, October 1971

The physical closure laws in the CATHARE code
journal, December 1990

A Jacobian-free Newton-Krylov method for thermalhydraulics simulations: A JFNK METHOD FOR THERMALHYDRAULICS SIMULATIONS
journal, January 2015

Modelling of Two-Phase Flow with Second-Order Accurate Scheme
journal, September 1997

A Numerical Method Using Upwind Schemes for the Resolution of Two-Phase Flows
journal, September 1997

Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model
journal, November 2003