On the characteristics-based ACM for incompressible flows

Xiaohui Su, Yong Zhao, Xiaoyang Huang

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475-484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667-685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466-1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309-325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657-663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584-607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756]. Detailed numerical experiments show that both methods give almost identical solutions and convergence rates. Both can generate solutions which agree well with published results and experimental measurements. We thus conclude that both methods, being upwind schemes designed for the ACM, have the same performances in terms of accuracy and convergence speed, even though the revised method is more complex with less stringent assumptions made, while the original CB method is simpler due to the use of extra simplifying assumptions.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Computational Physics
Volume227
Issue number1
DOIs
Publication statusPublished - Nov 10 2007
Externally publishedYes

Fingerprint

incompressible flow
Incompressible flow
Compressibility
compressibility
formulations
Heat transfer
Viscous flow
Unsteady flow
Density (specific gravity)
heat transfer
Flow of fluids
flow equations
unsteady flow
viscous flow
Fluids
fluid flow
derivation
simulation
heat
Experiments

Keywords

  • Artificial compressibility method (ACM)
  • Characteristics-based method
  • Compatibility equations
  • Incompressible flows

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

On the characteristics-based ACM for incompressible flows. / Su, Xiaohui; Zhao, Yong; Huang, Xiaoyang.

In: Journal of Computational Physics, Vol. 227, No. 1, 10.11.2007, p. 1-11.

Research output: Contribution to journalArticle

Su, Xiaohui ; Zhao, Yong ; Huang, Xiaoyang. / On the characteristics-based ACM for incompressible flows. In: Journal of Computational Physics. 2007 ; Vol. 227, No. 1. pp. 1-11.
@article{b9bee33be9cc4996b1bf08133128c561,
title = "On the characteristics-based ACM for incompressible flows",
abstract = "In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475-484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667-685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466-1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309-325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657-663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584-607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756]. Detailed numerical experiments show that both methods give almost identical solutions and convergence rates. Both can generate solutions which agree well with published results and experimental measurements. We thus conclude that both methods, being upwind schemes designed for the ACM, have the same performances in terms of accuracy and convergence speed, even though the revised method is more complex with less stringent assumptions made, while the original CB method is simpler due to the use of extra simplifying assumptions.",
keywords = "Artificial compressibility method (ACM), Characteristics-based method, Compatibility equations, Incompressible flows",
author = "Xiaohui Su and Yong Zhao and Xiaoyang Huang",
year = "2007",
month = "11",
day = "10",
doi = "10.1016/j.jcp.2007.08.009",
language = "English",
volume = "227",
pages = "1--11",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - On the characteristics-based ACM for incompressible flows

AU - Su, Xiaohui

AU - Zhao, Yong

AU - Huang, Xiaoyang

PY - 2007/11/10

Y1 - 2007/11/10

N2 - In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475-484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667-685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466-1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309-325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657-663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584-607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756]. Detailed numerical experiments show that both methods give almost identical solutions and convergence rates. Both can generate solutions which agree well with published results and experimental measurements. We thus conclude that both methods, being upwind schemes designed for the ACM, have the same performances in terms of accuracy and convergence speed, even though the revised method is more complex with less stringent assumptions made, while the original CB method is simpler due to the use of extra simplifying assumptions.

AB - In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475-484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667-685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466-1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309-325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657-663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584-607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756]. Detailed numerical experiments show that both methods give almost identical solutions and convergence rates. Both can generate solutions which agree well with published results and experimental measurements. We thus conclude that both methods, being upwind schemes designed for the ACM, have the same performances in terms of accuracy and convergence speed, even though the revised method is more complex with less stringent assumptions made, while the original CB method is simpler due to the use of extra simplifying assumptions.

KW - Artificial compressibility method (ACM)

KW - Characteristics-based method

KW - Compatibility equations

KW - Incompressible flows

UR - http://www.scopus.com/inward/record.url?scp=35348922896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35348922896&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2007.08.009

DO - 10.1016/j.jcp.2007.08.009

M3 - Article

AN - SCOPUS:35348922896

VL - 227

SP - 1

EP - 11

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -