More Web Proxy on the site http://driver.im/

article

Symmetry-preserving discretization of turbulent flow

Authors:

R. W. C. P. Verstappen,

A. E. P. VeldmanAuthors Info & Claims

Journal of Computational Physics, Volume 187, Issue 1

Pages 343 - 368

https://doi.org/10.1016/S0021-9991(03)00126-8

Published: 01 May 2003 Publication History

Abstract

We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators, i.e., the convective operator is represented by a skew-symmetric coefficient matrix and the diffusive operator is approximated by a symmetric, positive-definite matrix. Mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner. We give it a concrete form by noting that a symmetry-preserving discretization of the Navier-Stokes equations is stable on any grid, and conserves the total mass, momentum and kinetic energy (for the latter the physical dissipation is to be turned off, of coarse). Being stable on any grid, the choice of the grid may be based on the required accuracy solely, and the main question becomes: how accurate is a symmetry-preserving discretization? Its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies. The comparison is carried out for a Reynolds number of 5600, which is based on the channel width and the mean bulk velocity (based on the channel half-width and wall shear velocity the Reynolds number becomes 180). The comparison shows that with a fourth-order, symmetry-preserving method a 64 × 64 × 32 grid suffices to perform an accurate numerical simulation.

References

[1]

{1} R. Teman, Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF regional conference series in applied mathematics, vol. 66, second ed., SIAM, 1995, p. 13.

[2]

{2} T.A. Manteufel, A.B. White Jr., The numerical solution of second-order boundary value problems on nonuniform meshes, Math. Comput. 47 (1986) 511.

[3]

{3} A.E.P. Veldman, K. Rinzema, Playing with nonuniform grids, J. Eng. Math. 26 (1991) 119.

[4]

{4} Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comp. Phys. 143 (1998) 90.

Digital Library

[5]

{5} O.V. Vasilyev, High order finite difference schemes on non-uniform meshes with good conservation properties, J. Comp. Phys. 157 (2000) 746.

Digital Library

[6]

{6} F. Nicoud, Conservative high-order finite-difference schemes for low-Mach number flows, J. Comp. Phys. 158 (2000) 71.

Digital Library

[7]

{7} F. Ducros, F. Laporte, T. Soulères, V. Guinot, P. Moinat, B. Caruelle, High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows, J. Comp. Phys. 161 (2000) 114.

Digital Library

[8]

{8} A. Twerda, A.E.P. Veldman, S.W. de Leeuw, High order schemes for colocated grids: preliminary results. In: Proceedings of the 5th Annual Conference of the Advanced School for Computing and Imaging, 1999, p. 286.

[9]

{9} A. Twerda, Advanced computational methods for complex flow simulation, Ph.D. Thesis, Delft University of Technology, 2000.

[10]

{10} A. Jameson, W. Schmidt, E. Turkel, Numerical Solutions of the Euler Equations by Finite Volume Methods using Runge-Kutta Time Stepping, AIAA Paper 81-1259, 1981.

[11]

{11} D. Furihata, Finite difference schemes for that inherit energy conservation or dissipation property, J. Comp. Phys. 156 (1999) 181.

Digital Library

[12]

{12} J.M. Hyman, R.J. Knapp, J.C. Scovel, High order finite volume approximations of differential operators on nonuniform grids, Phys. D 60 (1992) 112.

Digital Library

[13]

{13} J.E. Castillo, J.M. Hyman, M.J. Shaskov, S. Steinberg, The sensitivity and accuracy of fourth order finite-difference schems on nonuniform grids in one dimension, Comput. Math. Appl. 30 (1995) 41.

[14]

{14} J.M. Hyman, M. Shashkov, Natural discretizations for the divergence, gradient and curl on logically rectangular grids, Comput. Math. Appl. 33 (1997) 81.

[15]

{15} R.W.C.P. Verstappen, R.M. van der Velde, Symmetry-preserving discretization of heat transfer in a complex turbulent flow, submitted.

[16]

{16} R.W.C.P. Verstappen, A.E.P. Veldman, Direct numerical simulation of turbulence at lower costs, J. Eng. Math. 32 (1997) 143.

[17]

{17} R.W.C.P. Verstappen, A.E.P. Veldman, Spectro-consistent discretization of Navier-Stokes: a challenge to RANS and LES, J. Eng. Math. 34 (1998) 163.

[18]

{18} F.H. Harlow, J.E. Welsh, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 8 (1965) 2182.

[19]

{19} M. Antonopoulos-Domis, Large-eddy simulation of a passive scalar in isotropic turbulence, J. Fluid Mech. 104 (1981) 55-79.

[20]

{20} J. Kim, P. Moin, R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177 (1987) 133.

[21]

{21} N. Gilbert, L. Kleiser, Turbulence model testing with the aid of direct numerical simulation results, in: Proceedings of the Turbulence Shear Flows 8, Paper 26-1, Munich, 1991.

[22]

{22} A. Kuroda, N. Kasagi, M. Hirata, Direct numerical simulation of turbulent plane Couette-Poisseuille flows: effect of mean shear rate on the near-wall turbulence structures, in: F. Durst, et al. (Eds.), Proc. Turb. Shear Flows. vol. 9, Springer, Berlin, 1995, pp. 241-257.

[23]

{23} H.P. Kreplin, H. Eckelmann, Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow, Phys. Fluids 22 (1979) 1233-1239.

[24]

{24} H. Eckelmann, The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow, J. Fluid Mech. 65 (1974) 439-459.

[25]

{25} R.B. Dean, Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow, J. Fluids Eng. 100 (1978) 215-223.

[26]

{26} T.J. Hanratty, L.G. Chorn, D.T. Hatziavramidis, Turbulent fluctuations in the viscous wall region for Newtonian and drag reducing fluids, Phys. Fluids 20 (1977) S112.

[27]

{27} D.S Finnicum, T.J. Hanratty, Turbulent normal velocity fluctuations close to a wall, Phys. Fluids 28 (1985) 1654-1658.

Cited By

van der Eijk MWellens P(2024)An efficient pressure-based multiphase finite volume method for interaction between compressible aerated water and moving bodiesJournal of Computational Physics10.1016/j.jcp.2024.113167514:COnline publication date: 18-Oct-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.113167
Boguslawski ATyliszczak AGeurts B(2024)Approximate deconvolution discretisationComputers & Mathematics with Applications10.1016/j.camwa.2023.11.039154:C(175-198)Online publication date: 15-Jan-2024
https://dl.acm.org/doi/10.1016/j.camwa.2023.11.039
Botchev M(2024)On convergence of waveform relaxation for nonlinear systems of ordinary differential equationsCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00578-061:2Online publication date: 5-Jun-2024
https://dl.acm.org/doi/10.1007/s10092-024-00578-0
Show More Cited By

Index Terms

Symmetry-preserving discretization of turbulent flow
1. Computing methodologies
  1. Modeling and simulation
    1. Model development and analysis
      1. Model verification and validation
    2. Simulation types and techniques
      1. Continuous simulation
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Numerical analysis
      1. Computations on matrices

Recommendations

Multifractal subgrid-scale modeling within a variational multiscale method for large-eddy simulation of turbulent flow

Multifractal subgrid-scale modeling within a variational multiscale method is proposed for large-eddy simulation of turbulent flow. In the multifractal subgrid-scale modeling approach, the subgrid-scale velocity is evaluated from a multifractal ...
Numerical flow visualization of a single large-sized bubble in turbulent Couette flow using OpenFOAM
Abstract
Owing to different flow conditions—for example, Poiseuille and Couette flow—one could expect different deformations of large-sized bubbles; however, bubble dynamics has been mostly investigated in channel flow. Consequently, an intermediate flow ...
Observation of Vortex Packets in Direct Numerical Simulation of Fully Turbulent Channel Flow

A number of experimental studies have inferred the existence of packets of inclined, hairpin-like vortices in wall turbulence on the basis of observations made in two-dimensional x-y planes using visualization and particle image velocimetry (PIV). ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 187, Issue 1

May 2003

369 pages

ISSN:0021-9991

Issue’s Table of Contents

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 May 2003

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

61
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 09 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

van der Eijk MWellens P(2024)An efficient pressure-based multiphase finite volume method for interaction between compressible aerated water and moving bodiesJournal of Computational Physics10.1016/j.jcp.2024.113167514:COnline publication date: 18-Oct-2024
https://dl.acm.org/doi/10.1016/j.jcp.2024.113167
Boguslawski ATyliszczak AGeurts B(2024)Approximate deconvolution discretisationComputers & Mathematics with Applications10.1016/j.camwa.2023.11.039154:C(175-198)Online publication date: 15-Jan-2024
https://dl.acm.org/doi/10.1016/j.camwa.2023.11.039
Botchev M(2024)On convergence of waveform relaxation for nonlinear systems of ordinary differential equationsCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00578-061:2Online publication date: 5-Jun-2024
https://dl.acm.org/doi/10.1007/s10092-024-00578-0
Coppola GVeldman A(2023)Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flowJournal of Computational Physics10.1016/j.jcp.2022.111879475:COnline publication date: 15-Feb-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111879
van der Eijk MWellens P(2023)Two-phase free-surface flow interaction with moving bodies using a consistent, momentum preserving methodJournal of Computational Physics10.1016/j.jcp.2022.111796474:COnline publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111796
Rozema GVeldman AMaurits N(2023)Quasi-simultaneous coupling methods for partitioned problems in computational hemodynamicsApplied Numerical Mathematics10.1016/j.apnum.2022.11.001184:C(461-481)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1016/j.apnum.2022.11.001
Zhang YPalha AGerritsma MRebholz L(2022)A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part IJournal of Computational Physics10.1016/j.jcp.2021.110868451:COnline publication date: 15-Feb-2022
https://dl.acm.org/doi/10.1016/j.jcp.2021.110868
Valle NTrias FCastro J(2020)An energy-preserving level set method for multiphase flowsJournal of Computational Physics10.1016/j.jcp.2019.108991400:COnline publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1016/j.jcp.2019.108991
Deriaz EHaldenwang P(2020)Non-linear CFL Conditions Issued from the von Neumann Stability Analysis for the Transport EquationJournal of Scientific Computing10.1007/s10915-020-01302-085:1Online publication date: 21-Sep-2020
https://dl.acm.org/doi/10.1007/s10915-020-01302-0
Naseri ATotounferoush AGonzález IMehl MPérez-Segarra C(2020)A scalable framework for the partitioned solution of fluid–structure interaction problemsComputational Mechanics10.1007/s00466-020-01860-y66:2(471-489)Online publication date: 1-Aug-2020
https://dl.acm.org/doi/10.1007/s00466-020-01860-y
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents