Application of a direct method for solving the Boltzmann equation in supersonic flow computation

The Boltzmann kinetic equation is used to numerically study the evolution of separated flows over a backward-facing step at low Knudsen numbers. The Boltzmann equation is solved by applying an explicit–implicit scheme. To improve the efficiency of the solution algorithm, it is parallelized with the...

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Vydané v:Computational mathematics and mathematical physics Ročník 56; číslo 11; s. 1938 - 1947
Hlavní autori: Aristov, V. V., Rovenskaya, O. I.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Moscow Pleiades Publishing 01.11.2016
Springer Nature B.V
Predmet:
Algorithms
Computational mathematics
Computational Mathematics and Numerical Analysis
Equilibrium
Fluid mechanics
Friction
Gas flow
Heat transfer
Kinetics
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Navier-Stokes equations
Reynolds number
Shock waves
Studies
Turbulence models
algorithm parallelization
explicit–implicit difference scheme
flow instability
Boltzmann kinetic equation
supersonic compressible flow
ISSN:0965-5425, 1555-6662
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Abstract The Boltzmann kinetic equation is used to numerically study the evolution of separated flows over a backward-facing step at low Knudsen numbers. The Boltzmann equation is solved by applying an explicit–implicit scheme. To improve the efficiency of the solution algorithm, it is parallelized with the help of MPI. The solution obtained with the kinetic equation is compared with those based on continuous medium equations. It is shown that the kinetic approach makes it possible to reproduce the distributions of surface pressure, friction coefficient, and heat transfer, as well as to obtain a flow structure close to experimental data.
AbstractList The Boltzmann kinetic equation is used to numerically study the evolution of separated flows over a backward-facing step at low Knudsen numbers. The Boltzmann equation is solved by applying an explicit–implicit scheme. To improve the efficiency of the solution algorithm, it is parallelized with the help of MPI. The solution obtained with the kinetic equation is compared with those based on continuous medium equations. It is shown that the kinetic approach makes it possible to reproduce the distributions of surface pressure, friction coefficient, and heat transfer, as well as to obtain a flow structure close to experimental data.
Author Rovenskaya, O. I.
Aristov, V. V.
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  givenname: O. I.
  surname: Rovenskaya
  fullname: Rovenskaya, O. I.
  organization: Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”, Russian Academy of Sciences
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Cites_doi 10.1016/j.compfluid.2015.01.012
10.1016/S0376-0421(02)00069-6
10.1017/S0022112006000930
10.1063/1.1561281
10.1134/S0965542507090151
10.1016/j.compfluid.2011.07.007
ContentType Journal Article
Copyright Pleiades Publishing, Ltd. 2016
Computational Mathematics and Mathematical Physics is a copyright of Springer, 2016.
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Keywords algorithm parallelization
explicit–implicit difference scheme
flow instability
Boltzmann kinetic equation
supersonic compressible flow
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References Fang, Yao, Lu, Zheltovodov (CR4) 2014
Sakurai, Takayama (CR9) 2003; 15
Tcheremissine, Capitelli (CR13) 2005
Aristov, Rovenskaya (CR10) 2015; 111
Aristov (CR11) 2004; 44
Knight, Yan, Panaras, Zheltovodov (CR1) 2003; 39
Aristov, Rovenskaya (CR8) 2011; 50
Bedarev, Fedorova (CR5) 2001; 42
Zheltovodov (CR3) 2006; 2006-496
Zheltovodov, Trofimov, Shilein, Yakovlev (CR14) 1990
Loginov, Adams, Zheltovodov (CR2) 2006; 565
Rovenskaya (CR7) 2007; 47
Wilcox (CR6) 1998
Kogan (CR12) 1967
A. A. Zheltovodov (280_CR3) 2006; 2006-496
V. V. Aristov (280_CR8) 2011; 50
J. Fang (280_CR4) 2014
V. V. Aristov (280_CR10) 2015; 111
A. Sakurai (280_CR9) 2003; 15
F. G. Tcheremissine (280_CR13) 2005
M. N. Kogan (280_CR12) 1967
I. A. Bedarev (280_CR5) 2001; 42
V. V. Aristov (280_CR11) 2004; 44
M. S. Loginov (280_CR2) 2006; 565
D. Knight (280_CR1) 2003; 39
O. I. Rovenskaya (280_CR7) 2007; 47
D. C. Wilcox (280_CR6) 1998
A. A. Zheltovodov (280_CR14) 1990
References_xml – year: 1998
  ident: CR6
  publication-title: Turbulence Modeling for CFD
– start-page: 69
  year: 2014
  end-page: 70
  ident: CR4
  article-title: Direct numerical simulation of supersonic turbulent flow in expansion-compression corner
  publication-title: International Conference on Methods of Aerophysical Research: Abstracts
– volume: 44
  start-page: 1069
  issue: 6
  year: 2004
  end-page: 1081
  ident: CR11
  article-title: Solution to the Boltzmann equation at small Knudsen numbers
  publication-title: Comput. Math. Math. Phys.
– year: 1967
  ident: CR12
  publication-title: Rarefied Gas Dynamics
– volume: 111
  start-page: 150
  year: 2015
  end-page: 158
  ident: CR10
  article-title: Kinetic description of the turbulence in the supersonic compressible flow over a backward/forward-facing step
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2015.01.012
– volume: 2006-496
  start-page: 1
  year: 2006
  end-page: 25
  ident: CR3
  article-title: Some advances in research of shock wave turbulent boundary layer interactions
  publication-title: AIAA Paper
– volume: 39
  start-page: 121
  year: 2003
  end-page: 184
  ident: CR1
  article-title: Advances in CFD prediction of shockwave turbulent boundary layer interactions
  publication-title: Progress Aerospace Sci.
  doi: 10.1016/S0376-0421(02)00069-6
– volume: 565
  start-page: 135
  year: 2006
  end-page: 169
  ident: CR2
  article-title: Large-eddy simulation of shock-wave/turbulent-boundary- layer interaction
  publication-title: J. Fluid Mech.
  doi: 10.1017/S0022112006000930
– year: 2005
  ident: CR13
  article-title: Direct numerical solution of the Boltzmann equation
  publication-title: AIP Conference Proceedings of 24th Symposium on Rarefied Gas Dynamics
– volume: 42
  start-page: 56
  issue: 1
  year: 2001
  end-page: 64
  ident: CR5
  article-title: Computation of gas dynamic parameters and heat transfer in supersonic turbulent separated flows near corners
  publication-title: Prikl. Mekh. Tekh. Fiz.
– volume: 15
  start-page: 1282
  year: 2003
  end-page: 1296
  ident: CR9
  article-title: Molecular kinetic approach to the problem of compressible turbulence
  publication-title: Phys. Fluids
  doi: 10.1063/1.1561281
– volume: 47
  start-page: 1544
  issue: 9
  year: 2007
  end-page: 1550
  ident: CR7
  article-title: Analysis of the evolution of an eddy system based on the Boltzmann equation
  publication-title: Comput. Math. Math. Phys.
  doi: 10.1134/S0965542507090151
– year: 1990
  ident: CR14
  publication-title: Documented experimental date on supersonic turbulent separated flows near sloping backward/forward-facing steps
– volume: 50
  start-page: 189
  year: 2011
  end-page: 198
  ident: CR8
  article-title: Application of the Boltzmann kinetic equation to the eddy problem
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2011.07.007
– volume: 15
  start-page: 1282
  year: 2003
  ident: 280_CR9
  publication-title: Phys. Fluids
  doi: 10.1063/1.1561281
– start-page: 69
  volume-title: International Conference on Methods of Aerophysical Research: Abstracts
  year: 2014
  ident: 280_CR4
– volume-title: Documented experimental date on supersonic turbulent separated flows near sloping backward/forward-facing steps
  year: 1990
  ident: 280_CR14
– volume-title: Rarefied Gas Dynamics
  year: 1967
  ident: 280_CR12
– volume: 42
  start-page: 56
  issue: 1
  year: 2001
  ident: 280_CR5
  publication-title: Prikl. Mekh. Tekh. Fiz.
– volume: 2006-496
  start-page: 1
  year: 2006
  ident: 280_CR3
  publication-title: AIAA Paper
– volume: 111
  start-page: 150
  year: 2015
  ident: 280_CR10
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2015.01.012
– volume: 50
  start-page: 189
  year: 2011
  ident: 280_CR8
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2011.07.007
– volume: 47
  start-page: 1544
  issue: 9
  year: 2007
  ident: 280_CR7
  publication-title: Comput. Math. Math. Phys.
  doi: 10.1134/S0965542507090151
– volume: 39
  start-page: 121
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  ident: 280_CR1
  publication-title: Progress Aerospace Sci.
  doi: 10.1016/S0376-0421(02)00069-6
– volume: 565
  start-page: 135
  year: 2006
  ident: 280_CR2
  publication-title: J. Fluid Mech.
  doi: 10.1017/S0022112006000930
– volume-title: Turbulence Modeling for CFD
  year: 1998
  ident: 280_CR6
– volume: 44
  start-page: 1069
  issue: 6
  year: 2004
  ident: 280_CR11
  publication-title: Comput. Math. Math. Phys.
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  year: 2005
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Snippet The Boltzmann kinetic equation is used to numerically study the evolution of separated flows over a backward-facing step at low Knudsen numbers. The Boltzmann...
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StartPage 1938
SubjectTerms Algorithms
Computational mathematics
Computational Mathematics and Numerical Analysis
Equilibrium
Fluid mechanics
Friction
Gas flow
Heat transfer
Kinetics
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Navier-Stokes equations
Reynolds number
Shock waves
Studies
Turbulence models
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Title Application of a direct method for solving the Boltzmann equation in supersonic flow computation
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Volume 56
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