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Volumn 36, Issue 9, 2007, Pages 1446-1459

Conservative numerical methods for model kinetic equations

Author keywords

[No Author keywords available]

Indexed keywords

CONSERVATIVE DISCRETE ORDINATE METHOD; RYKOV MODEL KINETIC EQUATION; SHAKHOV MODEL KINETIC EQUATION;

EID: 34447626807     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2007.01.009     Document Type: Article
Times cited : (99)

References (38)
  • 1
    • 0001291566 scopus 로고    scopus 로고
    • Numerical analysis of a supersonic rarefied gas flow past a flat plate
    • Aoki K., Kanba K., and Takata S. Numerical analysis of a supersonic rarefied gas flow past a flat plate. Phys Fluids 9 4 (1997) 1144-1161
    • (1997) Phys Fluids , vol.9 , Issue.4 , pp. 1144-1161
    • Aoki, K.1    Kanba, K.2    Takata, S.3
  • 2
    • 4644336206 scopus 로고    scopus 로고
    • Inverted velocity profile in the cylindrical Couette flow of a rarefied gas
    • Aoki K., Yoshida H., and Nakanishi T. Inverted velocity profile in the cylindrical Couette flow of a rarefied gas. Phys Rev E 68 (2003) 016302
    • (2003) Phys Rev E , vol.68 , pp. 016302
    • Aoki, K.1    Yoshida, H.2    Nakanishi, T.3
  • 3
    • 82455184101 scopus 로고
    • Method of adaptive meshes in velocity space for the intense shock wave problem
    • Aristov V.V. Method of adaptive meshes in velocity space for the intense shock wave problem. USSR J Comp Math Math Phys 27 (1977) 261-267
    • (1977) USSR J Comp Math Math Phys , vol.27 , pp. 261-267
    • Aristov, V.V.1
  • 4
    • 0008450393 scopus 로고
    • A conservative splitting method for solving the Boltzmann equation
    • Aristov V.V., and Cheremisin F.G. A conservative splitting method for solving the Boltzmann equation. USSR J Comp Math Math Phys 20 1 (1980) 191-207
    • (1980) USSR J Comp Math Math Phys , vol.20 , Issue.1 , pp. 191-207
    • Aristov, V.V.1    Cheremisin, F.G.2
  • 5
    • 33746594225 scopus 로고    scopus 로고
    • A deterministic method for solving the Boltzmann equation with parallel computations
    • Aristov V.V., and Zabelok S.A. A deterministic method for solving the Boltzmann equation with parallel computations. Comp Math Math Phys 42 3 (2002) 406-418
    • (2002) Comp Math Math Phys , vol.42 , Issue.3 , pp. 406-418
    • Aristov, V.V.1    Zabelok, S.A.2
  • 6
    • 26344468007 scopus 로고
    • A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems
    • Bhathnagar P.L., Gross E.P., and Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94 511 (1954) 1144-1161
    • (1954) Phys Rev , vol.94 , Issue.511 , pp. 1144-1161
    • Bhathnagar, P.L.1    Gross, E.P.2    Krook, M.3
  • 7
    • 0011100395 scopus 로고    scopus 로고
    • Conservative method for computing the Boltzmann collision integral
    • Cheremisin F.G. Conservative method for computing the Boltzmann collision integral. Dokl Akad Nauk 355 1 (1997) 53-56
    • (1997) Dokl Akad Nauk , vol.355 , Issue.1 , pp. 53-56
    • Cheremisin, F.G.1
  • 8
    • 0002854033 scopus 로고
    • Kinetic-theoretic description of the formation of a shock wave
    • Chu C.K. Kinetic-theoretic description of the formation of a shock wave. Phys Fluids 8 1 (1965) 12-22
    • (1965) Phys Fluids , vol.8 , Issue.1 , pp. 12-22
    • Chu, C.K.1
  • 9
    • 0000935267 scopus 로고
    • A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov S.K. A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics. Mat Sbornik 47 (1959) 357-393
    • (1959) Mat Sbornik , vol.47 , pp. 357-393
    • Godunov, S.K.1
  • 10
    • 27144485574 scopus 로고
    • Conservative method for numerical solution of the kinetic equations for small Knudsen numbers
    • Gradoboev M.I., and Rykov V.A. Conservative method for numerical solution of the kinetic equations for small Knudsen numbers. Comp Math Math Phys 34 2 (1994) 246-266
    • (1994) Comp Math Math Phys , vol.34 , Issue.2 , pp. 246-266
    • Gradoboev, M.I.1    Rykov, V.A.2
  • 11
    • 0036962219 scopus 로고    scopus 로고
    • Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer
    • Gusarov A.V., and Smurov I. Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer. Phys Fluids 14 12 (2002) 4242-4255
    • (2002) Phys Fluids , vol.14 , Issue.12 , pp. 4242-4255
    • Gusarov, A.V.1    Smurov, I.2
  • 12
    • 36849110965 scopus 로고
    • New statistical models for kinetic theory: methods of construction
    • Holway L.H. New statistical models for kinetic theory: methods of construction. Phys Fluids 9 9 (1966) 1658-1673
    • (1966) Phys Fluids , vol.9 , Issue.9 , pp. 1658-1673
    • Holway, L.H.1
  • 13
    • 24944505852 scopus 로고
    • Implicit scheme of S.K. Godunov with increased order of accuracy for Euler equations
    • Ivanov M.Ya., and Nigmatullin R.Z. Implicit scheme of S.K. Godunov with increased order of accuracy for Euler equations. USSR Comp Math Math Phys 27 11 (1987) 1725-1735
    • (1987) USSR Comp Math Math Phys , vol.27 , Issue.11 , pp. 1725-1735
    • Ivanov, M.Ya.1    Nigmatullin, R.Z.2
  • 14
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • Jiang G.S., and Shu C.W. Efficient implementation of weighted ENO schemes. J Comput Phys 126 (1996) 202-212
    • (1996) J Comput Phys , vol.126 , pp. 202-212
    • Jiang, G.S.1    Shu, C.W.2
  • 15
    • 0002898994 scopus 로고
    • Application of the minimum-derivative principle in the construction of finite-difference schemes for numerical analysis of discontinuous solutions in gas dynamics
    • [in Russian]
    • Kolgan V.P. Application of the minimum-derivative principle in the construction of finite-difference schemes for numerical analysis of discontinuous solutions in gas dynamics. Trans Central Aerohydrodyn Inst 3 6 (1972) 68-77 [in Russian]
    • (1972) Trans Central Aerohydrodyn Inst , vol.3 , Issue.6 , pp. 68-77
    • Kolgan, V.P.1
  • 16
    • 8744279475 scopus 로고
    • Finite-difference schemes for computation of three dimensional solutions of gas dynamics and calculation of a flow over a body under an angle of attack
    • [in Russian]
    • Kolgan V.P. Finite-difference schemes for computation of three dimensional solutions of gas dynamics and calculation of a flow over a body under an angle of attack. Trans Central Aerohydrodyn Inst 6 2 (1975) 1-6 [in Russian]
    • (1975) Trans Central Aerohydrodyn Inst , vol.6 , Issue.2 , pp. 1-6
    • Kolgan, V.P.1
  • 18
    • 33947521447 scopus 로고
    • Diatomic rarefied flow past a sphere on the basis of kinetic equations
    • Larina I.N., and Rykov V.A. Diatomic rarefied flow past a sphere on the basis of kinetic equations. Dokl Akad Nauk USSR 227 1 (1976) 60-62
    • (1976) Dokl Akad Nauk USSR , vol.227 , Issue.1 , pp. 60-62
    • Larina, I.N.1    Rykov, V.A.2
  • 19
    • 84935752981 scopus 로고
    • Diatomic rarefied flow past a sphere
    • Numerical methods in rarefied gas dynamics, Dorodnicyn Computing Center of Soviet Academy of Sciences
    • Larina I.N., and Rykov V.A. Diatomic rarefied flow past a sphere. Numerical methods in rarefied gas dynamics. Soobsheniya po prikladnoy matematike Vol. 4 (1979), Dorodnicyn Computing Center of Soviet Academy of Sciences 52-68
    • (1979) Soobsheniya po prikladnoy matematike , vol.4 , pp. 52-68
    • Larina, I.N.1    Rykov, V.A.2
  • 20
    • 34447635945 scopus 로고
    • Hypersonic flows of a rarefied gas past conical bodies
    • Dorodnicyn Computing Center of Soviet Academy of Sciences
    • Larina I.N., and Rykov V.A. Hypersonic flows of a rarefied gas past conical bodies. Soobsheniya po prikladnoy matematike (1990), Dorodnicyn Computing Center of Soviet Academy of Sciences
    • (1990) Soobsheniya po prikladnoy matematike
    • Larina, I.N.1    Rykov, V.A.2
  • 21
    • 0014734795 scopus 로고
    • Rotational relaxation in nonpolar diatomic gases
    • Lordi J.A., and Mates R.E. Rotational relaxation in nonpolar diatomic gases. Phys Fluids 13 2 (1970) 291-308
    • (1970) Phys Fluids , vol.13 , Issue.2 , pp. 291-308
    • Lordi, J.A.1    Mates, R.E.2
  • 22
    • 0037812320 scopus 로고    scopus 로고
    • Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries
    • Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J Comput Phys 162 2 (2000) 429-466
    • (2000) J Comput Phys , vol.162 , Issue.2 , pp. 429-466
    • Mieussens, L.1
  • 23
    • 3042764677 scopus 로고    scopus 로고
    • Study of a shock wave structure in gas mixtures on the basis of the Boltzmann equation
    • Raines A. Study of a shock wave structure in gas mixtures on the basis of the Boltzmann equation. Eur J Mech B/Fluids 202 (2002) 599-610
    • (2002) Eur J Mech B/Fluids , vol.202 , pp. 599-610
    • Raines, A.1
  • 24
    • 34250390011 scopus 로고
    • A model kinetic equation for a gas with rotational degrees of freedom
    • Rykov V.A. A model kinetic equation for a gas with rotational degrees of freedom. Fluid Dynamics 10 6 (1975) 959-966
    • (1975) Fluid Dynamics , vol.10 , Issue.6 , pp. 959-966
    • Rykov, V.A.1
  • 25
    • 33749011052 scopus 로고
    • Approximate kinetic equations in rarefied gas theory
    • Shakhov E.M. Approximate kinetic equations in rarefied gas theory. Fluid Dyn 3 1 (1968) 156-161
    • (1968) Fluid Dyn , vol.3 , Issue.1 , pp. 156-161
    • Shakhov, E.M.1
  • 26
    • 34250475794 scopus 로고
    • Generalization of the Krook kinetic relaxation equation
    • Shakhov E.M. Generalization of the Krook kinetic relaxation equation. Fluid Dynamics 3 5 (1968) 142-145
    • (1968) Fluid Dynamics , vol.3 , Issue.5 , pp. 142-145
    • Shakhov, E.M.1
  • 27
    • 33645732290 scopus 로고
    • Transverse flow of a rarefield gas around a plate
    • Shakhov E.M. Transverse flow of a rarefield gas around a plate. Fluid Dynamics 7 6 (1972) 961-966
    • (1972) Fluid Dynamics , vol.7 , Issue.6 , pp. 961-966
    • Shakhov, E.M.1
  • 28
    • 34447634545 scopus 로고
    • Method of investigation of rarefied gas flows
    • [in Russian]
    • Shakhov E.M. Method of investigation of rarefied gas flows. M: Nauka (1974) [in Russian]
    • (1974) M: Nauka
    • Shakhov, E.M.1
  • 29
    • 0346720508 scopus 로고    scopus 로고
    • Nonlinear Couette flow between two rotating cylinders
    • Sharipov F., and Kremer G.M. Nonlinear Couette flow between two rotating cylinders. Transport Theory Statist Phys 25 2 (1996) 217-229
    • (1996) Transport Theory Statist Phys , vol.25 , Issue.2 , pp. 217-229
    • Sharipov, F.1    Kremer, G.M.2
  • 30
    • 0032362164 scopus 로고    scopus 로고
    • Data on internal rarefied gas flows
    • Sharipov F., and Seleznev V. Data on internal rarefied gas flows. J Phys Chem Ref Data 27 3 (1998) 657-706
    • (1998) J Phys Chem Ref Data , vol.27 , Issue.3 , pp. 657-706
    • Sharipov, F.1    Seleznev, V.2
  • 31
    • 27544452297 scopus 로고    scopus 로고
    • An overview on high order numerical methods for convection dominated PDEs
    • Hou T.Y., and Tadmor E. (Eds), Springer-Verlag, Berlin
    • Shu C.-W. An overview on high order numerical methods for convection dominated PDEs. In: Hou T.Y., and Tadmor E. (Eds). Hyperbolic problems: theory, numerics, applications (2003), Springer-Verlag, Berlin 79-88
    • (2003) Hyperbolic problems: theory, numerics, applications , pp. 79-88
    • Shu, C.-W.1
  • 33
    • 34447639294 scopus 로고    scopus 로고
    • V.A. Titarev, Towards fully conservative numerical methods for the nonlinear model Boltzmann equation. Preprint NI03031-NPA, pp. 13. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, UK, 2003.
  • 34
    • 33747000932 scopus 로고    scopus 로고
    • Flow computation in the bottom vacuum region behind a plate in a hypersonic rarefied gas stream
    • Titarev V.A., and Shakhov E.M. Flow computation in the bottom vacuum region behind a plate in a hypersonic rarefied gas stream. J Comp Math Math Phys 41 9 (2001) 1372-1384
    • (2001) J Comp Math Math Phys , vol.41 , Issue.9 , pp. 1372-1384
    • Titarev, V.A.1    Shakhov, E.M.2
  • 36
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme V: a second order sequel to Godunov's method
    • van Leer B. Towards the ultimate conservative difference scheme V: a second order sequel to Godunov's method. J Comput Phys 32 (1979) 101-136
    • (1979) J Comput Phys , vol.32 , pp. 101-136
    • van Leer, B.1
  • 37
    • 0011008052 scopus 로고
    • Rarefied flow computations using nonlinear model Boltzmann equations
    • Yang J.Y., and Huang J.C. Rarefied flow computations using nonlinear model Boltzmann equations. J Comput Phys 120 2 (1995) 323-339
    • (1995) J Comput Phys , vol.120 , Issue.2 , pp. 323-339
    • Yang, J.Y.1    Huang, J.C.2
  • 38
    • 34250409467 scopus 로고
    • Kinetic models and the shock wave structure
    • Zhuk V.I., Rykov V.A., and Shakhov E.M. Kinetic models and the shock wave structure. Fluid Dynamics 8 4 (1973) 620-625
    • (1973) Fluid Dynamics , vol.8 , Issue.4 , pp. 620-625
    • Zhuk, V.I.1    Rykov, V.A.2    Shakhov, E.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.