메뉴 건너뛰기




Volumn 21, Issue 6, 2009, Pages 467-493

Towards physically realizable and hyperbolic moment closures for kinetic theory

Author keywords

Gas kinetic theory; Hyperbolic moment equations; Moment closures; Physically realizable moments

Indexed keywords

COLLISION OPERATORS; CURRENT CAPABILITY; DIATOMIC GAS; DIFFUSION EFFECTS; FLOW PROBLEMS; GAS KINETIC THEORY; GAUSSIANS; HIGHER ORDER TERMS; INTEGRABILITY; KINETIC EQUATIONS; MATHEMATICAL DESCRIPTIONS; MOMENT CLOSURE; MOMENT EQUATIONS; NON-EQUILIBRIUM FLOWS; NUMERICAL PREDICTIONS; NUMERICAL RESULTS; NUMERICAL SOLUTION; PREDICTIVE CAPABILITIES;

EID: 76449087294     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-009-0125-1     Document Type: Article
Times cited : (63)

References (62)
  • 1
    • 0001891327 scopus 로고
    • Mems: Mircoelectromechanical systems
    • 1165503
    • L. O'Connor 1992 Mems: mircoelectromechanical systems Mech. Eng. J. 114 2 40 47 1165503
    • (1992) Mech. Eng. J. , vol.114 , Issue.2 , pp. 40-47
    • O'Connor, L.1
  • 4
    • 0037847018 scopus 로고    scopus 로고
    • Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics
    • 10.1142/S0218202500000562 1792255
    • L. Mieussens 2000 Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics Math. Models Methods Appl. Sci. 10 8 1121 1149 10.1142/S0218202500000562 1792255
    • (2000) Math. Models Methods Appl. Sci. , vol.10 , Issue.8 , pp. 1121-1149
    • Mieussens, L.1
  • 5
    • 0000679271 scopus 로고    scopus 로고
    • Statistical simulation of low-speed rarefied gas flows
    • DOI 10.1006/jcph.2000.6681, PII S0021999100966816
    • J. Fan C. Shen 2001 Statistical simulation of low-speed rarefied gas flow J. Comput. Phys. 167 393 412 1052.76055 10.1006/jcph.2000.6681 2001JCoPh.167..393F (Pubitemid 33652970)
    • (2001) Journal of Computational Physics , vol.167 , Issue.2 , pp. 393-412
    • Fan, J.1    Shen, C.2
  • 6
    • 0036647480 scopus 로고    scopus 로고
    • A direct simulation method for subsonic, mircoscale gas flow
    • 1130.76416 10.1006/jcph.2002.7061 2002JCoPh.179.400S
    • Q. Sun I.D. Boyd 2002 A direct simulation method for subsonic, mircoscale gas flow J. Comput. Phys. 179 400 425 1130.76416 10.1006/jcph.2002.7061 2002JCoPh.179..400S
    • (2002) J. Comput. Phys. , vol.179 , pp. 400-425
    • Sun, Q.1    Boyd, I.D.2
  • 7
    • 84980081651 scopus 로고
    • On the kinetic theory of rarefied gases
    • 0037.13104 10.1002/cpa.3160020403 33674
    • H. Grad 1949 On the kinetic theory of rarefied gases Commun. Pure Appl. Math. 2 331 407 0037.13104 10.1002/cpa.3160020403 33674
    • (1949) Commun. Pure Appl. Math. , vol.2 , pp. 331-407
    • Grad, H.1
  • 8
    • 0030534703 scopus 로고    scopus 로고
    • Moment closure hierarchies for kinetic theories
    • 1081.82619 10.1007/BF02179552 1392419 1996JSP.83.1021L
    • C.D. Levermore 1996 Moment closure hierarchies for kinetic theories J. Stat. Phys. 83 1021 1065 1081.82619 10.1007/BF02179552 1392419 1996JSP....83.1021L
    • (1996) J. Stat. Phys. , vol.83 , pp. 1021-1065
    • Levermore, C.D.1
  • 11
    • 77953641147 scopus 로고
    • Numerical solution of a 10-moment model for nonequilibrium gasdynamics
    • AIAA, June
    • Brown, S.L., Roe, P.L., Groth, C.P.T.: Numerical solution of a 10-moment model for nonequilibrium gasdynamics. Paper 95-1677, AIAA, June (1995)
    • (1995) Paper 95-1677
    • Brown, S.L.1    Roe, P.L.2    Groth, C.P.T.3
  • 13
    • 0000935266 scopus 로고
    • Finite-difference method for numerical computations of discontinuous solutions of the equations of fluid dynamics
    • 119433
    • S.K. Godunov 1959 Finite-difference method for numerical computations of discontinuous solutions of the equations of fluid dynamics Math. Sb. 47 271 306 119433
    • (1959) Math. Sb. , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 14
    • 76449093674 scopus 로고    scopus 로고
    • Numerical modeling of micron-scale flows using the Gaussian moment closure
    • AIAA, June 2005
    • McDonald, J.G., Groth, C.P.T.: Numerical modeling of micron-scale flows using the Gaussian moment closure. Paper 2005-5035, AIAA, June 2005
    • Paper 2005-5035
    • McDonald, J.G.1    Groth, C.P.T.2
  • 15
    • 38849170593 scopus 로고    scopus 로고
    • Parallel AMR scheme for turbulent multi-phase rocket motor core flows
    • AIAA, June 2005
    • Sachdev, J.S., Groth, C.P.T., Gottlieb J.J.: Parallel AMR scheme for turbulent multi-phase rocket motor core flows. Paper 2005-5334, AIAA, June 2005
    • Paper 2005-5334
    • Sachdev, J.S.1    Groth, C.P.T.2    Gottlieb, J.J.3
  • 16
    • 38849196125 scopus 로고    scopus 로고
    • A mesh adjustment scheme for embedded boundaries
    • 1164.74549
    • J.S. Sachdev C.P.T. Groth 2007 A mesh adjustment scheme for embedded boundaries Commun. Computat. Phys. 2 6 1095 1124 1164.74549
    • (2007) Commun. Computat. Phys. , vol.2 , Issue.6 , pp. 1095-1124
    • Sachdev, J.S.1    Groth, C.P.T.2
  • 18
    • 76449120105 scopus 로고    scopus 로고
    • Gaussian moment closure for the modelling of continuum and micron-scale flows with moving boundaries
    • ICCFD4, Ghent, Belgium, July 10-14, 2006. Heidelberg, to appear. Springer-Verlag
    • McDonald, J.G., Sachdev, J.S., Groth, C.P.T.: Gaussian moment closure for the modelling of continuum and micron-scale flows with moving boundaries. In: Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD4, Ghent, Belgium, July 10-14, 2006. Heidelberg, to appear. Springer-Verlag
    • Proceedings of the Fourth International Conference on Computational Fluid Dynamics
    • McDonald, J.G.1    Sachdev, J.S.2    Groth, C.P.T.3
  • 19
    • 0141649317 scopus 로고    scopus 로고
    • Regularization of Grad's 13 moment equations: Derivation and linear analysis
    • DOI 10.1063/1.1597472
    • H. Struchtrup M. Torrilhon 2003 Regularization of grad's 13 moment equations: Derivation and linear analysis Phys. Fluids 15 2668 2680 10.1063/1.1597472 2060065 2003PhFl...15.2668S (Pubitemid 37207856)
    • (2003) Physics of Fluids , vol.15 , Issue.9 , pp. 2668-2680
    • Struchtrup, H.1    Torrilhon, M.2
  • 20
    • 34547278669 scopus 로고    scopus 로고
    • H theorem, regularization, and boundary conditions for linearized 13 moment equations
    • DOI 10.1103/PhysRevLett.99.014502
    • H. Struchtrup M. Torrilhon 2007 H theorem, regularization, and boundary conditions for the linearized 13 moment equations Phys. Rev. Lett. 99 014502 10.1103/PhysRevLett.99.014502 2007PhRvL..99a4502S (Pubitemid 47150522)
    • (2007) Physical Review Letters , vol.99 , Issue.1 , pp. 014502
    • Struchtrup, H.1    Torrilhon, M.2
  • 21
    • 37249021809 scopus 로고    scopus 로고
    • Boundary conditions for regularized 13 moment equations for micro-channel-flows
    • 1132.76049 10.1016/j.jcp.2007.10.006 2450981
    • M. Torrilhon H. Struchtrup 2008 Boundary conditions for regularized 13 moment equations for micro-channel-flows J. Comput. Phys. 227 1982 2011 1132.76049 10.1016/j.jcp.2007.10.006 2450981
    • (2008) J. Comput. Phys. , vol.227 , pp. 1982-2011
    • Torrilhon, M.1    Struchtrup, H.2
  • 23
    • 0029656933 scopus 로고    scopus 로고
    • Solution-adaptive Cartesian cell approach for viscous and inviscid flows
    • 0900.76407 10.2514/3.13171 1996AIAAJ.34.938C
    • W.J. Coirier K.G. Powell 1996 Solution-adaptive Cartesian cell approach for viscous and inviscid flows AIAA J. 34 5 938 945 0900.76407 10.2514/3.13171 1996AIAAJ..34..938C
    • (1996) AIAA J. , vol.34 , Issue.5 , pp. 938-945
    • Coirier, W.J.1    Powell, K.G.2
  • 25
    • 0032259525 scopus 로고    scopus 로고
    • Domain of definition of levermore's five-moment system
    • 0952.82024 10.1023/B:JOSS.0000033155.07331.d9 1666220 1998JSP.93.1143J
    • M. Junk 1998 Domain of definition of levermore's five-moment system J. Stat. Phys. 93 5/6 1143 1167 0952.82024 10.1023/B:JOSS.0000033155.07331.d9 1666220 1998JSP....93.1143J
    • (1998) J. Stat. Phys. , vol.93 , Issue.5-6 , pp. 1143-1167
    • Junk, M.1
  • 26
    • 0036027254 scopus 로고    scopus 로고
    • Maximum entropy moment systems and Galilean invariance
    • DOI 10.1007/s00161-002-0096-y
    • M. Junk 2002 Maximum entropy moment systems and galilean invariance Contin. Mech. Thermodyn. 14 563 576 1024.76044 10.1007/s00161-002-0096-y 1947087 2002CMT....14..563J (Pubitemid 36185477)
    • (2002) Continuum Mechanics and Thermodynamics , vol.14 , Issue.6 , pp. 563-576
    • Junk, M.1    Unterreiter, A.2
  • 27
    • 3142672977 scopus 로고    scopus 로고
    • Entropic approximation in kinetic theory
    • DOI 10.1051/m2an:2004025
    • J. Schneider 2004 Entropic approximation in kinetic theory Math. Model. Numer. Anal. 38 3 541 561 1084.82010 10.1051/m2an:2004025 2075759 (Pubitemid 38926386)
    • (2004) Mathematical Modelling and Numerical Analysis , vol.38 , Issue.3 , pp. 541-561
    • Schneider, J.1
  • 28
    • 55549148422 scopus 로고    scopus 로고
    • Convex duality and entropy-based moment closures: Characterizing degenerate densities
    • 1167.49033 10.1137/070691139 2421338
    • C.D. Hauck C.D. Levermore A.L. Tits 2008 Convex duality and entropy-based moment closures: Characterizing degenerate densities SIAM J. Control Opt. 47 4 1977 2015 1167.49033 10.1137/070691139 2421338
    • (2008) SIAM J. Control Opt. , vol.47 , Issue.4 , pp. 1977-2015
    • Hauck, C.D.1    Levermore, C.D.2    Tits, A.L.3
  • 31
    • 0000061169 scopus 로고
    • Hermitian transformations of deficiency-index (1, 1), jacobian matrices, and undetermined moment problems
    • 0061.25808 10.2307/2371763 11169
    • H.L. Hamburger 1944 Hermitian transformations of deficiency-index (1, 1), jacobian matrices, and undetermined moment problems Am. J. Math. 66 489 552 0061.25808 10.2307/2371763 11169
    • (1944) Am. J. Math. , vol.66 , pp. 489-552
    • Hamburger, H.L.1
  • 33
    • 0001187980 scopus 로고
    • An interesting class of quasilinear systems
    • 0125.06002
    • S.K. Godunov 1961 An interesting class of quasilinear systems Sov. Math. Dokl. 2 947 949 0125.06002
    • (1961) Sov. Math. Dokl. , vol.2 , pp. 947-949
    • Godunov, S.K.1
  • 34
    • 0001380483 scopus 로고
    • Systems of conservation laws with a convex extension
    • 0229.35061 285799 1971PNAS.68.1686F
    • K.O. Friedrichs P.D. Lax 1971 Systems of conservation laws with a convex extension ProcNAS 68 1686 1688 0229.35061 285799 1971PNAS...68.1686F
    • (1971) ProcNAS , vol.68 , pp. 1686-1688
    • Friedrichs, K.O.1    Lax, P.D.2
  • 35
    • 0002550838 scopus 로고
    • On the dynamical theory of gases
    • 10.1098/rstl.1867.0004
    • J.C. Maxwell 1867 On the dynamical theory of gases Philos. Trans. R. Soc. Lond. 157 49 88 10.1098/rstl.1867.0004
    • (1867) Philos. Trans. R. Soc. Lond. , vol.157 , pp. 49-88
    • Maxwell, J.C.1
  • 36
    • 0040731052 scopus 로고
    • Allgemeine 13-momenten-näherung zur fokker-planck-gleichung eines plasmas
    • 0127.21703 189434 1965ZNatA.20.1243H
    • F. Hertweck 1965 Allgemeine 13-momenten-näherung zur fokker-planck-gleichung eines plasmas Z. Naturforsch. 20 1243 1255 0127.21703 189434 1965ZNatA..20.1243H
    • (1965) Z. Naturforsch. , vol.20 , pp. 1243-1255
    • Hertweck, F.1
  • 37
    • 0039760999 scopus 로고
    • Hydrodynamic equations for plasmas in strong magnetic fields-i collisionless approximation
    • 10.1088/0032-1028/10/9/302 1968PlPh.10.819O
    • V. Oraevskii R. Chodura W. Feneberg 1968 Hydrodynamic equations for plasmas in strong magnetic fields-i collisionless approximation Plasma Phys. 10 819 828 10.1088/0032-1028/10/9/302 1968PlPh...10..819O
    • (1968) Plasma Phys. , vol.10 , pp. 819-828
    • Oraevskii, V.1    Chodura, R.2    Feneberg, W.3
  • 39
    • 0001228503 scopus 로고
    • Kinetic theory of shock structure using an ellipsoidal distribution function
    • J.H. de Leeuw (eds). Academic Press New York
    • Holway L.H.: Kinetic theory of shock structure using an ellipsoidal distribution function. In: de Leeuw, J.H. (eds) Rarefied Gas Dynamics, vol. I, pp. 193-215. Academic Press, New York (1966)
    • (1966) Rarefied Gas Dynamics, Vol. i , pp. 193-215
    • Holway, L.H.1
  • 40
    • 36849110965 scopus 로고
    • New statistical models for kinetic theory: Methods of construction
    • 10.1063/1.1761920 1966PhFl.9.1658H
    • L.H. Holway 1966 New statistical models for kinetic theory: Methods of construction Phys. Fluids 9 9 1658 1673 10.1063/1.1761920 1966PhFl....9.1658H
    • (1966) Phys. Fluids , vol.9 , Issue.9 , pp. 1658-1673
    • Holway, L.H.1
  • 41
    • 76449096620 scopus 로고
    • The effect of collisional models upon shock wave structure
    • C.L. Brundin (eds). Academic Press New York
    • Holway L.H.: The effect of collisional models upon shock wave structure. In: Brundin, C.L. (eds) Rarefied Gas Dynamics, vol. I, pp. 759-784. Academic Press, New York (1967)
    • (1967) Rarefied Gas Dynamics, Vol. i , pp. 759-784
    • Holway, L.H.1
  • 42
    • 26344468007 scopus 로고
    • A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems
    • 0055.23609 10.1103/PhysRev.94.511 1954PhRv.94.511B
    • P.L. Bhatnagar E.P. Gross M. Krook 1954 A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems Phys. Rev. 94 3 511 525 0055.23609 10.1103/PhysRev.94.511 1954PhRv...94..511B
    • (1954) Phys. Rev. , vol.94 , Issue.3 , pp. 511-525
    • Bhatnagar, P.L.1    Gross, E.P.2    Krook, M.3
  • 44
    • 76449108099 scopus 로고    scopus 로고
    • Extended fluid-dynamic model for micron-scale flows based on gaussian moment closure
    • AIAA, January 2008
    • McDonald, J.G., Groth, C.P.T.: Extended fluid-dynamic model for micron-scale flows based on gaussian moment closure. Paper 2008-0691, AIAA, January 2008
    • Paper 2008-0691
    • McDonald, J.G.1    Groth, C.P.T.2
  • 46
    • 77958477239 scopus 로고    scopus 로고
    • An analysis of a space-time discontinous-galerkin method for moment equations and its solid-boundary treatment
    • AIAA, June 2009
    • Khieu, L., van Leer, B., Suzuki, Y.: An analysis of a space-time discontinous-galerkin method for moment equations and its solid-boundary treatment. Paper 2009-3874, AIAA, June 2009
    • Paper 2009-3874
    • Khieu, L.1    Van Leer, B.2    Suzuki, Y.3
  • 47
    • 0018529022 scopus 로고
    • Geometric conservation laws and its application to flow computations on moving grids
    • 0436.76025 10.2514/3.61273 544850 1979AIAAJ.17.1030T
    • P.D. Thomas C.K. Lombard 1979 Geometric conservation laws and its application to flow computations on moving grids AIAA J. 17 10 1030 1037 0436.76025 10.2514/3.61273 544850 1979AIAAJ..17.1030T
    • (1979) AIAA J. , vol.17 , Issue.10 , pp. 1030-1037
    • Thomas, P.D.1    Lombard, C.K.2
  • 48
    • 0003967583 scopus 로고    scopus 로고
    • Recent developments in high order k-exact reconstruction on unstructured meshes
    • AIAA, January 1993
    • Barth, T.J.: Recent developments in high order k-exact reconstruction on unstructured meshes. Paper 93-0668, AIAA, January 1993
    • Paper 93-0668
    • Barth, T.J.1
  • 49
    • 0003740639 scopus 로고    scopus 로고
    • On the accuracy of limiters and convergence to steady state solutions
    • AIAA, January 1993
    • Venkatakrishnan, V.: On the accuracy of limiters and convergence to steady state solutions. Paper 93-0880, AIAA, January 1993
    • Paper 93-0880
    • Venkatakrishnan, V.1
  • 50
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • 0474.65066 10.1016/0021-9991(81)90128-5 640362 1981JCoPh.43.357R
    • P.L. Roe 1981 Approximate Riemann solvers, parameter vectors, and difference schemes J. Comput. Phys. 43 357 372 0474.65066 10.1016/0021-9991(81) 90128-5 640362 1981JCoPh..43..357R
    • (1981) J. Comput. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 56
    • 0024737429 scopus 로고
    • Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low reynolds numbers
    • 10.1017/S0022112089002429 1989JFM.206.579W
    • C.H.K. Williamson 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low reynolds numbers J. Fluid Mech. 206 579 627 10.1017/S0022112089002429 1989JFM...206..579W
    • (1989) J. Fluid Mech. , vol.206 , pp. 579-627
    • Williamson, C.H.K.1
  • 57
    • 0022698249 scopus 로고
    • Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder
    • 0596.76047 10.1017/S0022112086003014 846291 1986JFM.165.79B
    • M. Braza P. Chassaing H. Ha Minh 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder J. Fluid Mech. 165 79 130 0596.76047 10.1017/S0022112086003014 846291 1986JFM...165...79B
    • (1986) J. Fluid Mech. , vol.165 , pp. 79-130
    • Braza, M.1    Chassaing, P.2    Ha Minh, H.3
  • 60
    • 78149422690 scopus 로고    scopus 로고
    • Application of the 10-moment model to MEMS flows
    • AIAA, January
    • Suzuki, Y., van Leer, B.: Application of the 10-moment model to MEMS flows. Paper 2005-1398, AIAA, January (2005)
    • (2005) Paper 2005-1398
    • Suzuki, Y.1    Van Leer, B.2
  • 62
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
    • 0565.65051 10.1137/1025002 693713
    • A. Harten P.D. Lax B. van Leer 1983 On upstream differencing and Godunov-type schemes for hyperbolic conservation laws SIAM Rev. 25 1 35 61 0565.65051 10.1137/1025002 693713
    • (1983) SIAM Rev. , vol.25 , Issue.1 , pp. 35-61
    • Harten, A.1    Lax, P.D.2    Van Leer, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.