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Volumn 34, Issue 5, 1997, Pages 1865-1883

A consistency result for a discrete-velocity model of the boltzmann equation

Author keywords

Boltzmann equation; Consistency; Discrete velocity models; Numerical methods

Indexed keywords


EID: 0008492827     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142995289007     Document Type: Article
Times cited : (98)

References (31)
  • 1
    • 0022593645 scopus 로고
    • On a simulation scheme for the Boltzmann equation
    • H. BABOVSKY, On a simulation scheme for the Boltzmann equation, Math. Methods Appl. Sci., 8 (1986), pp. 223-233.
    • (1986) Math. Methods Appl. Sci. , vol.8 , pp. 223-233
    • Babovsky, H.1
  • 5
    • 0000199825 scopus 로고
    • On approximation of the Boltzmann equation by discrete velocity models
    • A. V. BOBYLEV, A. PALCZEWSKI, AND J. SCHNEIDER, On approximation of the Boltzmann equation by discrete velocity models, C. R. Acad. Sci. Paris Sér. I, 320 (1995), pp. 639-644.
    • (1995) C. R. Acad. Sci. Paris Sér. I , vol.320 , pp. 639-644
    • Bobylev, A.V.1    Palczewski, A.2    Schneider, J.3
  • 6
    • 84958443216 scopus 로고
    • Study of a rarefied shear flow by discrete velocity model
    • J. BROADWELL, Study of a rarefied shear flow by discrete velocity model, J. Fluid Mech., 19 (1964), pp. 367-370.
    • (1964) J. Fluid Mech. , vol.19 , pp. 367-370
    • Broadwell, J.1
  • 7
    • 0030547664 scopus 로고    scopus 로고
    • A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics
    • C. BUET, A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics, Transport Theory Statist. Phys., 25 (1996), pp. 33-60.
    • (1996) Transport Theory Statist. Phys. , vol.25 , pp. 33-60
    • Buet, C.1
  • 8
    • 0003704503 scopus 로고
    • The Discrete Boltzmann Equation (Theory and Application)
    • University of California, Berkeley
    • H. CABANNES, The Discrete Boltzmann Equation (Theory and Application), Lecture Notes, University of California, Berkeley, 1980.
    • (1980) Lecture Notes
    • Cabannes, H.1
  • 9
    • 23444438725 scopus 로고
    • Problèmes mathèmatiques dans la théorie cinetique des gas
    • Almqvist-Wiksell, Upsala
    • T. CARLEMAN, Problèmes mathèmatiques dans la théorie cinetique des gas, Publ. Sci. Inst. Mittag-Leffler, Almqvist-Wiksell, Upsala, 1957.
    • (1957) Publ. Sci. Inst. Mittag-Leffler
    • Carleman, T.1
  • 11
    • 0030363548 scopus 로고    scopus 로고
    • About the splitting algorithm for Boltzmann and BGK equations
    • L. DESVILLETTES AND S. MISCHLER, About the splitting algorithm for Boltzmann and BGK equations, Math. Models Methods Appl. Sci., 6 (1996), pp. 1079-1101.
    • (1996) Math. Models Methods Appl. Sci. , vol.6 , pp. 1079-1101
    • Desvillettes, L.1    Mischler, S.2
  • 12
    • 34250086530 scopus 로고
    • Hyperbolic distribution problems and half-integer weight Maaβ forms
    • W. DUKE, Hyperbolic distribution problems and half-integer weight Maaβ forms, Invent. Math., 92 (1988), pp. 73-90.
    • (1988) Invent. Math. , vol.92 , pp. 73-90
    • Duke, W.1
  • 13
    • 0002358904 scopus 로고
    • Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
    • W. DUKE AND R. SCHULZE-PILLOT, Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids, Invent. Math., 99 (1990), pp. 49-57.
    • (1990) Invent. Math. , vol.99 , pp. 49-57
    • Duke, W.1    Schulze-Pillot, R.2
  • 14
    • 0004001984 scopus 로고
    • Théorie cinétique des gaz à répartition discrète des vitesses
    • Springer-Verlag, Berlin, Heidelberg, New York
    • R. GATIGNOL, Théorie cinétique des gaz à répartition discrète des vitesses, Lecture Notes in Physics 36, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
    • (1975) Lecture Notes in Physics , vol.36
    • Gatignol, R.1
  • 15
    • 0001776391 scopus 로고
    • Investigation of the motion of discrete-velocity gases
    • Rarefied Gas Dynamics: Theoretical and Computational Techniques, E. P. Muntz, D. P. Weaver, and D. H. Campbell, eds., AIAA, Washington, DC
    • D. GOLDSTEIN, B. STURTEVANT, AND J. E. BROADWELL, Investigation of the motion of discrete-velocity gases, in Rarefied Gas Dynamics: Theoretical and Computational Techniques, E. P. Muntz, D. P. Weaver, and D. H. Campbell, eds., Progress in Astronautics and Aeronautics 118, AIAA, Washington, DC, 1989, pp. 100-117.
    • (1989) Progress in Astronautics and Aeronautics , vol.118 , pp. 100-117
    • Goldstein, D.1    Sturtevant, B.2    Broadwell, J.E.3
  • 16
    • 85002536064 scopus 로고
    • Discrete Velocity Gasdynamics Simulations in a Parallel Processing Environment
    • D. B. GOLDSTEIN AND B. STURTEVANT, Discrete Velocity Gasdynamics Simulations in a Parallel Processing Environment, AIAA Paper No. 89-1668, 1989.
    • (1989) AIAA Paper No. 89-1668
    • Goldstein, D.B.1    Sturtevant, B.2
  • 17
    • 0346730461 scopus 로고
    • Asymptotic equidistribution of integral points on the three-dimensional sphere (in Russian)
    • E. P. GOLUBEVA AND O. M. FOMENKO, Asymptotic equidistribution of integral points on the three-dimensional sphere (in Russian), Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov 160 (1987), pp. 54-71.
    • (1987) Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov , vol.160 , pp. 54-71
    • Golubeva, E.P.1    Fomenko, O.M.2
  • 19
    • 21144478796 scopus 로고
    • A random discrete velocity model and approximation of the Boltzmann equation
    • R. ILLNER AND W. WAGNER, A random discrete velocity model and approximation of the Boltzmann equation, J. Statist. Phys., 70 (1993), pp. 773-792.
    • (1993) J. Statist. Phys. , vol.70 , pp. 773-792
    • Illner, R.1    Wagner, W.2
  • 20
    • 0000109201 scopus 로고
    • Numerical study of discrete-velocity gases
    • T. INAMURO AND B. STURTEVANT, Numerical study of discrete-velocity gases, Phys. Fluids A, 2 (1990), pp. 2196-2203.
    • (1990) Phys. Fluids A , vol.2 , pp. 2196-2203
    • Inamuro, T.1    Sturtevant, B.2
  • 21
    • 0000207773 scopus 로고
    • Fourier coefficients of modular forms of half integral weight
    • H. IWANIEC, Fourier coefficients of modular forms of half integral weight, Invent. Math., 87 (1987), pp. 385-401.
    • (1987) Invent. Math. , vol.87 , pp. 385-401
    • Iwaniec, H.1
  • 24
    • 0346099898 scopus 로고
    • On the representation of large integers by integral ternary positive definite quadratic forms
    • B. Z. MOROZ, On the representation of large integers by integral ternary positive definite quadratic forms, Astérisque, 209 (1992), pp. 275-278.
    • (1992) Astérisque , vol.209 , pp. 275-278
    • Moroz, B.Z.1
  • 25
    • 4243366477 scopus 로고
    • Direct simulation scheme derived from the Boltzmann equation
    • K. NANBU, Direct simulation scheme derived from the Boltzmann equation, J. Phys. Soc. Japan, 49 (1980), pp. 2042-2049.
    • (1980) J. Phys. Soc. Japan , vol.49 , pp. 2042-2049
    • Nanbu, K.1
  • 26
    • 36449006713 scopus 로고
    • Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules
    • T. OHWADA, Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules, Phys. Fluids A, 5 (1993), pp. 217-234.
    • (1993) Phys. Fluids A , vol.5 , pp. 217-234
    • Ohwada, T.1
  • 27
    • 0000434123 scopus 로고
    • An analysis of particle methods
    • Numerical Methods in Fluid Dynamics, F. Brezzi, ed., Springer-Verlag, Berlin, Heidelberg, New York
    • P. A. RAVIART, An analysis of particle methods, in Numerical Methods in Fluid Dynamics, F. Brezzi, ed., Lecture Notes in Mathematics 1127, Springer-Verlag, Berlin, Heidelberg, New York, 1984, pp. 243-324.
    • (1984) Lecture Notes in Mathematics , vol.1127 , pp. 243-324
    • Raviart, P.A.1
  • 29
    • 0040347813 scopus 로고
    • A direct method for solving the Boltzmann equation
    • F. ROGIER AND J. SCHNEIDER, A direct method for solving the Boltzmann equation, Transport Theory Statist. Phys., 23 (1994), pp. 313-338.
    • (1994) Transport Theory Statist. Phys. , vol.23 , pp. 313-338
    • Rogier, F.1    Schneider, J.2
  • 31
    • 0002097616 scopus 로고
    • Über die Klassenzahl quadratischer Zahlkörper
    • C. L. SIEGEL, Über die Klassenzahl quadratischer Zahlkörper, Acta Arith., 1 (1935), pp. 83-86.
    • (1935) Acta Arith. , vol.1 , pp. 83-86
    • Siegel, C.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.