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Volumn 18, Issue 1, 2002, Pages 37-62

A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion

Author keywords

Boltzmann equation; Burnett equations; Central schemes; Chapman Enskog expansion; Relaxation

Indexed keywords


EID: 0141641004     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/s102550200003     Document Type: Article
Times cited : (26)

References (39)
  • 1
    • 84875609208 scopus 로고    scopus 로고
    • Beyond Navier-Stokes: Burnett equations for flow simulations in continuum-transition regime
    • Norfolk, VA, 28 June-1 July
    • Agarwal, R., Yun, K., Balakrishnan, R. Beyond Navier-Stokes: Burnett Equations for Flow Simulations in Continuum-transition Regime. AIAA 99-3580, 30th AIAA Fluid Dynamics Conference, Norfolk, VA, 28 June-1 July, 1999
    • (1999) AIAA 99-3580, 30th AIAA Fluid Dynamics Conference
    • Agarwal, R.1    Yun, K.2    Balakrishnan, R.3
  • 2
    • 0031269714 scopus 로고    scopus 로고
    • Implicit-explicit Runge-Kutta methods for time dependent PDE's
    • Ascher, U., Ruth, S., Spiteri, R.J. Implicit-explicit Runge-Kutta Methods for Time Dependent PDE's. Appl. Numer. Math., 1997, 25: 151-161
    • (1997) Appl. Numer. Math. , vol.25 , pp. 151-161
    • Ascher, U.1    Ruth, S.2    Spiteri, R.J.3
  • 5
    • 0001848552 scopus 로고
    • The Chapman-Enskog and grad methods for solving the Boltzmann equation
    • Bobylev, A.V. The Chapman-Enskog and Grad Methods for Solving the Boltzmann Equation. Soviet Physics Doklady, 1982, 27(1): 71-75
    • (1982) Soviet Physics Doklady , vol.27 , Issue.1 , pp. 71-75
    • Bobylev, A.V.1
  • 6
    • 0007070179 scopus 로고
    • On the structure of spatially homogeneous normal solutions of a nonlinear Boltzmann equation for a mixture of gases
    • Bobylev, A.V. On the Structure of Spatially Homogeneous Normal Solutions of a Nonlinear Boltzmann Equation for a Mixture of Gases. Soviet Physics Doklady, 1980, 25: 30-32
    • (1980) Soviet Physics Doklady , vol.25 , pp. 30-32
    • Bobylev, A.V.1
  • 9
    • 0001130290 scopus 로고    scopus 로고
    • Relaxation of energy and approximate Riemann solvers for general pressure laws in fluid dynamics
    • Coquel, F., Perthame, B. Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics. SIAM J. Num. Anal., 1998, 35: 2223-2249
    • (1998) SIAM J. Num. Anal. , vol.35 , pp. 2223-2249
    • Coquel, F.1    Perthame, B.2
  • 11
    • 0001279602 scopus 로고
    • Comparison of Burnett, super-Burnett and Monte-Carlo solutions for hypersonic shock structure
    • Pasadena, California, July 11-15
    • Fiscko, K.A., Chapman, D.R. Comparison of Burnett, Super-Burnett and Monte-Carlo Solutions for Hypersonic Shock Structure. Proc.16th International Symposium on Rarefied Gas Dynamics, Pasadena, California, July 11-15, 1988
    • (1988) Proc.16th International Symposium on Rarefied Gas Dynamics
    • Fiscko, K.A.1    Chapman, D.R.2
  • 12
    • 0001201394 scopus 로고
    • On the higher order hydrodynamic theories of shock structure
    • Foch, T.D. On the Higher Order Hydrodynamic Theories of Shock Structure. Acta Physica, Austriaca, Supplement, 1973, X: 123-140
    • (1973) Acta Physica, Austriaca, Supplement , vol.10 , pp. 123-140
    • Foch, T.D.1
  • 13
    • 0001351025 scopus 로고
    • Asymptotic theory of the Boltzmann equation
    • Grad, H. Asymptotic Theory of the Boltzmann Equation. Physics of Fluids, 1963, 6: 147-181
    • (1963) Physics of Fluids , vol.6 , pp. 147-181
    • Grad, H.1
  • 14
    • 0023329384 scopus 로고
    • Uniformly high order accurate non-oscillatory scheme I
    • Harten, A., Osher, S. Uniformly High Order Accurate Non-oscillatory Scheme I. SIAM J. Numer. Anal., 1987, 24: 279-309
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 15
    • 0000238594 scopus 로고    scopus 로고
    • High-resolution non-oscillatory central schemes with non-staggered grids for hyperbolic conservation laws
    • Jang, G.S., Levy, D., Lin, C.T., Osher, S., Tadmor, E. High-resolution Non-oscillatory Central Schemes with Non-staggered Grids for Hyperbolic Conservation Laws. SIAM J. Num. Anal., 1998, 35: 1892-1917
    • (1998) SIAM J. Num. Anal. , vol.35 , pp. 1892-1917
    • Jang, G.S.1    Levy, D.2    Lin, C.T.3    Osher, S.4    Tadmor, E.5
  • 16
    • 0035536415 scopus 로고    scopus 로고
    • Regularization of the Burnett equations via relaxation
    • Jin, S., Slemrod, M. Regularization of the Burnett Equations via relaxation. J. Stat. Phys., 2001, 103(5-6): 1009-1033
    • (2001) J. Stat. Phys. , vol.103 , Issue.5-6 , pp. 1009-1033
    • Jin, S.1    Slemrod, M.2
  • 17
    • 0035311845 scopus 로고    scopus 로고
    • Regularization of the Burnett equations for fast granular flows via relaxation
    • Jin, S., Slemrod, M. Regularization of the Burnett Equations for Fast Granular Flows via Relaxation. Physica D, 2001, 150: 207-218
    • (2001) Physica D , vol.150 , pp. 207-218
    • Jin, S.1    Slemrod, M.2
  • 18
    • 84990701264 scopus 로고
    • The relaxation schemes for systems of conservation laws in arbitrary space dimensions
    • Jin, S., Xin, Z.P. The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions. Comm. Pure Appl. Math., 1995, 48: 235-276
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 235-276
    • Jin, S.1    Xin, Z.P.2
  • 20
    • 0030534703 scopus 로고    scopus 로고
    • Moment closure hierarchies for kinetic
    • Levermore, C.D. Moment Closure Hierarchies for Kinetic Theories. J. Stat. Phys., 1996, 83: 1021-1065
    • (1996) Theories. J. Stat. Phys. , vol.83 , pp. 1021-1065
    • Levermore, C.D.1
  • 21
    • 0032153743 scopus 로고    scopus 로고
    • The Gaussian moment closure for gas dynamics
    • Levermore, C.D., Morokoff, W.J. The Gaussian Moment Closure for Gas Dynamics. SIAM J. Appl. Math., 1998, 59: 72-96
    • (1998) SIAM J. Appl. Math. , vol.59 , pp. 72-96
    • Levermore, C.D.1    Morokoff, W.J.2
  • 22
    • 0034431558 scopus 로고    scopus 로고
    • Central schemes for balance laws of relaxation type
    • Liotta, F., Romano, V., Russo, G. Central Schemes for Balance Laws of Relaxation Type. SIAM J. Numer. Anal., 2000, 38: 1337-1356
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1337-1356
    • Liotta, F.1    Romano, V.2    Russo, G.3
  • 23
    • 0007018122 scopus 로고
    • On the method of derivation of closed systems for macroparameters of distribution function for small Knudsen numbers
    • Luk'shin, A.V. On the Method of Derivation of Closed Systems for Macroparameters of Distribution Function for Small Knudsen Numbers. Doklady AN SSSR, 1983, 170: 869-873
    • (1983) Doklady AN SSSR , vol.170 , pp. 869-873
    • Luk'Shin, A.V.1
  • 24
    • 0007058921 scopus 로고
    • English Translation
    • English Translation in Soviet Physics Doklady, 1983, 28: 454-456
    • (1983) Soviet Physics Doklady , vol.28 , pp. 454-456
  • 25
    • 0007020251 scopus 로고
    • Hydrodynamical limit for the Boltzmann equation and its different analogs
    • Moscow Aviation Institute, Moscow
    • Luk'shin, A.V. Hydrodynamical Limit for the Boltzmann Equation and Its Different Analogs. In: Numerical and Analytical Methods in Rarefied Gas Dynamics, Moscow Aviation Institute, Moscow 1986, 37-43
    • (1986) Numerical and Analytical Methods in Rarefied Gas Dynamics , pp. 37-43
    • Luk'Shin, A.V.1
  • 26
    • 0007113729 scopus 로고
    • The cauchy problem for the Boltzmann equation. Hydrodynamical limit
    • Moscow State University, Moscow
    • Luk'shin, A.V. The Cauchy Problem for the Boltzmann Equation. Hydrodynamical limit. In: Numerical Methods in Mathematical Physics, Moscow State University, Moscow 1986, 61-91
    • (1986) Numerical Methods in Mathematical Physics , pp. 61-91
    • Luk'shin, A.V.1
  • 28
    • 28144455569 scopus 로고
    • Nonoscillatory central differencing for hyperbolic conservation laws
    • Nessyahu, H., Tadmor, E. Nonoscillatory Central Differencing for Hyperbolic Conservation Laws. J. Comp. Phys., 1990, 87: 408-463
    • (1990) J. Comp. Phys. , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 29
    • 0035453003 scopus 로고    scopus 로고
    • Central differencing based numerical schemes for hyperbolic conservation laws with relaxation terms
    • Pareschi, L. Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms. SIAM J. Num. Anal., 2001, 39(4): 1395-1417
    • (2001) SIAM J. Num. Anal. , vol.39 , Issue.4 , pp. 1395-1417
    • Pareschi, L.1
  • 32
    • 0021156247 scopus 로고
    • On the domain space for constitutive laws in linear viscoelasticity
    • Renardy, M. On the Domain Space for Constitutive Laws in Linear Viscoelasticity. Arch. Rat. Mech. Anal., 1984, 85: 21-26
    • (1984) Arch. Rat. Mech. Anal. , vol.85 , pp. 21-26
    • Renardy, M.1
  • 33
    • 0024754230 scopus 로고
    • A high order staggered grid method for hyperbolic systems of conservation laws in one space dimension
    • Sanders, R., Weiser, A. A High Order Staggered Grid Method for Hyperbolic Systems of Conservation Laws in One Space Dimension. Comp. Meth. in App. Mech. an Engrg., 1989, 75: 91-107
    • (1989) Comp. Meth. in App. Mech. An Engrg. , vol.75 , pp. 91-107
    • Sanders, R.1    Weiser, A.2
  • 34
    • 0033265465 scopus 로고    scopus 로고
    • Constitutive relations for monatomic gases based on a generalized rational approximation to the sum of the Chapman-Enskog expansion
    • Slemrod, M. Constitutive Relations for Monatomic Gases Based on a Generalized Rational Approximation to the Sum of the Chapman-Enskog Expansion. To Appear, Arch. Rational Mech. Anal., 1999, 150(1): 1-22
    • (1999) To Appear, Arch. Rational Mech. Anal. , vol.150 , Issue.1 , pp. 1-22
    • Slemrod, M.1
  • 36
    • 0001518684 scopus 로고
    • On the construction and the comparison of difference schemes
    • Strang, G. On the Construction and the Comparison of Difference Schemes. Siam J. Numer. Anal., 1968, 5: 506-517
    • (1968) Siam J. Numer. Anal. , vol.5 , pp. 506-517
    • Strang, G.1


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