메뉴 건너뛰기




Volumn 224, Issue 2, 2007, Pages 1223-1242

A Runge-Kutta discontinuous Galerkin method for viscous flow equations

Author keywords

Discontinuous Galerkin method; Gas kinetic scheme; Viscous flow simulations

Indexed keywords

DISTRIBUTION FUNCTIONS; GALERKIN METHODS; GASES; KINETIC THEORY OF GASES; KINETICS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; PHASE INTERFACES; RUNGE KUTTA METHODS;

EID: 34248657568     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.11.014     Document Type: Article
Times cited : (59)

References (28)
  • 1
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • Bassi F., and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267
    • (1997) J. Comput. Phys. , vol.131 , pp. 267
    • Bassi, F.1    Rebay, S.2
  • 2
    • 85190771190 scopus 로고    scopus 로고
    • F. Bassi, S. Rebay, An implicit high-order discontinuous Galerkin method for the steady state compressible Navier-Stokes equations, Computational Fluid Dynamics '98, Proceedings of the Fourth European Computational Fluid Dynamics Conference, vol. 2, 1998, p. 1226.
  • 3
    • 26344468007 scopus 로고
    • A model for collision processes in gases I: Small amplitude processes in charged and neutral one-component systems
    • Bhatnagar 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 (1954) 511
    • (1954) Phys. Rev. , vol.94 , pp. 511
    • Bhatnagar, P.L.1    Gross, E.P.2    Krook, M.3
  • 4
    • 0031568155 scopus 로고    scopus 로고
    • Kinetic flux-vector splitting for the Navier-Stokes equations
    • Chou S.Y., and Baganoff D. Kinetic flux-vector splitting for the Navier-Stokes equations. J. Comput. Phys. 130 (1997) 217
    • (1997) J. Comput. Phys. , vol.130 , pp. 217
    • Chou, S.Y.1    Baganoff, D.2
  • 5
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2002) 1749
    • (2002) SIAM J. Numer. Anal. , vol.39 , pp. 1749
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 7
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General framework
    • Cockburn B., and Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General framework. Math. Comput. 52 (1989) 411
    • (1989) Math. Comput. , vol.52 , pp. 411
    • Cockburn, B.1    Shu, C.W.2
  • 8
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems
    • Cockburn B., Lin S.Y., and Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems. J. Comput. Phys. 84 (1989) 90
    • (1989) J. Comput. Phys. , vol.84 , pp. 90
    • Cockburn, B.1    Lin, S.Y.2    Shu, C.W.3
  • 9
    • 84966261380 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case
    • Cockburn B., Hou S., and Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comput. 54 (1990) 545
    • (1990) Math. Comput. , vol.54 , pp. 545
    • Cockburn, B.1    Hou, S.2    Shu, C.W.3
  • 10
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems
    • Cockburn B., and Shu C.W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems. J. Comput. Phys. 141 (1998) 199
    • (1998) J. Comput. Phys. , vol.141 , pp. 199
    • Cockburn, B.1    Shu, C.W.2
  • 11
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • Cockburn B., and Shu C.W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2440
    • Cockburn, B.1    Shu, C.W.2
  • 12
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin method for convection-dominated problems
    • Cockburn B., and Shu C.W. Runge-Kutta discontinuous Galerkin method for convection-dominated problems. J. Sci. Comput. 16 (2001) 173
    • (2001) J. Sci. Comput. , vol.16 , pp. 173
    • Cockburn, B.1    Shu, C.W.2
  • 13
    • 85190775906 scopus 로고    scopus 로고
    • R.J. Hakkinen, L. Greber, L. Trilling, S.S. Abarbanel, The interaction of an oblique shock wave with a laminar boundary layer, NASA Memo. 2-18-59W, NASA, 1959.
  • 14
    • 0032720726 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for the Euler and Navier-Stokes equations
    • Baumann C.E., and Oden J.T. A discontinuous hp finite element method for the Euler and Navier-Stokes equations. Int. J. Numer. Methods Fluids 31 (1999) 79
    • (1999) Int. J. Numer. Methods Fluids , vol.31 , pp. 79
    • Baumann, C.E.1    Oden, J.T.2
  • 15
    • 10944272687 scopus 로고    scopus 로고
    • A Runge-Kutta discontinuous Galerkin method for the Euler equations
    • Tang H.Z., and Warnecke G. A Runge-Kutta discontinuous Galerkin method for the Euler equations. Comput. Fluids 34 (2005) 375
    • (2005) Comput. Fluids , vol.34 , pp. 375
    • Tang, H.Z.1    Warnecke, G.2
  • 16
    • 0037139655 scopus 로고    scopus 로고
    • On the construction of kinetic schemes
    • Ohwada T. On the construction of kinetic schemes. J. Comput. Phys. 177 (2002) 156
    • (2002) J. Comput. Phys. , vol.177 , pp. 156
    • Ohwada, T.1
  • 17
    • 26944487244 scopus 로고    scopus 로고
    • Simple derivation of high-resolution schemes for compressible flows by kinetic approach
    • Ohwada T., and Fukata S. Simple derivation of high-resolution schemes for compressible flows by kinetic approach. J. Comput. Phys. 211 (2006) 424
    • (2006) J. Comput. Phys. , vol.211 , pp. 424
    • Ohwada, T.1    Fukata, S.2
  • 18
    • 0344981340 scopus 로고    scopus 로고
    • Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one dimensional case
    • Qiu J., and Shu C.W. Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one dimensional case. J. Comput. Phys. 193 (2004) 115
    • (2004) J. Comput. Phys. , vol.193 , pp. 115
    • Qiu, J.1    Shu, C.W.2
  • 19
    • 0001568854 scopus 로고
    • Efficient implementation of essential non-oscillatory shock capturing schemes, II
    • Shu C.W., and Osher S. Efficient implementation of essential non-oscillatory shock capturing schemes, II. J. Comput. Phys. 83 (1989) 32
    • (1989) J. Comput. Phys. , vol.83 , pp. 32
    • Shu, C.W.1    Osher, S.2
  • 20
    • 84966251037 scopus 로고
    • TVB uniformly high-order schemes for conservation laws
    • Shu C.W. TVB uniformly high-order schemes for conservation laws. Math. Comput. 49 (1987) 105
    • (1987) Math. Comput. , vol.49 , pp. 105
    • Shu, C.W.1
  • 21
    • 49449129017 scopus 로고
    • Towards the ultimate conservative difference scheme IV. A new approach to numerical convection
    • van Leer B. Towards the ultimate conservative difference scheme IV. A new approach to numerical convection. J. Comput. Phys. 23 (1977) 276
    • (1977) J. Comput. Phys. , vol.23 , pp. 276
    • van Leer, B.1
  • 22
    • 85190821218 scopus 로고    scopus 로고
    • B. van Leer, S. Nomura, Discontinuous Galerkin for diffusion, AIAA-2005-5108, 17th AIAA Computational Fluid Dynamics Conference, 2005.
  • 23
    • 85190761183 scopus 로고    scopus 로고
    • K. Xu, Gas-kinetic schemes for unsteady compressible flow simulations, VKI for Fluid Dynamics Lecture Series 1998-03, 1998.
  • 24
    • 0001445852 scopus 로고    scopus 로고
    • A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method
    • Xu K. A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. J. Comput. Phys. 171 (2001) 289
    • (2001) J. Comput. Phys. , vol.171 , pp. 289
    • Xu, K.1
  • 25
    • 85190781074 scopus 로고    scopus 로고
    • K. Xu and A. Jameson, Gas-kinetic relaxation (BGK-type) schemes for the compressible Euler equations, AIAA-95-1736, 12th AIAA Computational Fluid Dynamics Conference, 1995.
  • 26
    • 0035884718 scopus 로고    scopus 로고
    • Dissipative mechanism in Godunov-type schemes
    • Xu K., and Li Z.W. Dissipative mechanism in Godunov-type schemes. Int. J. Numer. Methods Fluids 37 (2001) 1
    • (2001) Int. J. Numer. Methods Fluids , vol.37 , pp. 1
    • Xu, K.1    Li, Z.W.2
  • 27
    • 13644273552 scopus 로고    scopus 로고
    • A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow
    • Xu K., Mao M.L., and Tang L. A multidimensional gas-kinetic BGK scheme for hypersonic viscous flow. J. Comput. Phys. 203 (2005) 405
    • (2005) J. Comput. Phys. , vol.203 , pp. 405
    • Xu, K.1    Mao, M.L.2    Tang, L.3
  • 28
    • 10244259321 scopus 로고    scopus 로고
    • Discontinuous Galerkin BGK method for viscous flow equations: one-dimensional systems
    • Xu K. Discontinuous Galerkin BGK method for viscous flow equations: one-dimensional systems. SIAM J. Sci. Comput. 23 (2004) 1941
    • (2004) SIAM J. Sci. Comput. , vol.23 , pp. 1941
    • Xu, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.