메뉴 건너뛰기




Volumn 227, Issue 4, 2008, Pages 2481-2513

Solvers for the high-order Riemann problem for hyperbolic balance laws

Author keywords

ADER methods; Classical Riemann problem; Euler equations; Godunov method; High order Riemann problem; Hyperbolic equations; Shallow water equations; Source terms; Unstructured meshes; Well balanced schemes

Indexed keywords

NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EID: 38049038823     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.11.013     Document Type: Article
Times cited : (101)

References (48)
  • 1
    • 48349083249 scopus 로고
    • A second order Godunov-type scheme for compressible fluid dynamics
    • Ben-Artzi M., and Falcovitz J. A second order Godunov-type scheme for compressible fluid dynamics. J. Comput. Phys. 55 (1984) 1-32
    • (1984) J. Comput. Phys. , vol.55 , pp. 1-32
    • Ben-Artzi, M.1    Falcovitz, J.2
  • 3
    • 33748558739 scopus 로고    scopus 로고
    • A direct Eulerian GRP scheme for compressible fluid flows
    • Ben-Artzi M., Li J., and Warnecke G. A direct Eulerian GRP scheme for compressible fluid flows. J. Comput. Phys. 218 (2006) 19-43
    • (2006) J. Comput. Phys. , vol.218 , pp. 19-43
    • Ben-Artzi, M.1    Li, J.2    Warnecke, G.3
  • 4
    • 34248146085 scopus 로고    scopus 로고
    • Hyperbolic balance laws: Riemann invariants and hyperbolic balance laws
    • Ben-Artzi M., and Li J. Hyperbolic balance laws: Riemann invariants and hyperbolic balance laws. Numerische Mathematik 106 (2007) 369-425
    • (2007) Numerische Mathematik , vol.106 , pp. 369-425
    • Ben-Artzi, M.1    Li, J.2
  • 5
    • 0040686631 scopus 로고
    • An Asymptotic expansion for the solution of the generalized Riemann problem. Part 2: Application to the Euler equations of gas dynamics
    • Bourgeade A., LeFloch P., and Raviart P.A. An Asymptotic expansion for the solution of the generalized Riemann problem. Part 2: Application to the Euler equations of gas dynamics. Ann. Inst. Henri Poincaré. Analyse non Lineáre 6 6 (1989) 437-480
    • (1989) Ann. Inst. Henri Poincaré. Analyse non Lineáre , vol.6 , Issue.6 , pp. 437-480
    • Bourgeade, A.1    LeFloch, P.2    Raviart, P.A.3
  • 6
    • 0000480805 scopus 로고
    • A direct Eulerian MUSCL scheme for gas dynamics
    • Colella P. A direct Eulerian MUSCL scheme for gas dynamics. SIAM J. Sci. Stat. Comput. 6 (1985) 104-117
    • (1985) SIAM J. Sci. Stat. Comput. , vol.6 , pp. 104-117
    • Colella, P.1
  • 7
    • 85190765045 scopus 로고    scopus 로고
    • M. Dumbser, Arbitrary high order schemes for the solution of hyperbolic conservation laws in complex domains. PhD thesis, Institut für Aero- un Gasdynamik, Universität Stuttgart, Germany, 2005.
  • 8
    • 33846336138 scopus 로고    scopus 로고
    • Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
    • Dumbser M., and Käser M. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J. Comput. Phys. 221 (2007) 693-723
    • (2007) J. Comput. Phys. , vol.221 , pp. 693-723
    • Dumbser, M.1    Käser, M.2
  • 9
    • 27144507034 scopus 로고    scopus 로고
    • ADER discontinuous Galerkin schemes for aeroacoustics
    • Dumbser M., and Munz C.D. ADER discontinuous Galerkin schemes for aeroacoustics. Comptes Rendus Mécanique 333 (2005) 683-687
    • (2005) Comptes Rendus Mécanique , vol.333 , pp. 683-687
    • Dumbser, M.1    Munz, C.D.2
  • 11
    • 34548397128 scopus 로고    scopus 로고
    • Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
    • Dumbser M., Käser M., Titarev V.A., and Toro E.F. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J. Comput. Phys. 226 (2007) 204-243
    • (2007) J. Comput. Phys. , vol.226 , pp. 204-243
    • Dumbser, M.1    Käser, M.2    Titarev, V.A.3    Toro, E.F.4
  • 12
    • 85190774173 scopus 로고    scopus 로고
    • S.K. Fok, Extension of Glimm's method to the problem of gas flow in a duct of variable cross-section. PhD Thesis, Department of Mathematics, University of California, Berkeley, 1981.
  • 13
    • 84981759861 scopus 로고
    • Solution in the large for nonlinear hyperbolic systems of equations
    • Glimm J. Solution in the large for nonlinear hyperbolic systems of equations. Commun. Pure Appl. Math. 18 (1965) 697-715
    • (1965) Commun. Pure Appl. Math. , vol.18 , pp. 697-715
    • Glimm, J.1
  • 14
    • 0002259954 scopus 로고
    • A generalized Riemann problem for quasi one-dimensional gas flows
    • Glimm J., Marshall G., and Plohr B. A generalized Riemann problem for quasi one-dimensional gas flows. Advances in Applied Mathematics 5 (1984) 1-30
    • (1984) Advances in Applied Mathematics , vol.5 , pp. 1-30
    • Glimm, J.1    Marshall, G.2    Plohr, B.3
  • 15
    • 0000935266 scopus 로고
    • Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov S.K. Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47 (1959) 271-306
    • (1959) Mat. Sb. , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 16
    • 0038868514 scopus 로고
    • A convergent series expansion for hyperbolic systems of conservation laws
    • Harabetian E. A convergent series expansion for hyperbolic systems of conservation laws. Trans Am. Math. Soc. 294 (1986) 383-424
    • (1986) Trans Am. Math. Soc. , vol.294 , pp. 383-424
    • Harabetian, E.1
  • 17
    • 33749725182 scopus 로고
    • Uniformly high order accuracy essentially non-oscillatory schemes III
    • Harten A., Engquist B., Osher S., and Chakravarthy S.R. Uniformly high order accuracy essentially non-oscillatory schemes III. J. Comput. Phys. 71 (1987) 231-303
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.R.4
  • 18
    • 0023329384 scopus 로고
    • Uniformly high-order accurate nonoscillatory schemes I
    • Harten A., and Osher S. Uniformly high-order accurate nonoscillatory schemes I. SIAM J. Numer. Anal. 24 2 (1987) 279-309
    • (1987) SIAM J. Numer. Anal. , vol.24 , Issue.2 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 19
    • 0003140474 scopus 로고    scopus 로고
    • Weighted essentially non-oscillatory schemes on triangular meshes
    • Hu C., and Shu C.W. Weighted essentially non-oscillatory schemes on triangular meshes. J. Comput. Phys. 150 (1999) 97-127
    • (1999) J. Comput. Phys. , vol.150 , pp. 97-127
    • Hu, C.1    Shu, C.W.2
  • 20
    • 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. 126 130 (1996) 202-228
    • (1996) J. Comput. Phys. , vol.126 , Issue.130 , pp. 202-228
    • Jiang, G.S.1    Shu, C.W.2
  • 21
    • 85190808562 scopus 로고    scopus 로고
    • M. Käser, Adaptive Methods for the Numerical Simulation of Transport Processes. PhD thesis, Institute of Numerical Mathematics and Scientific Computing, University of Munich, Germany, 2003.
  • 23
    • 17144370650 scopus 로고    scopus 로고
    • Adaptive ADER schemes for the solution of scalar non-linear hyperbolic problems
    • Käser M., and Iske A. Adaptive ADER schemes for the solution of scalar non-linear hyperbolic problems. J. Comput. Phys. 205 (2005) 486-508
    • (2005) J. Comput. Phys. , vol.205 , pp. 486-508
    • Käser, M.1    Iske, A.2
  • 24
    • 85190817895 scopus 로고    scopus 로고
    • L. Tatsien, Y. Wenci. Boundary-value problems for quasi-linear hyperbolic systems, Duke University Mathematics Series, 1985.
  • 25
    • 0038908817 scopus 로고
    • An asymptotic expansion for the solution of the generalized riemann problem. Part 1: General theory
    • Le Floch P., and Raviart P.A. An asymptotic expansion for the solution of the generalized riemann problem. Part 1: General theory. Ann. Inst. Henri Poincaré. Analyse non Lineáre 5 2 (1988) 179-207
    • (1988) Ann. Inst. Henri Poincaré. Analyse non Lineáre , vol.5 , Issue.2 , pp. 179-207
    • Le Floch, P.1    Raviart, P.A.2
  • 26
    • 84974774414 scopus 로고
    • A global asymptotic expansion for the solution of the generalized riemann problem
    • Le Floch P., and Tatsien L. A global asymptotic expansion for the solution of the generalized riemann problem. Ann. Inst. Henri Poincaré. Analyse non Lineáre 3 (1991) 321-340
    • (1991) Ann. Inst. Henri Poincaré. Analyse non Lineáre , vol.3 , pp. 321-340
    • Le Floch, P.1    Tatsien, L.2
  • 27
    • 0000709778 scopus 로고
    • Quasilinear hyperbolic systems
    • Liu T.P. Quasilinear hyperbolic systems. Commun. Math. Phys. 68 (1979) 141-172
    • (1979) Commun. Math. Phys. , vol.68 , pp. 141-172
    • Liu, T.P.1
  • 28
    • 15944418424 scopus 로고
    • Increasing the order of approximation of Godunov's scheme using the generalized Riemann problem
    • Men'shov I.S. Increasing the order of approximation of Godunov's scheme using the generalized Riemann problem. USSR Comput. Math. Phys. 30 5 (1990) 54-65
    • (1990) USSR Comput. Math. Phys. , vol.30 , Issue.5 , pp. 54-65
    • Men'shov, I.S.1
  • 29
    • 0002898994 scopus 로고
    • Application of the principle of minimum derivatives to the construction of difference schemes for computing discontinuous solutions of Gas dynamics (in Russian)
    • Kolgan V.P. Application of the principle of minimum derivatives to the construction of difference schemes for computing discontinuous solutions of Gas dynamics (in Russian). Uch. Zap. TsaGI, Russia 3 6 (1972) 68-77
    • (1972) Uch. Zap. TsaGI, Russia , vol.3 , Issue.6 , pp. 68-77
    • Kolgan, V.P.1
  • 30
    • 85190772033 scopus 로고    scopus 로고
    • H. Schardin, in: Proceedings of VII International Congress on High Speed Photg. Darmstadt, O. Helwich Verlag, 1965.
  • 31
    • 85190776722 scopus 로고    scopus 로고
    • T. Schwartzkopff, Finite-Volumen Verfahren hoher Ordnung und heterogene Gebietszerlegung ü die numerische Aeroakustik. PhD thesis, Institut für Aero- un Gasdynamik, Universität Stuttgart, Germany, 2005.
  • 32
    • 0042572998 scopus 로고    scopus 로고
    • ADER: high-order approach for linear hyperbolic systems in 2D
    • Schwartzkopff T., Munz C.D., and Toro E.F. ADER: high-order approach for linear hyperbolic systems in 2D. J. Sci.Comput. 17 (2002) 231-240
    • (2002) J. Sci.Comput. , vol.17 , pp. 231-240
    • Schwartzkopff, T.1    Munz, C.D.2    Toro, E.F.3
  • 33
    • 3242721112 scopus 로고    scopus 로고
    • Fast high-order ADER schemes or linear hyperbolic equations
    • Schwartzkopff T., Dumbser M., and Munz C.D. Fast high-order ADER schemes or linear hyperbolic equations. J. Comput. Phys. 197 (2004) 532-539
    • (2004) J. Comput. Phys. , vol.197 , pp. 532-539
    • Schwartzkopff, T.1    Dumbser, M.2    Munz, C.D.3
  • 34
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes II
    • Shu C.W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes II. J. Comput. Phys. 83 (1988) 32-78
    • (1988) J. Comput. Phys. , vol.83 , pp. 32-78
    • Shu, C.W.1    Osher, S.2
  • 35
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • Shu C.W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439-471
    • (1988) J. Comput. Phys. , vol.77 , pp. 439-471
    • Shu, C.W.1    Osher, S.2
  • 36
    • 0042572999 scopus 로고    scopus 로고
    • Arbitrarily accurate non-oscillatory schemes for a non-linear conservation law
    • Takakura Y., and Toro E.F. Arbitrarily accurate non-oscillatory schemes for a non-linear conservation law. J. Comput. Fluid Dyn. 11 1 (2002) 7-18
    • (2002) J. Comput. Fluid Dyn. , vol.11 , Issue.1 , pp. 7-18
    • Takakura, Y.1    Toro, E.F.2
  • 37
    • 0008392886 scopus 로고    scopus 로고
    • ADER: arbitrary high order Godunov approach
    • Titarev V.A., and Toro E.F. ADER: arbitrary high order Godunov approach. J. Sci. Comput. 17 (2002) 609-618
    • (2002) J. Sci. Comput. , vol.17 , pp. 609-618
    • Titarev, V.A.1    Toro, E.F.2
  • 38
    • 15944366192 scopus 로고    scopus 로고
    • ADER schemes for three-dimensional hyperbolic systems
    • Titarev V.A., and Toro E.F. ADER schemes for three-dimensional hyperbolic systems. J. Comput. Phys. 204 (2005) 715-736
    • (2005) J. Comput. Phys. , vol.204 , pp. 715-736
    • Titarev, V.A.1    Toro, E.F.2
  • 40
    • 0003338927 scopus 로고    scopus 로고
    • Primitive, conservative and adaptive schemes for hyperbolic conservation laws
    • Toro E.F., and Clarke J.F. (Eds), Kluwer Academic Publishers
    • Toro E.F. Primitive, conservative and adaptive schemes for hyperbolic conservation laws. In: Toro E.F., and Clarke J.F. (Eds). Numerical Methods for Wave Propagation (1998), Kluwer Academic Publishers 323-385
    • (1998) Numerical Methods for Wave Propagation , pp. 323-385
    • Toro, E.F.1
  • 42
    • 0042072022 scopus 로고    scopus 로고
    • Towards very high-order Godunov schemes
    • Toro E.F. (Ed), Kluwer Academic/Plenum Publishers (Edited Review)
    • Toro E.F., Millington R.C., and Nejad L.A.M. Towards very high-order Godunov schemes. In: Toro E.F. (Ed). Godunov Methods: Theory and Applications (2001), Kluwer Academic/Plenum Publishers 905-937 (Edited Review)
    • (2001) Godunov Methods: Theory and Applications , pp. 905-937
    • Toro, E.F.1    Millington, R.C.2    Nejad, L.A.M.3
  • 44
    • 57249099681 scopus 로고    scopus 로고
    • Solution of the generalised Riemann problem for advection-reaction equations
    • Toro E.F., and Titarev V.A. Solution of the generalised Riemann problem for advection-reaction equations. Proc. Roy. Soc. London A 458 (2002) 271-281
    • (2002) Proc. Roy. Soc. London A , vol.458 , pp. 271-281
    • Toro, E.F.1    Titarev, V.A.2
  • 45
    • 8744299687 scopus 로고    scopus 로고
    • ADER schemes for scalar hyperbolic conservation laws with source terms in three space dimensions
    • Toro E.F., and Titarev V.A. ADER schemes for scalar hyperbolic conservation laws with source terms in three space dimensions. J. Comput. Phys. 202 1 (2005) 196-215
    • (2005) J. Comput. Phys. , vol.202 , Issue.1 , pp. 196-215
    • Toro, E.F.1    Titarev, V.A.2
  • 46
    • 29144466580 scopus 로고    scopus 로고
    • Derivative Riemann solvers for systems of conservation laws and ADER methods
    • Toro E.F., and Titarev V.A. Derivative Riemann solvers for systems of conservation laws and ADER methods. J. Comput Phys. 212 1 (2006) 150-165
    • (2006) J. Comput Phys. , vol.212 , Issue.1 , pp. 150-165
    • Toro, E.F.1    Titarev, V.A.2
  • 47
    • 0000327531 scopus 로고
    • Towards the ultimate conservative difference Scheme I. The quest for monotonicity
    • van Leer B. Towards the ultimate conservative difference Scheme I. The quest for monotonicity. Lecture Notes in Physics 18 (1973) 163-168
    • (1973) Lecture Notes in Physics , vol.18 , pp. 163-168
    • van Leer, B.1
  • 48
    • 0002187037 scopus 로고
    • On the relationship between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe
    • van Leer B. On the relationship between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. SIAM J. Sci. Stat. Comput. 5 1 (1985) 1-20
    • (1985) SIAM J. Sci. Stat. Comput. , vol.5 , Issue.1 , pp. 1-20
    • van Leer, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.