메뉴 건너뛰기




Volumn 66, Issue 1, 2010, Pages 237-251

A rarefaction-tracking method for hyperbolic conservation laws

Author keywords

Method of characteristics; Network flow; Particle method; Reaction kinetics; Similarity solution

Indexed keywords

METHOD OF CHARACTERISTICS; NETWORK FLOWS; PARTICLE METHOD; PARTICLE METHODS; SIMILARITY SOLUTION;

EID: 75749088843     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-009-9338-3     Document Type: Article
Times cited : (6)

References (24)
  • 2
    • 0000935266 scopus 로고
    • A difference scheme for the numerical computation of a discontinuous solution of the hydrodynamic equations
    • Godunov SK (1959) A difference scheme for the numerical computation of a discontinuous solution of the hydrodynamic equations. Math Sb 47: 271-306.
    • (1959) Math Sb , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 3
    • 34249988639 scopus 로고
    • Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme
    • van Leer B (1974) Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme. J Comput Phys 14: 361-370.
    • (1974) J Comput Phys , vol.14 , pp. 361-370
    • van Leer, B.1
  • 4
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes. III
    • Harten A, Engquist B, Osher S, Chakravarthy S (1987) Uniformly high order accurate essentially non-oscillatory schemes. III. J Comput Phys 71(2): 231-303.
    • (1987) J Comput Phys , vol.71 , Issue.2 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 5
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • Liu X-D, Osher S, Chan T (1994) Weighted essentially non-oscillatory schemes. J Comput Phys 115: 200-212.
    • (1994) J Comput Phys , vol.115 , pp. 200-212
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 6
    • 84980076280 scopus 로고
    • On the solution of nonlinear hyperbolic differential equations by finite differences
    • Courant R, Isaacson E, Rees M (1952) On the solution of nonlinear hyperbolic differential equations by finite differences. Commun Pure Appl Math 5: 243-255.
    • (1952) Commun Pure Appl Math , vol.5 , pp. 243-255
    • Courant, R.1    Isaacson, E.2    Rees, M.3
  • 7
    • 0023859716 scopus 로고
    • A numerical method for first order nonlinear scalar conservation laws in one dimension
    • Holden H, Holden L, Hegh-Krohn R (1988) A numerical method for first order nonlinear scalar conservation laws in one dimension. Comput Math Appl 15(6-8): 595-602.
    • (1988) Comput Math Appl , vol.15 , Issue.6-8 , pp. 595-602
    • Holden, H.1    Holden, L.2    Hegh-Krohn, R.3
  • 8
    • 22544448703 scopus 로고    scopus 로고
    • Smoothed particle hydrodynamics
    • Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68(8): 1703-1759.
    • (2005) Rep Prog Phys , vol.68 , Issue.8 , pp. 1703-1759
    • Monaghan, J.J.1
  • 9
    • 48749145227 scopus 로고
    • Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
    • Harten A, Hyman JM (1983) Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. J Comput Phys 50: 235-269.
    • (1983) J Comput Phys , vol.50 , pp. 235-269
    • Harten, A.1    Hyman, J.M.2
  • 11
    • 67349126189 scopus 로고    scopus 로고
    • An exactly conservative particle method for one dimensional scalar conservation laws
    • Farjoun Y, Seibold B (2009) An exactly conservative particle method for one dimensional scalar conservation laws. J Comput Phys 228(14): 5298-5315.
    • (2009) J Comput Phys , vol.228 , Issue.14 , pp. 5298-5315
    • Farjoun, Y.1    Seibold, B.2
  • 14
    • 75749121510 scopus 로고    scopus 로고
    • Clawpack
    • Clawpack. http://www. clawpack.org.
  • 15
    • 75749120295 scopus 로고    scopus 로고
    • Particleclaw
    • Particleclaw. http://www. math. temple. edu/~seibold/research/particleclaw/.
  • 17
    • 58149260297 scopus 로고    scopus 로고
    • Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation
    • Karlsen KH, Mishra S, Risebro NH (2009) Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. Math Comput 78: 55-78.
    • (2009) Math Comput , vol.78 , pp. 55-78
    • Karlsen, K.H.1    Mishra, S.2    Risebro, N.H.3
  • 18
    • 2942573195 scopus 로고    scopus 로고
    • Modelling, simulation and optimization of traffic flow networks
    • Herty M, Klar A (2003) Modelling, simulation and optimization of traffic flow networks. SIAM J Sci Comput 25(3): 1066-1087.
    • (2003) SIAM J Sci Comput , vol.25 , Issue.3 , pp. 1066-1087
    • Herty, M.1    Klar, A.2
  • 19
    • 0000090588 scopus 로고
    • On kinematic waves. ii. A theory of traffic flow on long crowded roads
    • Piccadilly, London
    • Lighthill MJ, Whitham GB (1955) On kinematic waves. ii. A theory of traffic flow on long crowded roads. In: Proceedings of the Royal Society, section A, vol 229. Piccadilly, London, pp 317-345.
    • (1955) Proceedings of the Royal Society, Section A , vol.229 , pp. 317-345
    • Lighthill, M.J.1    Whitham, G.B.2
  • 20
    • 0041920783 scopus 로고
    • A mathematical model of traffic flow on a network of unidirectional roads
    • Holden H, Risebro NH (1995) A mathematical model of traffic flow on a network of unidirectional roads. SIAM J Math Anal 26(4): 999-1017.
    • (1995) SIAM J Math Anal , vol.26 , Issue.4 , pp. 999-1017
    • Holden, H.1    Risebro, N.H.2
  • 22
    • 0034879512 scopus 로고    scopus 로고
    • A modified fractional step method for the accurate approximation of detonation waves
    • Helzel C, LeVeque RJ, Warnecke G (2000) A modified fractional step method for the accurate approximation of detonation waves. SIAM J Sci Comput 22(4): 1489-1510.
    • (2000) SIAM J Sci Comput , vol.22 , Issue.4 , pp. 1489-1510
    • Helzel, C.1    Leveque, R.J.2    Warnecke, G.3
  • 23
    • 0034634860 scopus 로고    scopus 로고
    • Zero reaction limit for hyperbolic conservation laws with source terms
    • Fan H, Jin S, Teng Z-H (2000) Zero reaction limit for hyperbolic conservation laws with source terms. J Differ Equ 168(2): 270-294.
    • (2000) J Differ Equ , vol.168 , Issue.2 , pp. 270-294
    • Fan, H.1    Jin, S.2    Teng, Z.-H.3
  • 24
    • 0000311896 scopus 로고    scopus 로고
    • Quasiperiodic solutions in weakly nonlinear gas dynamics. Part I. Numerical results in the inviscid case
    • Shefter M, Rosales RR (1999) Quasiperiodic solutions in weakly nonlinear gas dynamics. Part I. Numerical results in the inviscid case. Stud Appl Math 103: 279-337.
    • (1999) Stud Appl Math , vol.103 , pp. 279-337
    • Shefter, M.1    Rosales, R.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.