메뉴 건너뛰기




Volumn 10, Issue 3, 2008, Pages 399-421

Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I

Author keywords

[No Author keywords available]

Indexed keywords


EID: 75349104464     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/195     Document Type: Article
Times cited : (24)

References (38)
  • 1
    • 0008894832 scopus 로고
    • Kinetic relations and the propagation of phase boundaries in solids
    • Zbl 0745.73001 MR 1094433
    • ABEYARATNE, R., & KNOWLES, J. K. Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114 (1991), 119-154. Zbl 0745.73001 MR 1094433
    • (1991) Arch. Ration. Mech. Anal , vol.114 , pp. 119-154
    • ABEYARATNE, R.1    KNOWLES, J.K.2
  • 2
    • 0026237436 scopus 로고
    • Implications of viscosity and strain gradient effects for the kinetics of propagating phase boundaries
    • Zbl 0764.73013 MR 1127848
    • ABEYARATNE, R., & KNOWLES, J. K. Implications of viscosity and strain gradient effects for the kinetics of propagating phase boundaries. SIAM J. Appl. Math. 51 (1991), 1205-1221. Zbl 0764.73013 MR 1127848
    • (1991) SIAM J. Appl. Math , vol.51 , pp. 1205-1221
    • ABEYARATNE, R.1    KNOWLES, J.K.2
  • 3
    • 0000864923 scopus 로고    scopus 로고
    • Diffusive-dispersive traveling waves and kinetic relations. III. A hyperbolic model of elastodynamics
    • Zbl 1119.35340 MR 1897563
    • BEDJAOUI, N., & LEFLOCH, P. G. Diffusive-dispersive traveling waves and kinetic relations. III. A hyperbolic model of elastodynamics. Ann. Univ. Ferrara Sci. Mat. 47 (2001), 117-144. Zbl 1119.35340 MR 1897563
    • (2001) Ann. Univ. Ferrara Sci. Mat , vol.47 , pp. 117-144
    • BEDJAOUI, N.1    LEFLOCH, P.G.2
  • 4
    • 0036340678 scopus 로고    scopus 로고
    • Diffusive-dispersive travelling waves and kinetic relations. II. A hyperbolic-elliptic model of phase-transition dynamics
    • Zbl 1082.35104 MR 1912415
    • BEDJAOUI, N., & LEFLOCH, P. G. Diffusive-dispersive travelling waves and kinetic relations. II. A hyperbolic-elliptic model of phase-transition dynamics. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 545-565. Zbl 1082.35104 MR 1912415
    • (2002) Proc. Roy. Soc. Edinburgh Sect. A , vol.132 , pp. 545-565
    • BEDJAOUI, N.1    LEFLOCH, P.G.2
  • 5
    • 10044220725 scopus 로고    scopus 로고
    • Diffusive-dispersive travelling waves and kinetic relations. V. Singular diffusion and nonlinear dispersion
    • Zbl 1065.35182 MR 2099566
    • BEDJAOUI, N., & LEFLOCH, P. G. Diffusive-dispersive travelling waves and kinetic relations. V. Singular diffusion and nonlinear dispersion. Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 815-843. Zbl 1065.35182 MR 2099566
    • (2004) Proc. Roy. Soc. Edinburgh Sect. A , vol.134 , pp. 815-843
    • BEDJAOUI, N.1    LEFLOCH, P.G.2
  • 6
    • 75349107865 scopus 로고    scopus 로고
    • Convergent and conservative schemes for nonclassical solutions based on kinetic relations. II
    • Preprint
    • BOUTIN, B., CHALONS, C., LAGOUTIÈRE, F., & LEFLOCH, P. G. Convergent and conservative schemes for nonclassical solutions based on kinetic relations. II. Preprint (2008).
    • (2008)
    • BOUTIN, B.1    CHALONS, C.2    LAGOUTIÈRE, F.3    LEFLOCH, P.G.4
  • 7
    • 46949086578 scopus 로고    scopus 로고
    • Transport-equilibrium schemes for computing nonclassical shocks. Scalar conservation laws
    • Zbl pre05303288
    • CHALONS, C. Transport-equilibrium schemes for computing nonclassical shocks. Scalar conservation laws. Numer. Methods Partial Differential Equations 24 (2008), 1127-1147. Zbl pre05303288
    • (2008) Numer. Methods Partial Differential Equations , vol.24 , pp. 1127-1147
    • CHALONS, C.1
  • 8
    • 41449106745 scopus 로고    scopus 로고
    • Numerical approximation of a macroscopic model of pedestrian flows
    • Zbl pre05256878 MR 2306257
    • CHALONS, C. Numerical approximation of a macroscopic model of pedestrian flows. SIAM J. Sci. Comput. 29 (2007), 539-555. Zbl pre05256878 MR 2306257
    • (2007) SIAM J. Sci. Comput , vol.29 , pp. 539-555
    • CHALONS, C.1
  • 9
    • 0040433291 scopus 로고    scopus 로고
    • A fully discrete scheme for diffusive-dispersive conservation laws
    • Zbl 1013.65096 MR 1864428
    • CHALONS, C., & LEFLOCH, P. G. A fully discrete scheme for diffusive-dispersive conservation laws. Numer. Math. 89 (2001), 493-509. Zbl 1013.65096 MR 1864428
    • (2001) Numer. Math , vol.89 , pp. 493-509
    • CHALONS, C.1    LEFLOCH, P.G.2
  • 10
    • 0347748099 scopus 로고    scopus 로고
    • High-order entropy conservative schemes and kinetic relations for van der Waals fluids
    • Zbl 1074.76583 MR 1826913
    • CHALONS, C., & LEFLOCH, P. G. High-order entropy conservative schemes and kinetic relations for van der Waals fluids. J. Comput. Phys. 168 (2001), 184-206. Zbl 1074.76583 MR 1826913
    • (2001) J. Comput. Phys , vol.168 , pp. 184-206
    • CHALONS, C.1    LEFLOCH, P.G.2
  • 11
    • 85016350873 scopus 로고    scopus 로고
    • Computing undercompressive waves with the random choice scheme. Nonclassical shock waves
    • Zbl 1038.35134 MR 1979428
    • CHALONS, C., & LEFLOCH, P. G. Computing undercompressive waves with the random choice scheme. Nonclassical shock waves. Interfaces Free Bound. 5 (2003), 129-158. Zbl 1038.35134 MR 1979428
    • (2003) Interfaces Free Bound , vol.5 , pp. 129-158
    • CHALONS, C.1    LEFLOCH, P.G.2
  • 12
    • 1642352182 scopus 로고    scopus 로고
    • Contact discontinuity capturing schemes for linear advection and compressible gas dynamics
    • Zbl 0999.76091 MR 1881855
    • DESPRÉS, B., & LAGOUTIÈRE, F. Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. SIAM J. Sci. Comput. 16 (2001), 479-524. Zbl 0999.76091 MR 1881855
    • (2001) SIAM J. Sci. Comput , vol.16 , pp. 479-524
    • DESPRÉS, B.1    LAGOUTIÈRE, F.2
  • 13
    • 75349104249 scopus 로고    scopus 로고
    • FAN, H.-T., & SLEMROD, M. The Riemann problem for systems of conservation laws of mixed type. Shock Induced Transitions and Phase Structures in General Media (Minneapolis, MN, 1990), J. E. Dunn et al. (eds.), IMA Math. Appl. 52, Springer (1993), 61-91. Zbl 0807.76031 MR 1240333
    • FAN, H.-T., & SLEMROD, M. The Riemann problem for systems of conservation laws of mixed type. Shock Induced Transitions and Phase Structures in General Media (Minneapolis, MN, 1990), J. E. Dunn et al. (eds.), IMA Vol. Math. Appl. 52, Springer (1993), 61-91. Zbl 0807.76031 MR 1240333
  • 14
    • 84981759861 scopus 로고
    • Solutions in the large time for nonlinear hyperbolic systems of equations
    • Zbl 0141.28902 MR 0194770
    • GLIMM, J. Solutions in the large time for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697-715. Zbl 0141.28902 MR 0194770
    • (1965) Comm. Pure Appl. Math , vol.18 , pp. 697-715
    • GLIMM, J.1
  • 15
    • 0031508127 scopus 로고    scopus 로고
    • Nonclassical shocks and kinetic relations: Scalar conservation laws
    • Zbl 0902.76053 MR 1475777
    • HAYES, B. T., & LEFLOCH, P. G. Nonclassical shocks and kinetic relations: Scalar conservation laws. Arch. Ration. Mech. Anal. 139 (1997), 1-56. Zbl 0902.76053 MR 1475777
    • (1997) Arch. Ration. Mech. Anal , vol.139 , pp. 1-56
    • HAYES, B.T.1    LEFLOCH, P.G.2
  • 16
    • 0001203812 scopus 로고    scopus 로고
    • Nonclassical shocks and kinetic relations: Finite difference schemes
    • Zbl 0938.35096 MR 1655842
    • HAYES, B. T., & LEFLOCH, P. G. Nonclassical shocks and kinetic relations: Finite difference schemes. SIAM J. Numer. Anal. 35 (1998), 2169-2194. Zbl 0938.35096 MR 1655842
    • (1998) SIAM J. Numer. Anal , vol.35 , pp. 2169-2194
    • HAYES, B.T.1    LEFLOCH, P.G.2
  • 17
    • 0034345304 scopus 로고    scopus 로고
    • Nonclassical shock waves and kinetic relations: Strictly hyperbolic systems
    • Zbl 0953.35095 MR 1759195
    • HAYES, B. T., & LEFLOCH, P. G. Nonclassical shock waves and kinetic relations: Strictly hyperbolic systems. SIAM J. Math. Anal. 31 (2000), 941-991. Zbl 0953.35095 MR 1759195
    • (2000) SIAM J. Math. Anal , vol.31 , pp. 941-991
    • HAYES, B.T.1    LEFLOCH, P.G.2
  • 18
    • 0000704953 scopus 로고    scopus 로고
    • A level-set approach to the computation of twinning and phase transition dynamics
    • Zbl 0936.74052 MR 1684914
    • HOU, T. Y., LEFLOCH, P. G., & ROSAKIS, P. A level-set approach to the computation of twinning and phase transition dynamics. J. Comput. Phys. 150 (1999), 302-331. Zbl 0936.74052 MR 1684914
    • (1999) J. Comput. Phys , vol.150 , pp. 302-331
    • HOU, T.Y.1    LEFLOCH, P.G.2    ROSAKIS, P.3
  • 19
    • 0030101555 scopus 로고    scopus 로고
    • Converging methods for the computation of propagating solid-solid phase boundaries
    • HOU, T. Y., LEFLOCH, P. G., & ZHONG, X. Converging methods for the computation of propagating solid-solid phase boundaries. J. Comput. Phys. 124 (1996), 192-216.
    • (1996) J. Comput. Phys , vol.124 , pp. 192-216
    • HOU, T.Y.1    LEFLOCH, P.G.2    ZHONG, X.3
  • 21
    • 42649128021 scopus 로고    scopus 로고
    • Stability of reconstruction schemes for scalar hyperbolic conservation laws
    • MR 2397997
    • LAGOUTIÈRE, F., Stability of reconstruction schemes for scalar hyperbolic conservation laws. Comm. Math. Sci. 6 (2008), 57-70. MR 2397997
    • (2008) Comm. Math. Sci , vol.6 , pp. 57-70
    • LAGOUTIÈRE, F.1
  • 22
    • 50849105275 scopus 로고    scopus 로고
    • Non-dissipative entropic discontinuous reconstruction schemes for hyperbolic conservation laws
    • Submitted
    • LAGOUTIÈRE, F. Non-dissipative entropic discontinuous reconstruction schemes for hyperbolic conservation laws. Submitted.
    • LAGOUTIÈRE, F.1
  • 23
    • 21144471185 scopus 로고
    • Propagating phase boundaries: Formulation of the problem and existence via the Glimm scheme
    • MR 1219421
    • LEFLOCH, P. G. Propagating phase boundaries: formulation of the problem and existence via the Glimm scheme. Arch. Ration. Mech. Anal. 123 (1993), 153-197. MR 1219421
    • (1993) Arch. Ration. Mech. Anal , vol.123 , pp. 153-197
    • LEFLOCH, P.G.1
  • 24
    • 75349092070 scopus 로고    scopus 로고
    • LEFLOCH, P. G. Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, E. T. H. Lecture Notes Ser., Birkhäuser (2002). Zbl 1019.35001 MR 1927887
    • LEFLOCH, P. G. Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, E. T. H. Lecture Notes Ser., Birkhäuser (2002). Zbl 1019.35001 MR 1927887
  • 25
    • 40249111458 scopus 로고    scopus 로고
    • Why many shock wave theories are necessary. Fourthorder models, kinetic functions, and equivalent equations
    • Zbl pre05273734 MR 2403880
    • LEFLOCH, P. G., & MOHAMMADIAN, M. Why many shock wave theories are necessary. Fourthorder models, kinetic functions, and equivalent equations. J. Comput. Phys. 227 (2008), 4162-4189. Zbl pre05273734 MR 2403880
    • (2008) J. Comput. Phys , vol.227 , pp. 4162-4189
    • LEFLOCH, P.G.1    MOHAMMADIAN, M.2
  • 26
    • 0000339031 scopus 로고    scopus 로고
    • High-order schemes, entropy inequalities, and nonclassical shocks
    • Zbl 0959.35117 MR 1766858
    • LEFLOCH, P. G., & ROHDE, C. High-order schemes, entropy inequalities, and nonclassical shocks. SIAM J. Numer. Anal. 37 (2000), 2023-2060. Zbl 0959.35117 MR 1766858
    • (2000) SIAM J. Numer. Anal , vol.37 , pp. 2023-2060
    • LEFLOCH, P.G.1    ROHDE, C.2
  • 27
    • 10044240404 scopus 로고    scopus 로고
    • LEFLOCH, P. G., & SHEARER, M. Nonclassical Riemann solvers with nucleation. Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 941-964. Zbl 1090.35121
    • LEFLOCH, P. G., & SHEARER, M. Nonclassical Riemann solvers with nucleation. Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 941-964. Zbl 1090.35121
  • 28
    • 0035537080 scopus 로고    scopus 로고
    • Nonclassical Riemann solvers and kinetic relations I: A nonconvex hyperbolic model of phase transitions
    • Zbl 1020.35056 MR 1856989
    • LEFLOCH, P. G., & THANH, M. D. Nonclassical Riemann solvers and kinetic relations I: A nonconvex hyperbolic model of phase transitions. Z. Angew. Math. Phys. 52 (2001), 597-619. Zbl 1020.35056 MR 1856989
    • (2001) Z. Angew. Math. Phys , vol.52 , pp. 597-619
    • LEFLOCH, P.G.1    THANH, M.D.2
  • 29
    • 0036990230 scopus 로고    scopus 로고
    • Nonclassical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transition dynamics
    • Zbl 1021.35073 MR 1884477
    • LEFLOCH, P. G., & THANH, M. D. Nonclassical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase transition dynamics. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 181-219. Zbl 1021.35073 MR 1884477
    • (2002) Proc. Roy. Soc. Edinburgh Sect. A , vol.132 , pp. 181-219
    • LEFLOCH, P.G.1    THANH, M.D.2
  • 30
    • 1642450911 scopus 로고    scopus 로고
    • Properties of Rankine-Hugoniot curves for van der Waals fluids
    • Zbl 1044.76029 MR 1985510
    • LEFLOCH, P. G., & THANH, M. D. Properties of Rankine-Hugoniot curves for van der Waals fluids. Japan J. Indust. Appl. Math. 20 (2003), 211-238. Zbl 1044.76029 MR 1985510
    • (2003) Japan J. Indust. Appl. Math , vol.20 , pp. 211-238
    • LEFLOCH, P.G.1    THANH, M.D.2
  • 31
    • 33745958763 scopus 로고    scopus 로고
    • Computations of dynamical phase transitions in solids
    • Zbl 1116.74049 MR 2245467
    • MERKLE, C., & ROHDE, C. Computations of dynamical phase transitions in solids. Appl. Numer. Math. 56 (2006), 1450-1463. Zbl 1116.74049 MR 2245467
    • (2006) Appl. Numer. Math , vol.56 , pp. 1450-1463
    • MERKLE, C.1    ROHDE, C.2
  • 32
    • 37449014907 scopus 로고    scopus 로고
    • The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
    • Zbl 1134.35074 MR 2377108
    • MERKLE, C., & ROHDE, C. The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. ESAIM Math. Model. Numer. Anal. 41 (2007), 1089-1123. Zbl 1134.35074 MR 2377108
    • (2007) ESAIM Math. Model. Numer. Anal , vol.41 , pp. 1089-1123
    • MERKLE, C.1    ROHDE, C.2
  • 33
    • 0000993611 scopus 로고    scopus 로고
    • Under compressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
    • Zbl 0930.35106 MR 1664281
    • SCHULZE, S., & SHEARER, M. Under compressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity. J. Math. Anal. Appl. 229 (1999), 344-362. Zbl 0930.35106 MR 1664281
    • (1999) J. Math. Anal. Appl , vol.229 , pp. 344-362
    • SCHULZE, S.1    SHEARER, M.2
  • 34
    • 84972277804 scopus 로고
    • The Riemann problem for the p-system of conservation laws of mixed type with a cubic nonlinearity
    • Zbl 0843.35064 MR 1357378
    • SHEARER, M., & YANG, Y. The Riemann problem for the p-system of conservation laws of mixed type with a cubic nonlinearity. Proc. A Roy. Soc. Edinburgh Sect. A 125 (1995), 675-699. Zbl 0843.35064 MR 1357378
    • (1995) Proc. A Roy. Soc. Edinburgh Sect. A , vol.125 , pp. 675-699
    • SHEARER, M.1    YANG, Y.2
  • 35
    • 0020500507 scopus 로고
    • Admissibility criteria for propagating phase boundaries in a van der Waals fluid
    • Zbl 0505.76082 MR 0683192
    • SLEMROD, M. Admissibility criteria for propagating phase boundaries in a van der Waals fluid. Arch. Ration. Mech. Anal. 81 (1983), 301-315. Zbl 0505.76082 MR 0683192
    • (1983) Arch. Ration. Mech. Anal , vol.81 , pp. 301-315
    • SLEMROD, M.1
  • 36
    • 0000697848 scopus 로고
    • A limiting viscosity approach to the Riemann problem for materials exhibiting change of phase
    • Zbl 0701.35101 MR 0973246
    • SLEMROD, M. A limiting viscosity approach to the Riemann problem for materials exhibiting change of phase. Arch. Ration. Mech. Anal. 105 (1989), 327-365. Zbl 0701.35101 MR 0973246
    • (1989) Arch. Ration. Mech. Anal , vol.105 , pp. 327-365
    • SLEMROD, M.1
  • 37
    • 2442677705 scopus 로고
    • Dynamics of non-equilibrium phase boundaries in a heat conducting nonlinear elastic medium
    • MR 0988048
    • TRUSKINOVSKY, L. Dynamics of non-equilibrium phase boundaries in a heat conducting nonlinear elastic medium. J. Appl. Math. Mech. 51 (1987), 777-784. MR 0988048
    • (1987) J. Appl. Math. Mech , vol.51 , pp. 777-784
    • TRUSKINOVSKY, L.1
  • 38
    • 75349109805 scopus 로고    scopus 로고
    • TRUSKINOVSKY, L. Kinks versus shocks. Shock Induced Transitions and Phase Structures in General Media, R. Fosdick et al. (eds.), IMA Math. Appl. 52, Springer, New York (1993), 185-229.
    • TRUSKINOVSKY, L. Kinks versus shocks. Shock Induced Transitions and Phase Structures in General Media, R. Fosdick et al. (eds.), IMA Vol. Math. Appl. 52, Springer, New York (1993), 185-229.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.