메뉴 건너뛰기




Volumn 45, Issue 1-3, 2003, Pages 131-163

A study of moving mesh methods applied to a thin flame propagating in a detonator delay element

Author keywords

Detonator delay element problems; Moving mesh methods; Parabolic partial differential equations

Indexed keywords

GRADIENT METHODS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

EID: 0037284787     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)80012-3     Document Type: Article
Times cited : (5)

References (56)
  • 1
    • 0028446372 scopus 로고
    • Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle
    • W. Huang, Y. Ren and R.D. Russell, Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle, SIAM J. Nuraer. Anal. 31, 709-730, (1994).
    • (1994) SIAM J. Nuraer. Anal. , vol.31 , pp. 709-730
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 3
    • 0000664743 scopus 로고
    • Review of some adaptive node-movement techniques in finite dement and finite difference solutions of PDEs
    • D.F. Hawken, J.J. Gottlieb and J.S. Hansen, Review of some adaptive node-movement techniques in finite dement and finite difference solutions of PDEs, J. Comput. Phys. 95, 254-302, (1991).
    • (1991) J. Comput. Phys. , vol.95 , pp. 254-302
    • Hawken, D.F.1    Gottlieb, J.J.2    Hansen, J.S.3
  • 4
    • 0000495580 scopus 로고
    • Effects of solid to gas conversion in detonator delay elements
    • A.H.C. Norgrove, A.F. Jones and J.A. King-Hele, Effects of solid to gas conversion in detonator delay elements, Combust. Sci. Tech. 76, 133-157, (1991).
    • (1991) Combust. Sci. Tech. , vol.76 , pp. 133-157
    • Norgrove, A.H.C.1    Jones, A.F.2    King-Hele, J.A.3
  • 5
    • 0001750088 scopus 로고
    • Effect of axial heat conduction in the metal wall of a detonator delay element
    • A.H.C. Norgrove, A.F. Jones and J.A. King-Hele, Effect of axial heat conduction in the metal wall of a detonator delay element, Combust. Sci. Tech. 97, 449-468, (1994).
    • (1994) Combust. Sci. Tech. , vol.97 , pp. 449-468
    • Norgrove, A.H.C.1    Jones, A.F.2    King-Hele, J.A.3
  • 9
    • 0002791812 scopus 로고
    • Good approximation by splines with variable knots II
    • Springer-Verlag, Berlin
    • C. de Boor, Good approximation by splines with variable knots II, In Springer Lecture Notes Series, Vol. 363, Springer-Verlag, Berlin, (1973).
    • (1973) Springer Lecture Notes Series , vol.363
    • De Boor, C.1
  • 11
    • 0022768316 scopus 로고
    • A moving finite element method with error estimation and refinement for one-dimensional time-dependent partial differential equations
    • J.E. Adjerid and A. Flaherty, A moving finite element method with error estimation and refinement for one-dimensional time-dependent partial differential equations, SIAM J. Numer. Anal. 23, 778-795, (1986).
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 778-795
    • Adjerid, J.E.1    Flaherty, A.2
  • 12
    • 0013398486 scopus 로고
    • Adaptive mesh schemes based on grid speeds
    • D.A. Anderson, Adaptive mesh schemes based on grid speeds, AIAA Paper, pp. 311-318, (1983).
    • (1983) AIAA Paper , pp. 311-318
    • Anderson, D.A.1
  • 14
    • 0013453754 scopus 로고
    • A new approach to truly adaptive grid generation
    • R.G. Hindman and J. Spencer, A new approach to truly adaptive grid generation, AIAA Paper 83-0450, p. 1, (1983).
    • (1983) AIAA Paper , vol.83 , Issue.450 , pp. 1
    • Hindman, R.G.1    Spencer, J.2
  • 15
    • 0000882461 scopus 로고
    • Moving mesh techniques based upon equidistribution, and their stability
    • Y. Ren and R.D. Russell, Moving mesh techniques based upon equidistribution, and their stability, SIAM J. Sci. Statist. Comput. 13, 1265-1286, (1992).
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 1265-1286
    • Ren, Y.1    Russell, R.D.2
  • 16
    • 0000342281 scopus 로고
    • On selection of equidistributing meshes for two-point boundary value problems
    • A.B. White, Jr., On selection of equidistributing meshes for two-point boundary value problems, SIAM J. Numer. Anal. 16, 472-502, (1979).
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 472-502
    • White A.B., Jr.1
  • 17
    • 0004147741 scopus 로고
    • Adaptive finite element methods for parabolic partial differential equations
    • (Edited by I. Babuska, J. Chandra and J.E. Flaherty), SIAM, Philadelphia
    • J.E. Flaherty, J.M. Coyle, R. Ludwig and S.F. Davis, Adaptive finite element methods for parabolic partial differential equations, In Adaptive Computational Methods for Partial Differential Equations, (Edited by I. Babuska, J. Chandra and J.E. Flaherty), pp. 144-164, SIAM, Philadelphia, (1983).
    • (1983) Adaptive Computational Methods for Partial Differential Equations , pp. 144-164
    • Flaherty, J.E.1    Coyle, J.M.2    Ludwig, R.3    Davis, S.F.4
  • 18
    • 0013349339 scopus 로고
    • Application of adaptive grids to transient problems
    • (Edited by I. Babuska, J. Chandra and J.E. Flaherty), SIAM, Philadelphia, PA
    • D.A. Anderson, Application of adaptive grids to transient problems, In Adaptive Computational Methods for Partial Differential Equations, (Edited by I. Babuska, J. Chandra and J.E. Flaherty), pp. 208-223, SIAM, Philadelphia, PA, (1983).
    • (1983) Adaptive Computational Methods for Partial Differential Equations , pp. 208-223
    • Anderson, D.A.1
  • 19
    • 0001121137 scopus 로고
    • Simple adaptive grids for 1-D initial value problems
    • A. Dorfi and L.O'C. Drury, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys. 69, 175-195, (1987).
    • (1987) J. Comput. Phys. , vol.69 , pp. 175-195
    • Dorfi, A.1    Drury, L.O'C.2
  • 20
    • 0000105971 scopus 로고
    • Moving mesh methods based on moving mesh partial differential equations
    • W. Huang, Y. Ren and R.D. Russell, Moving mesh methods based on moving mesh partial differential equations, J. Comput. Phys. 113, 279-290, (1994).
    • (1994) J. Comput. Phys. , vol.113 , pp. 279-290
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 21
    • 0001367417 scopus 로고
    • A numerical study of three moving grid methods for one dimensional partial differential equations which are based on the method of lines
    • R.M. Furzeland, J.G. Verwer and P.A. Zegeling, A numerical study of three moving grid methods for one dimensional partial differential equations which are based on the method of lines, J. Comput. Phys. 89, 349-388, (1990).
    • (1990) J. Comput. Phys. , vol.89 , pp. 349-388
    • Furzeland, R.M.1    Verwer, J.G.2    Zegeling, P.A.3
  • 22
    • 0001319952 scopus 로고
    • An adaptive moving grid method for one-dimensional systems of partial differential equations
    • J.G. Verwer, J.G. Blom and J.M. Sanz-Serna, An adaptive moving grid method for one-dimensional systems of partial differential equations, J. Comput. Physics 82, 454-486, (1989).
    • (1989) J. Comput. Physics , vol.82 , pp. 454-486
    • Verwer, J.G.1    Blom, J.G.2    Sanz-Serna, J.M.3
  • 23
    • 0000448909 scopus 로고    scopus 로고
    • Analysis of moving mesh partial differential equations with spatial smoothing
    • W. Huang and R.D. Russell, Analysis of moving mesh partial differential equations with spatial smoothing, SIAM Y. Numer. Anal. 34, 1106-1126, (1997).
    • (1997) SIAM Y. Numer. Anal. , vol.34 , pp. 1106-1126
    • Huang, W.1    Russell, R.D.2
  • 25
    • 0030081518 scopus 로고    scopus 로고
    • A moving collocation method for time dependent partial differential equations
    • W. Huang and R.D. Russell, A moving collocation method for time dependent partial differential equations, Appl. Numer. Math. 20, 101-115, (1996).
    • (1996) Appl. Numer. Math. , vol.20 , pp. 101-115
    • Huang, W.1    Russell, R.D.2
  • 27
    • 0001043857 scopus 로고
    • Relationship between the truncation errors of centered finite-difference approximations on uniform and nonuniform meshes
    • J.D. Hoffman, Relationship between the truncation errors of centered finite-difference approximations on uniform and nonuniform meshes, J. Comput. Phys. 46, 469-474, (1982).
    • (1982) J. Comput. Phys. , vol.46 , pp. 469-474
    • Hoffman, J.D.1
  • 29
    • 85207662751 scopus 로고    scopus 로고
    • A study of moving mesh methods applied to a thin flame propagating in a detonator delay element
    • T. Basebi and R.M. Thomas, A study of moving mesh methods applied to a thin flame propagating in a detonator delay element, MCCM Technical Report, No. 375, (2001).
    • (2001) MCCM Technical Report , vol.375
    • Basebi, T.1    Thomas, R.M.2
  • 30
    • 0001468509 scopus 로고
    • An adaptive mesh moving and refinement procedure for onedimensional conservation laws
    • D.C. Arney, R. Biswas and J.E. Flaherty, An adaptive mesh moving and refinement procedure for onedimensional conservation laws, Appl. Numer. Math. 11, 259-282, (1993).
    • (1993) Appl. Numer. Math. , vol.11 , pp. 259-282
    • Arney, D.C.1    Biswas, R.2    Flaherty, J.E.3
  • 33
    • 0345554304 scopus 로고
    • Modification of the burning rate of antimony/potassium permanganate pyrotechnic compositions
    • M.W. Beck and M.E. Brown, Modification of the burning rate of antimony/potassium permanganate pyrotechnic compositions, Combustion and Flame 66, 67-75, (1986).
    • (1986) Combustion and Flame , vol.66 , pp. 67-75
    • Beck, M.W.1    Brown, M.E.2
  • 34
    • 0022783871 scopus 로고
    • Burning of antimony/potassium permanganate pyrotechnic compositions in closed systems
    • M.W. Beck and M.E. Brown, Burning of antimony/potassium permanganate pyrotechnic compositions in closed systems, Combustion and Flame 65, 263-271, (1986).
    • (1986) Combustion and Flame , vol.65 , pp. 263-271
    • Beck, M.W.1    Brown, M.E.2
  • 36
    • 0000458449 scopus 로고    scopus 로고
    • Moving mesh methods for problems with blow-up
    • C.J. Budd, W. Huang and R.D. Russell, Moving mesh methods for problems with blow-up, SIAM J. Sci. Comp. 17, 305-327, (1996).
    • (1996) SIAM J. Sci. Comp. , vol.17 , pp. 305-327
    • Budd, C.J.1    Huang, W.2    Russell, R.D.3
  • 38
    • 38249041847 scopus 로고
    • On the stability of mesh equidistribution strategies for time-dependent partial differential equations
    • J.M. Coyle, J.E. Flaherty and R. Ludwig, On the stability of mesh equidistribution strategies for time-dependent partial differential equations, J. Comput. Phys. 62, 26-39, (1986).
    • (1986) J. Comput. Phys. , vol.62 , pp. 26-39
    • Coyle, J.M.1    Flaherty, J.E.2    Ludwig, R.3
  • 40
    • 0019071046 scopus 로고
    • Adaptive grid method for problems in fluid mechanics and heat transfer
    • H.A. Dwyer, R.J. Kee and B.R. Sanders, Adaptive grid method for problems in fluid mechanics and heat transfer, AIAA J. 10, 1205-1212, (1980).
    • (1980) AIAA J. , vol.10 , pp. 1205-1212
    • Dwyer, H.A.1    Kee, R.J.2    Sanders, B.R.3
  • 45
    • 0018517232 scopus 로고
    • PDECOL: General collocation software for partial differential equations
    • N.K. Madsen and R.F. Sincovec, PDECOL: General collocation software for partial differential equations, ACM Trans. Math. Software 5, 326-351, (1979).
    • (1979) ACM Trans. Math. Software , vol.5 , pp. 326-351
    • Madsen, N.K.1    Sincovec, R.F.2
  • 46
    • 0001296580 scopus 로고
    • Moving finite elements II
    • K. Miller, Moving finite elements II, SIAM J. Numer. Anal. 18, 1033-1057, (1981).
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 1033-1057
    • Miller, K.1
  • 51
    • 0023393821 scopus 로고
    • Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations
    • L.R. Petzold, Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations, Appl. Numer. Math. 3, 347-360, (1987).
    • (1987) Appl. Numer. Math. , vol.3 , pp. 347-360
    • Petzold, L.R.1
  • 55
    • 0003983881 scopus 로고
    • A moving grid method for one-dimensional partial differential equations based on the method of lines
    • (Edited by J.E. Flaherty, P.J. Paslow, M.S. Shephard and J.D. Vasilakis), SIAM, Philadelphia, PA
    • J.G. Verwer, J.G. Blom, R.M. Furzeland and P.A. Zegeling, A moving grid method for one-dimensional partial differential equations based on the method of lines, In Adaptive Methods for Partial Differential Equations, (Edited by J.E. Flaherty, P.J. Paslow, M.S. Shephard and J.D. Vasilakis), pp. 160-175, SIAM, Philadelphia, PA, (1988).
    • (1988) Adaptive Methods for Partial Differential Equations , pp. 160-175
    • Verwer, J.G.1    Blom, J.G.2    Furzeland, R.M.3    Zegeling, P.A.4
  • 56
    • 0001537313 scopus 로고
    • On the numerical solution of initial/boundary-value problems in one space dimension
    • A.B. White, Jr., On the numerical solution of initial/boundary-value problems in one space dimension, SIAM J. Numer. Anal. 19, 683-697, (1982).
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 683-697
    • White A.B., Jr.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.