메뉴 건너뛰기




Volumn 1, Issue 1, 2003, Pages 152-179

ADAPTIVE MESH REDISTRIBUTION METHOD BASED ON GODUNOVS SCHEME

Author keywords

Adaptive mesh redistribution algorithm; Godunov's scheme; Hyperbolic conservation laws; Moving mesh method

Indexed keywords


EID: 0037689751     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2003.v1.n1.a10     Document Type: Article
Times cited : (36)

References (41)
  • 1
    • 0008983727 scopus 로고    scopus 로고
    • Application of adaptive grids in numerical anal-ysis of time-dependent problems in gas dynamics
    • [1]
    • [1] B.N. Azarenok and S.A. Ivanenko, Application of adaptive grids in numerical anal-ysis of time-dependent problems in gas dynamics. Comput. Maths. Math. Phys., 40:1330-1349, 2000.
    • (2000) Comput. Maths. Math. Phys , vol.40 , pp. 1330-1349
    • Azarenok, B.N.1    Ivanenko, S.A.2
  • 2
    • 0034276023 scopus 로고    scopus 로고
    • Realization of a second-order Godunoυ7s scheme
    • [2]
    • [2] B.N. Azarenok, Realization of a second-order Godunoυ7s scheme. Comput. Math, in Appl. Mech. and Engin., 189:1031-1052, 2000.
    • (2000) Comput. Math, in Appl. Mech. and Engin , vol.189 , pp. 1031-1052
    • Azarenok, B.N.1
  • 3
    • 0038355027 scopus 로고    scopus 로고
    • Variational barrier method of adaptive grid generation in hyperbolic problems of gas dynamics
    • [3]
    • [3] B.N. Azarenok, Variational barrier method of adaptive grid generation in hyperbolic problems of gas dynamics. SIAM J. Numer. Anal., 40:651-682, 2002.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 651-682
    • Azarenok, B.N.1
  • 4
    • 48349083249 scopus 로고
    • A second order Godunov-type scheme for compressible fluid dynamics
    • [4]
    • [4] M. Ben-Artzi and J. Falcovitcz, A second order Godunov-type scheme for compressible fluid dynamics. J. Comput. Phys. 55:1-32, 1984.
    • (1984) J. Comput. Phys , vol.55 , pp. 1-32
    • Ben-Artzi, M.1    Falcovitcz, J.2
  • 5
    • 0000359177 scopus 로고    scopus 로고
    • An r-adaptive finite element method based upon moving mesh PDEs
    • [5]
    • [5] W.M. Cao, W.Z. Huang, and R.D. Russell, An r-adaptive finite element method based upon moving mesh PDEs. J. Comput. Phys. 149:221-244, 1999.
    • (1999) J. Comput. Phys , vol.149 , pp. 221-244
    • Cao, W.M.1    Huang, W.Z.2    Russell, R.D.3
  • 6
    • 0035922234 scopus 로고    scopus 로고
    • An efficient dynamically adaptive mesh for potentially singular solutions
    • [6]
    • [6] H.D. Ceniceros and T.Y. Hou, An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys., 172:609-639, 2001.
    • (2001) J. Comput. Phys , vol.172 , pp. 609-639
    • Ceniceros, H.D.1    Hou, T.Y.2
  • 8
    • 0031572059 scopus 로고    scopus 로고
    • A variational form of the Winslow grid gen-erator
    • [8]
    • [8] A.A. Charakhch,yan and S.A. Ivanenko, A variational form of the Winslow grid gen-erator. J. Comput. Phys. 136:385-398, 1997.
    • (1997) J. Comput. Phys , vol.136 , pp. 385-398
    • Charakhch, A.A.1    yan2    Ivanenko, S.A.3
  • 9
    • 34547419627 scopus 로고
    • The piecewise parabolic method (PMM) for gas-dynamical simulations
    • [9]
    • [9] P. Colella and P.R. Woodward, The piecewise parabolic method (PMM) for gas-dynamical simulations. J. Comput. Phys., 54:174-201, 1984.
    • (1984) J. Comput. Phys , vol.54 , pp. 174-201
    • Colella, P.1    Woodward, P.R.2
  • 11
    • 38249027477 scopus 로고
    • Efficient volume computation for three-dimensional hexahedral cells
    • [11]
    • [11] J.K. Dukowicz, Efficient volume computation for three-dimensional hexahedral cells.J. Comput. Phys., 74:493-496, 1988.
    • (1988) J. Comput. Phys , vol.74 , pp. 493-496
    • Dukowicz, J.K.1
  • 12
    • 0000379994 scopus 로고
    • Adaptive grid generation from harmonic maps on Riemannian mani-folds
    • [12]
    • [12] A.S. Dvinsky, Adaptive grid generation from harmonic maps on Riemannian mani-folds. J. Comput. Phys. 95:450-476, 1991.
    • (1991) J. Comput. Phys , vol.95 , pp. 450-476
    • Dvinsky, A.S.1
  • 13
    • 0000935266 scopus 로고
    • A finite difference method for the Computation ofDiscontinuous Solu-tions of the Equations of Fluid Dynamics
    • [13]
    • [13] S.K. Godunov, A finite difference method for the Computation ofDiscontinuous Solu-tions of the Equations of Fluid Dynamics. Mat. Sb., 47:357-393, 1959.
    • (1959) Mat. Sb , vol.47 , pp. 357-393
    • Godunov, S.K.1
  • 15
    • 48749145227 scopus 로고
    • Self-adjusting grid methods for one-dimensional hyper-bolic conservation laws
    • [15]
    • [15] A. Harten and J.M. Hyman, Self-adjusting grid methods for one-dimensional hyper-bolic conservation laws. J. Comput. Phys. 50:235-269, 1983.
    • (1983) J. Comput. Phys , vol.50 , pp. 235-269
    • Harten, A.1    Hyman, J.M.2
  • 16
    • 85128860345 scopus 로고    scopus 로고
    • Extension of a dynamic solution-adaptive grid algorithm and solver to general structured milti-block configurations
    • [16] AIAA 96-0294, Reno, NV, Jan
    • [16] C.L. Ingram and D.S. McRay, Extension of a dynamic solution-adaptive grid algorithm and solver to general structured milti-block configurations. AIAA 96-0294, AIAA 34th Aerospace Science Meeting, Reno, NV, Jan. 1996.
    • (1996) AIAA 34th Aerospace Science Meeting
    • Ingram, C.L.1    McRay, D.S.2
  • 17
    • 0000440740 scopus 로고
    • Adaptive grids and grids on surfaces
    • [17]
    • [17] S.A. Ivanenko, Adaptive grids and grids on surfaces. Comp. Maths. Math. Phys,33:1179-1193, 1993.
    • (1993) Comp. Maths. Math. Phys , vol.33 , pp. 1179-1193
    • Ivanenko, S.A.1
  • 19
    • 0037052854 scopus 로고    scopus 로고
    • Application of moving adaptive grids for numerical solution of nonstationary problems in gas dynamics
    • [19] also)
    • [19] S.A. Ivanenko and B.N. Azarenok, Application of moving adaptive grids for numerical solution of nonstationary problems in gas dynamics. Int. J. for Numer. Meth, in Fluids, 39:1-22, 2002. (See also http://www.math.ntnu.no/conservation/2001/043.html).
    • (2002) Int. J. for Numer. Meth, in Fluids , vol.39 , pp. 1-22
    • Ivanenko, S.A.1    Azarenok, B.N.2
  • 20
    • 0037050821 scopus 로고    scopus 로고
    • Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods
    • [20]
    • [20] P. Knupp, L. Margolin, and M. Shashkov, Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods. J. Comput. Phys., 176:93-128, 2002.
    • (2002) J. Comput. Phys , vol.176 , pp. 93-128
    • Knupp, P.1    Margolin, L.2    Shashkov, M.3
  • 21
    • 0002898994 scopus 로고
    • Application of the principle of minimal derivatives towards construct-ing finite difference schemes to compute discontinuous solutions in gas dynamics
    • [21] Moscow
    • [21] V.P. Kolgan, Application of the principle of minimal derivatives towards construct-ing finite difference schemes to compute discontinuous solutions in gas dynamics. Scientific Notes of Central Aerohydrodynamical Institute (in Russian), Moscow, 3:68-77, 1972.
    • (1972) Scientific Notes of Central Aerohydrodynamical Institute (in Russian) , vol.3 , pp. 68-77
    • Kolgan, V.P.1
  • 23
    • 0012062674 scopus 로고    scopus 로고
    • A wave propagation method for 3D hyperbolic con-servation laws
    • [23]
    • [23] J.O. Langseth and R.J. LeVeque, A wave propagation method for 3D hyperbolic con-servation laws. J. Comput. Phys. 165:126-166, 2000.
    • (2000) J. Comput. Phys , vol.165 , pp. 126-166
    • Langseth, J.O.1    LeVeque, R.J.2
  • 24
    • 0032226419 scopus 로고    scopus 로고
    • An adaptive grid method and its application to steady Euler flow calculations
    • [24]
    • [24] F. Liu, S. Ji, and G. Liao, An adaptive grid method and its application to steady Euler flow calculations. SIAM J. Sci. Comput. 20:811-825, 1998.
    • (1998) SIAM J. Sci. Comput , vol.20 , pp. 811-825
    • Liu, F.1    Ji, S.2    Liao, G.3
  • 25
    • 44949285630 scopus 로고
    • On generation of regular grids on n-dimensional surfaces
    • [25]
    • [25] V.D. Liseikin, On generation of regular grids on n-dimensional surfaces. USSR Com-put. Math. Math. Phys. 31:47-57, 1991.
    • (1991) USSR Com-put. Math. Math. Phys , vol.31 , pp. 47-57
    • Liseikin, V.D.1
  • 27
    • 0000501759 scopus 로고    scopus 로고
    • Moving mesh methods in multiple dimensions based on harmonic maps
    • [27]
    • [27] R. Li, T. Tang, and P. Zhang, Moving mesh methods in multiple dimensions based on harmonic maps. J. Comput. Phys. 170:562-588, 2001.
    • (2001) J. Comput. Phys , vol.170 , pp. 562-588
    • Li, R.1    Tang, T.2    Zhang, P.3
  • 28
    • 0037052068 scopus 로고    scopus 로고
    • A moving mesh finite element algorithm for singularproblems in two and three space dimensions
    • [28]
    • [28] R. Li, T. Tang, and P. Zhang, A moving mesh finite element algorithm for singularproblems in two and three space dimensions. J. Comput. Phys., 177:365-393, 2002.
    • (2002) J. Comput. Phys , vol.177 , pp. 365-393
    • Li, R.1    Tang, T.2    Zhang, P.3
  • 29
    • 0034774698 scopus 로고    scopus 로고
    • A moving mesh method for one di-mensional hyperbolic conservation law
    • [29]
    • [29] J.A. Mackenzie, R.D. Russell, and J.M. Stockie, A moving mesh method for one di-mensional hyperbolic conservation law. SIAM J. Sci. Comput. 22:1791-1813, 2000.
    • (2000) SIAM J. Sci. Comput , vol.22 , pp. 1791-1813
    • Mackenzie, J.A.1    Russell, R.D.2    Stockie, J.M.3
  • 31
    • 0001343401 scopus 로고
    • Increase of accuracy of the Godunoυ7s scheme
    • [31]
    • [31] A.V. Rodionov, Increase of accuracy of the Godunoυ7s scheme. USSR ComputationalMath, and Math. Phys., 27:1853-1860, 1987.
    • (1987) USSR ComputationalMath, and Math. Phys , vol.27 , pp. 1853-1860
    • Rodionov, A.V.1
  • 32
    • 0003872030 scopus 로고
    • Systems of Quasilinear Equations and Their Applications to Gas Dynamics
    • [32] AMS, Providence, RI
    • [32] B.L. Rozhdestvenskii and N.N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics. Amer. Math. Soc. Transl. of Math. Monographs, 55, AMS, Providence, RI, 1983.
    • (1983) Amer. Math. Soc. Transl. of Math. Monographs , vol.55
    • Rozhdestvenskii, B.L.1    Yanenko, N.N.2
  • 33
    • 0000376868 scopus 로고
    • Some properties and applications of harmonic mappings
    • [33]
    • [33] J.S. Sampson, Some properties and applications of harmonic mappings. Ann. École Norm. Sup. 11:211-228, 1978.
    • (1978) Ann. École Norm. Sup , vol.11 , pp. 211-228
    • Sampson, J.S.1
  • 34
    • 0001201969 scopus 로고
    • On univalent harmonic maps between surfaces
    • [34]
    • [34] R. Schoen and S.T. Yau, On univalent harmonic maps between surfaces, Invent. Math.44:265-278, 1978.
    • (1978) Invent. Math , vol.44 , pp. 265-278
    • Schoen, R.1    Yau, S.T.2
  • 35
    • 2942705023 scopus 로고
    • A survey offinite difference methods for the systems of nonlinear hyperbolic conservation laws
    • [35]
    • [35] G.A. Sod, A survey offinite difference methods for the systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27:1-31, 1978.
    • (1978) J. Comput. Phys , vol.27 , pp. 1-31
    • Sod, G.A.1
  • 37
    • 0021781423 scopus 로고
    • A survey of dynamically-adaptive grids in the numerical solution of partial differential equations
    • [37]
    • [37] J.F. Thompson, A survey of dynamically-adaptive grids in the numerical solution of partial differential equations. Appl. Numer. Maths, 1:3-27, 1985.
    • (1985) Appl. Numer. Maths , vol.1 , pp. 3-27
    • Thompson, J.F.1
  • 38
    • 0036345178 scopus 로고    scopus 로고
    • Conditions of nondegeneracy of three-dimensional cells. A formula of a volume of cells
    • [38]
    • [38] O.V. Ushakova, Conditions of nondegeneracy of three-dimensional cells. A formula of a volume of cells. SIAM J. Sci. Comput., 23:1273-1289, 2001.
    • (2001) SIAM J. Sci. Comput , vol.23 , pp. 1273-1289
    • Ushakova, O.V.1
  • 39
    • 0013670786 scopus 로고
    • Methods for Localization of Singularities in Nu-merical Solution of Gasdynamics Problems
    • [39]
    • [39] E.V. Vorozhtsov and N.N. Yanenko, Methods for Localization of Singularities in Nu-merical Solution of Gasdynamics Problems. Springer Series in Computational Physics, 1990.
    • (1990) Springer Series in Computational Physics
    • Vorozhtsov, E.V.1    Yanenko, N.N.2
  • 40
    • 0001424722 scopus 로고    scopus 로고
    • An iterative grid redistribution method for singular problems in multiple dimensions
    • [40]
    • [40] W. Ren and X.P. Wang, An iterative grid redistribution method for singular problems in multiple dimensions. J. Comput. Phys., 159:246-273, 2002.
    • (2002) J. Comput. Phys , vol.159 , pp. 246-273
    • Ren, W.1    Wang, X.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.