메뉴 건너뛰기




Volumn 3, Issue 1, 2007, Pages 49-64

Adaptive 3D finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage

Author keywords

Finite elements; Mesh adaptation; Navier Stokes; Phase field; Solidification

Indexed keywords

ASPECT RATIO; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); DENSITY OF LIQUIDS; FINITE ELEMENT METHOD; FLOW OF FLUIDS; MESH GENERATION; SOLIDIFICATION;

EID: 34249743629     PISSN: 1555256X     EISSN: 15552578     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (48)
  • 1
    • 0242666435 scopus 로고    scopus 로고
    • Alauzet, F.; George, P. L.; Mohammadi, B.; Frey, P.; Borouchaki, H. (2003): Transient fixed point-based unstructured mesh adaptation. Internat. J. Numer Methods Fluids, 43, no. 6-7, pp. 729-745. ECCOMAS Computational Fluid Dynamics Conference, Part II (Swansea, 2001).
    • Alauzet, F.; George, P. L.; Mohammadi, B.; Frey, P.; Borouchaki, H. (2003): Transient fixed point-based unstructured mesh adaptation. Internat. J. Numer Methods Fluids, vol. 43, no. 6-7, pp. 729-745. ECCOMAS Computational Fluid Dynamics Conference, Part II (Swansea, 2001).
  • 2
    • 0040927870 scopus 로고    scopus 로고
    • A phase-field model of solidification with convection
    • Anderson, D. M.; McFadden, G. B.; Wheeler, A. A. (2000): A phase-field model of solidification with convection. Phys. D, vol. 135, no. 1-2, pp. 175-194.
    • (2000) Phys. D , vol.135 , Issue.1-2 , pp. 175-194
    • Anderson, D.M.1    McFadden, G.B.2    Wheeler, A.A.3
  • 3
    • 0035338878 scopus 로고    scopus 로고
    • A phase-field model with convection: Sharp-interface asymptotics
    • Anderson, D. M.; McFadden, G. B.; Wheeler, A. A. (2001): A phase-field model with convection: sharp-interface asymptotics. Phys. D, vol. 151, no. 2-4, pp. 305-331.
    • (2001) Phys. D , vol.151 , Issue.2-4 , pp. 305-331
    • Anderson, D.M.1    McFadden, G.B.2    Wheeler, A.A.3
  • 4
    • 0002500769 scopus 로고    scopus 로고
    • Modeling melt convection in phase-field simulations of solidification
    • Beckermann, C.; Diepers, H.; Steinbach, I.; Karma, A.; Tong, X. (1999): Modeling melt convection in phase-field simulations of solidification. J. Comput. Phys., vol. 154, no. 2, pp. 468-496.
    • (1999) J. Comput. Phys , vol.154 , Issue.2 , pp. 468-496
    • Beckermann, C.1    Diepers, H.2    Steinbach, I.3    Karma, A.4    Tong, X.5
  • 7
    • 0345447627 scopus 로고    scopus 로고
    • Gradient superconvergence on uniform simplicial partitions of polytopes
    • Brandts, J.; Yřížek, M. (2003): Gradient superconvergence on uniform simplicial partitions of polytopes. IMA J. Numer Anal., vol. 23, no. 3, pp. 489-505.
    • (2003) IMA J. Numer Anal , vol.23 , Issue.3 , pp. 489-505
    • Brandts, J.1    Yřížek, M.2
  • 8
    • 1542531175 scopus 로고    scopus 로고
    • Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model
    • Burman, E.; Jacot, A.; Picasso, M. (2004): Adaptive finite elements with high aspect ratio for the computation of coalescence using a phase-field model. J. Comput. Phys., vol. 195, no. 1, pp. 153-174.
    • (2004) J. Comput. Phys , vol.195 , Issue.1 , pp. 153-174
    • Burman, E.1    Jacot, A.2    Picasso, M.3
  • 9
    • 85006910088 scopus 로고    scopus 로고
    • Anisotropic, adaptive finite elements for the computation of a solutal dendrite
    • Burman, E.; Picasso, M. (2003): Anisotropic, adaptive finite elements for the computation of a solutal dendrite. Interfaces Free Bound., vol. 5, no. 2, pp. 103-127.
    • (2003) Interfaces Free Bound , vol.5 , Issue.2 , pp. 103-127
    • Burman, E.1    Picasso, M.2
  • 10
    • 0042524340 scopus 로고    scopus 로고
    • Existence of solutions to an anisotropic phase-field model
    • Burman, E.; Rappaz, J. (2003): Existence of solutions to an anisotropic phase-field model. Math. Methods Appl. Sci., vol. 26, no. 13, pp. 1137-1160.
    • (2003) Math. Methods Appl. Sci , vol.26 , Issue.13 , pp. 1137-1160
    • Burman, E.1    Rappaz, J.2
  • 11
    • 0001299959 scopus 로고
    • Phase-field and sharp-interface alloy models
    • Caginalp, G.; Xie, W. (1993): Phase-field and sharp-interface alloy models. Phys. Rev. E (3), vol. 48, no. 3, pp. 1897-1909.
    • (1993) Phys. Rev. E (3) , vol.48 , Issue.3 , pp. 1897-1909
    • Caginalp, G.1    Xie, W.2
  • 12
    • 0036036465 scopus 로고    scopus 로고
    • Phase-field models for microstructure evolutions
    • Chen, L. (2002): Phase-field models for microstructure evolutions. Annual Rev. Mater Res., vol. 32, pp. 163-194.
    • (2002) Annual Rev. Mater Res , vol.32 , pp. 163-194
    • Chen, L.1
  • 13
    • 0000405986 scopus 로고
    • Diffuse interface model of diffusion-limited crystal growth
    • Collins, J.; Levine, H. (1985): Diffuse interface model of diffusion-limited crystal growth. Phys. Rev. B, vol. 31, no. 9, pp. 6119-6122.
    • (1985) Phys. Rev. B , vol.31 , Issue.9 , pp. 6119-6122
    • Collins, J.1    Levine, H.2
  • 14
    • 0035509612 scopus 로고    scopus 로고
    • Density change effects on crystal growth from the melt
    • Conti, M. (2001): Density change effects on crystal growth from the melt. Phys. Rev. E, vol. 64, no. 5, pp. 051601.
    • (2001) Phys. Rev. E , vol.64 , Issue.5 , pp. 051601
    • Conti, M.1
  • 16
    • 33645006151 scopus 로고    scopus 로고
    • Anisotropic a posteriori error estimation for the mixed discontinuous Galerkin approximation of the Stokes problem
    • Creusé, E.; Nicaise, S. (2006): Anisotropic a posteriori error estimation for the mixed discontinuous Galerkin approximation of the Stokes problem. Numer. Methods Partial Differential Equations, vol. 22, no. 2, pp. 449-483.
    • (2006) Numer. Methods Partial Differential Equations , vol.22 , Issue.2 , pp. 449-483
    • Creusé, E.1    Nicaise, S.2
  • 17
    • 34249678306 scopus 로고    scopus 로고
    • Distene (2003): MeshAdapt: A mesh adaptation tool, User's manual Version 3.0. Distene S.A.S., Pôle Teratec - BARD-1, Domaine du Grand Rué, 91680 Bruyères-le-Chatel, France, 2003.
    • Distene (2003): MeshAdapt: A mesh adaptation tool, User's manual Version 3.0. Distene S.A.S., Pôle Teratec - BARD-1, Domaine du Grand Rué, 91680 Bruyères-le-Chatel, France, 2003.
  • 18
    • 37649029615 scopus 로고    scopus 로고
    • Quantitative phase-field model of alloy solidification
    • Echebarria, B.; Folch, R.; Karma, A.; Plapp, M. (2004): Quantitative phase-field model of alloy solidification. Phys. Rev. E, vol. 70, no. 6, pp. 061604.
    • (2004) Phys. Rev. E , vol.70 , Issue.6 , pp. 061604
    • Echebarria, B.1    Folch, R.2    Karma, A.3    Plapp, M.4
  • 19
    • 7544240625 scopus 로고    scopus 로고
    • Anisotropic mesh adaption in computational fluid dynamics: Application to the advection-diffusion-reaction and the Stokes problems
    • Formaggia, L.; Micheletti, S.; Perotto, S. (2004): Anisotropic mesh adaption in computational fluid dynamics: application to the advection-diffusion-reaction and the Stokes problems. Appl. Numer. Math., vol. 51, no. 4, pp. 511-533.
    • (2004) Appl. Numer. Math , vol.51 , Issue.4 , pp. 511-533
    • Formaggia, L.1    Micheletti, S.2    Perotto, S.3
  • 20
    • 0035602908 scopus 로고    scopus 로고
    • New anisotropic a priori effor estimates
    • Formaggia, L.; Perotto, S. (2001): New anisotropic a priori effor estimates. Numer Math., vol. 89, no. 4, pp. 641-667.
    • (2001) Numer Math , vol.89 , Issue.4 , pp. 641-667
    • Formaggia, L.1    Perotto, S.2
  • 21
    • 0142118651 scopus 로고    scopus 로고
    • Anisotropic error estimates for elliptic problems
    • Formaggia, L.; Perotto, S. (2003): Anisotropic error estimates for elliptic problems. Numer Math., vol. 94, pp. 67-92.
    • (2003) Numer Math , vol.94 , pp. 67-92
    • Formaggia, L.1    Perotto, S.2
  • 22
    • 19844376237 scopus 로고    scopus 로고
    • A level set based finite element algorithm for the simulation of dendritic growth
    • Fried, M. (2004): A level set based finite element algorithm for the simulation of dendritic growth. Comput. Vis. Sci., vol. 7, no. 2, pp. 97-110.
    • (2004) Comput. Vis. Sci , vol.7 , Issue.2 , pp. 97-110
    • Fried, M.1
  • 23
    • 0042164092 scopus 로고    scopus 로고
    • A level set approach for the numerical simulation of dendritic growth
    • Gibou, F.; Fedkiw, R.; Caffisch, R.; Osher, S. (2003): A level set approach for the numerical simulation of dendritic growth. J. Sci. Comput., vol. 19, no. 1-3, pp. 183-199.
    • (2003) J. Sci. Comput , vol.19 , Issue.1-3 , pp. 183-199
    • Gibou, F.1    Fedkiw, R.2    Caffisch, R.3    Osher, S.4
  • 24
    • 34249724909 scopus 로고    scopus 로고
    • Mathematical modeling and numerical simulation of freezing processes of a supercooled melt under consideration of density changes
    • Griebel, M.; Merz, W.; Neunhoeffer, T. (1999): Mathematical modeling and numerical simulation of freezing processes of a supercooled melt under consideration of density changes. Comp. Vis. Sci., vol. 1, no. 4, pp. 201-219.
    • (1999) Comp. Vis. Sci , vol.1 , Issue.4 , pp. 201-219
    • Griebel, M.1    Merz, W.2    Neunhoeffer, T.3
  • 25
    • 2342658400 scopus 로고    scopus 로고
    • Convection modeling in directional solidification
    • Heinrich, J. C.; Poirier, D. R. (2004): Convection modeling in directional solidification. C. R. Mecanique, vol. 332, pp. 429-445.
    • (2004) C. R. Mecanique , vol.332 , pp. 429-445
    • Heinrich, J.C.1    Poirier, D.R.2
  • 26
    • 34249698926 scopus 로고    scopus 로고
    • Modeling of dendritic growth in alloy solidification with melt convection
    • Hong, C. P.; Zhu, M. F.; Lee, S. Y. (2006): Modeling of dendritic growth in alloy solidification with melt convection. FDMP: Fluid Dynamics & Materials Processing, vol. 2, no. 4, pp. 247-260.
    • (2006) FDMP: Fluid Dynamics & Materials Processing , vol.2 , Issue.4 , pp. 247-260
    • Hong, C.P.1    Zhu, M.F.2    Lee, S.Y.3
  • 27
    • 0037042092 scopus 로고    scopus 로고
    • A pseudo-front tracking technique for the modelling of solidification microstructures in multi-component alloys
    • Jacot, A.; Rappaz, M. (2002): A pseudo-front tracking technique for the modelling of solidification microstructures in multi-component alloys. Acta Mater., vol. 50, no. 8, pp. 1909-1926.
    • (2002) Acta Mater , vol.50 , Issue.8 , pp. 1909-1926
    • Jacot, A.1    Rappaz, M.2
  • 28
    • 0035473973 scopus 로고    scopus 로고
    • Phase field model for three-dimensional dendritic growth with fluid flow
    • Jeong, J.; Goldenfeld, N.; Dantzig, J. (2001): Phase field model for three-dimensional dendritic growth with fluid flow. Phys. Rev. E, vol. 64, no. 4, pp. 041602.
    • (2001) Phys. Rev. E , vol.64 , Issue.4 , pp. 041602
    • Jeong, J.1    Goldenfeld, N.2    Dantzig, J.3
  • 29
    • 0029684784 scopus 로고    scopus 로고
    • A front-tracking method for dendritic solidification
    • Juric, D.; Tryggvason, G. (1996): A front-tracking method for dendritic solidification. J. Comput. Phys., vol. 123, no. 1, pp. 127-148.
    • (1996) J. Comput. Phys , vol.123 , Issue.1 , pp. 127-148
    • Juric, D.1    Tryggvason, G.2
  • 30
    • 5544229221 scopus 로고
    • Phase-field model of eutectic growth
    • Karma, A. (1994): Phase-field model of eutectic growth. Phys. Rev. E, vol. 49, pp. 2245-2250.
    • (1994) Phys. Rev. E , vol.49 , pp. 2245-2250
    • Karma, A.1
  • 31
    • 34249817369 scopus 로고
    • Modeling and numerical simulations of dendritic crystal growth
    • Kobayashi, R. (1993): Modeling and numerical simulations of dendritic crystal growth. Physica D, vol. 63, pp. 410-423.
    • (1993) Physica D , vol.63 , pp. 410-423
    • Kobayashi, R.1
  • 32
    • 0034394001 scopus 로고    scopus 로고
    • An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
    • Kunert, G. (2000): An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer Math., vol. 86, no. 3, pp. 471-490.
    • (2000) Numer Math , vol.86 , Issue.3 , pp. 471-490
    • Kunert, G.1
  • 33
    • 3142737182 scopus 로고    scopus 로고
    • Micheletti, S.; Perotto, S.; Picasso, M. (2003): Stabilized finite elements on anisotropic meshes: a priori error estimates for the advection-diffusion and the Stokes problems. SIAM J. Numer. Anal., 41, no. 3, pp. 1131-1162 (electronic).
    • Micheletti, S.; Perotto, S.; Picasso, M. (2003): Stabilized finite elements on anisotropic meshes: a priori error estimates for the advection-diffusion and the Stokes problems. SIAM J. Numer. Anal., vol. 41, no. 3, pp. 1131-1162 (electronic).
  • 34
    • 34249670626 scopus 로고    scopus 로고
    • Adaptive finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage
    • submitted to
    • Narski, J.; Picasso, M. (2006): Adaptive finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage. submitted to Computer Methods in Applied Mechanics and Engineering.
    • (2006) Computer Methods in Applied Mechanics and Engineering
    • Narski, J.1    Picasso, M.2
  • 35
    • 0347110007 scopus 로고    scopus 로고
    • Phase-field model for solidification of a monotectic alloy with convection
    • Nestler, B.; Wheeler, A. A.; Ratke, L.; Stöcker, C. (2000): Phase-field model for solidification of a monotectic alloy with convection. Phys. D, vol. 141, no. 1-2, pp. 133-154.
    • (2000) Phys. D , vol.141 , Issue.1-2 , pp. 133-154
    • Nestler, B.1    Wheeler, A.A.2    Ratke, L.3    Stöcker, C.4
  • 36
    • 51249172169 scopus 로고
    • A volume-averaged 2-phase model for transport phenomena during solidification
    • Ni, J.; Beckermann, C. (1991): A volume-averaged 2-phase model for transport phenomena during solidification. Metall. Trans. B, vol. 22, no. 3, pp. 349-361.
    • (1991) Metall. Trans. B , vol.22 , Issue.3 , pp. 349-361
    • Ni, J.1    Beckermann, C.2
  • 37
    • 0042931313 scopus 로고    scopus 로고
    • An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: Application to elliptic and parabolic problems
    • electronic
    • Picasso, M. (2003): An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: application to elliptic and parabolic problems. SIAM J Sci. Comput., vol. 24, no. 4, pp. 1328-1355 (electronic).
    • (2003) SIAM J Sci. Comput , vol.24 , Issue.4 , pp. 1328-1355
    • Picasso, M.1
  • 38
    • 0037280081 scopus 로고    scopus 로고
    • Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator
    • Picasso, M. (2003): Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator. Comm. Numer Methods Engrg., vol. 19, no. 1, pp. 13-23.
    • (2003) Comm. Numer Methods Engrg , vol.19 , Issue.1 , pp. 13-23
    • Picasso, M.1
  • 39
    • 20444457092 scopus 로고    scopus 로고
    • An adaptive algorithm for the stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio
    • Picasso, M. (2005): An adaptive algorithm for the stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio. Appl. Numer Math., vol. 54, no. 3-4, pp. 470-490.
    • (2005) Appl. Numer Math , vol.54 , Issue.3-4 , pp. 470-490
    • Picasso, M.1
  • 40
    • 20444457092 scopus 로고    scopus 로고
    • An adaptive algorithm for the Stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio
    • Picasso, M. (2005): An adaptive algorithm for the Stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio. Appl. Numer. Math., vol. 54, no. 3-4, pp. 470-490.
    • (2005) Appl. Numer. Math , vol.54 , Issue.3-4 , pp. 470-490
    • Picasso, M.1
  • 41
    • 33846635611 scopus 로고    scopus 로고
    • Adaptive finite elements with large aspect ratio based on an anisotropic error estimator involving first order derivatives
    • Picasso, M. (2006): Adaptive finite elements with large aspect ratio based on an anisotropic error estimator involving first order derivatives. Comput. Methods Appl. Mech. Engrg., vol. 196, no. 1-3, pp. 14-23.
    • (2006) Comput. Methods Appl. Mech. Engrg , vol.196 , Issue.1-3 , pp. 14-23
    • Picasso, M.1
  • 42
    • 0035499483 scopus 로고    scopus 로고
    • Stability of time-splitting schemes for the Stokes problem with stabilized finite elements
    • Picasso, M.; Rappaz, J. (2001): Stability of time-splitting schemes for the Stokes problem with stabilized finite elements. Numer Methods Partial Differential Equations, vol. 17, no. 6, pp. 632-656.
    • (2001) Numer Methods Partial Differential Equations , vol.17 , Issue.6 , pp. 632-656
    • Picasso, M.1    Rappaz, J.2
  • 43
    • 0000945296 scopus 로고    scopus 로고
    • Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
    • Provatas, N.; Goldenfeld, N.; Dantzig, J. (1999): Adaptive mesh refinement computation of solidification microstructures using dynamic data structures. J. Comput. Phys., vol. 148, no. 1, pp. 265-290.
    • (1999) J. Comput. Phys , vol.148 , Issue.1 , pp. 265-290
    • Provatas, N.1    Goldenfeld, N.2    Dantzig, J.3
  • 44
    • 4444251778 scopus 로고    scopus 로고
    • Anisotropic finite elements for the Stokes problem: A posteriori error estimator and adaptive mesh
    • Randrianarivony, M. (2004): Anisotropic finite elements for the Stokes problem: a posteriori error estimator and adaptive mesh. J. Comput. Appl. Math., vol. 169, no. 2, pp. 255-275.
    • (2004) J. Comput. Appl. Math , vol.169 , Issue.2 , pp. 255-275
    • Randrianarivony, M.1
  • 45
    • 0030137571 scopus 로고    scopus 로고
    • Computation of three dimensional dendrites with finite elements
    • Schmidt, A. (1996): Computation of three dimensional dendrites with finite elements. J. Comput. Phys., vol. 125, no. 2, pp. 293-312.
    • (1996) J. Comput. Phys , vol.125 , Issue.2 , pp. 293-312
    • Schmidt, A.1
  • 46
    • 9544244768 scopus 로고    scopus 로고
    • Diffuse interface modeling of two-phase flows based on averaging: Mass and momentum equations
    • Sun, Y.; Beckermann, C. (2004): Diffuse interface modeling of two-phase flows based on averaging: mass and momentum equations. Phys. D, vol. 198, no. 3-4, pp. 281-308.
    • (2004) Phys. D , vol.198 , Issue.3-4 , pp. 281-308
    • Sun, Y.1    Beckermann, C.2
  • 47
    • 0038505458 scopus 로고    scopus 로고
    • Simulation of natural convection effects on succinonitrile crystals
    • Tönhardt, R.; Amberg, G. (2000): Simulation of natural convection effects on succinonitrile crystals. Phys. Rev. E, vol. 62, pp. 828.
    • (2000) Phys. Rev. E , vol.62 , pp. 828
    • Tönhardt, R.1    Amberg, G.2
  • 48
    • 0029254965 scopus 로고
    • Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field model
    • Warren, J.; Boettinger, W. (1995): Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field model. Acta Metall. Mater., vol. 43, no. 2, pp. 689-703.
    • (1995) Acta Metall. Mater , vol.43 , Issue.2 , pp. 689-703
    • Warren, J.1    Boettinger, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.