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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 35, 1999 - Issue 4
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Original Articles

FAST AND ACCURATE NUMERICAL APPROACHES FOR STEFAN PROBLEMS AND CRYSTAL GROWTH

Zhilin Li, Bharat Soni
Pages 461-484 | Published online: 29 Oct 2010

Citations (29)

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Lan Peng, You-Rong Li, Ying-Jie Liu, Nobuyuki Imaishi, Tien-Chien Jen & Qing-Hua Chen. (2007) Bifurcation and Hysteresis of Flow Pattern Transition in a Shallow Molten Silicon Pool with Cz Configuration. Numerical Heat Transfer, Part A: Applications 51:3, pages 211-223.
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Cheng-Feng Tai & Wei Shyy. (2005) Multigrid Computations and Conservation Law Treatment of a Sharp Interface Method. Numerical Heat Transfer, Part B: Fundamentals 48:5, pages 405-424.
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Articles from other publishers (27)

Baiying Dong, Zhilin Li & Juan Ruiz-Álvarez. (2023) A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces. Communications on Applied Mathematics and Computation.
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Gule Rana, Muhammad Asif, Nadeem Haider, Rubi Bilal, Muhammad Ahsan, Qasem Al-Mdallal & Fahd Jarad. (2022) A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models. Journal of Function Spaces 2022, pages 1-15.
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Tomás Chacón Rebollo, Macarena Gómez Mármol & Isabel Sánchez Muñoz. (2022) Numerical Analysis of a Finite Element Approximation to a Level Set Model for Free-Surface Flows. Computational Methods in Applied Mathematics 22:1, pages 155-179.
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Faranak Gholampour, Esmail Hesameddini & Ameneh Taleei. (2020) A global RBF-QR collocation technique for solving two-dimensional elliptic problems involving arbitrary interface. Engineering with Computers 37:4, pages 3793-3811.
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Xufeng Xiao, Xinlong Feng & Zhilin Li. (2021) The local tangential lifting method for moving interface problems on surfaces with applications. Journal of Computational Physics 431, pages 110146.
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Elyes Ahmed, Caroline Japhet & Michel Kern. (2020) Space–time domain decomposition for two-phase flow between different rock types. Computer Methods in Applied Mechanics and Engineering 371, pages 113294.
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Abhishek Kumar Singh, Ajay Kumar & Rajeev. (2019) A Stefan problem with variable thermal coefficients and moving phase change material. Journal of King Saud University - Science 31:4, pages 1064-1069.
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Zhilin Li, Haifeng Ji & Xiaohong Chen. (2017) Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients. SIAM Journal on Numerical Analysis 55:2, pages 570-597.
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Heping Ma, Yonghui Qin & Qiuli Ou. (2017) Multidomain Legendre–Galerkin Chebyshev-collocation method for one-dimensional evolution equations with discontinuity. Applied Numerical Mathematics 111, pages 246-259.
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Haifeng Ji, Feng Wang & Jinru Chen. (2017) Unfitted finite element methods for the heat conduction in composite media with contact resistance. Numerical Methods for Partial Differential Equations 33:1, pages 354-380.
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Lennart Schneiders, Claudia Günther, Matthias Meinke & Wolfgang Schröder. (2016) An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows. Journal of Computational Physics 311, pages 62-86.
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ATUL SHARMA. (2015) Level set method for computational multi-fluid dynamics: A review on developments, applications and analysis. Sadhana 40:3, pages 627-652.
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Jian-kang Liu & Zhou-shun Zheng. (2014) Efficient high-order immersed interface methods for heat equations with interfaces. Applied Mathematics and Mechanics 35:9, pages 1189-1202.
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Jiankang Liu & Zhoushun Zheng. (2014) A dimension by dimension splitting immersed interface method for heat conduction equation with interfaces. Journal of Computational and Applied Mathematics 261, pages 221-231.
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Michael C Dallaston & Scott W McCue. (2013) Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularization. Nonlinearity 26:6, pages 1639-1665.
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Jiankang Liu & Zhoushun Zheng. (2013) IIM-based ADI finite difference scheme for nonlinear convection–diffusion equations with interfaces. Applied Mathematical Modelling 37:3, pages 1196-1207.
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Mayur Sutaria, Vinesh H. Gada, Atul Sharma & B. Ravi. (2012) Computation of feed-paths for casting solidification using level-set-method. Journal of Materials Processing Technology 212:6, pages 1236-1249.
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Xiaohai Wan & Zhilin Li. (2012) Some new finite difference methods for Helmholtz equations on irregular domains or with interfaces. Discrete and Continuous Dynamical Systems - Series B 17:4, pages 1155-1174.
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Manoj Kumar & Pratibha Joshi. (2010) Some numerical techniques for solving elliptic interface problems. Numerical Methods for Partial Differential Equations 28:1, pages 94-114.
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Jing-Rebecca Li, Donna Calhoun & Lucien Brush. (2009) Efficient thermal field computation in phase-field models. Journal of Computational Physics 228:24, pages 8945-8957.
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M.C. Olguín, M.A. Medina, M.C. Sanziel & D.A. Tarzia. (2007) Behavior of the solution of a Stefan problem by changing thermal coefficients of the substance. Applied Mathematics and Computation 190:1, pages 765-780.
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Pierre A. Gremaud, Christopher M. Kuster & Zhilin Li. (2007) A study of numerical methods for the level set approach. Applied Numerical Mathematics 57:5-7, pages 837-846.
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M Khenner. (2004) Enhancement of epitaxial lateral overgrowth by vapor-phase diffusion. International Journal of Engineering Science 42:13-14, pages 1439-1457.
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H.S. Udaykumar, R. Mittal, P. Rampunggoon & A. Khanna. (2001) A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries. Journal of Computational Physics 174:1, pages 345-380.
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Kazufumi Ito, Karl Kunisch & Zhilin Li. (2001) Level-set function approach to an inverse interface problem. Inverse Problems 17:5, pages 1225-1242.
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R.J. Goldstein, E.R.G. Eckert, W.E. Ibele, S.V. Patankar, T.W. Simon, T.H. Kuehn, P.J. Strykowski, K.K. Tamma, A. Bar-Cohen, J.V.R. Heberlein, J.H. Davidson, J. Bischof, F.A. Kulacki, U. Kortshagen & S. Garrick. (2001) Heat transfer – a review of 1999 literature. International Journal of Heat and Mass Transfer 44:19, pages 3579-3699.
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Zhilin Li & Ming-Chih Lai. (2001) The Immersed Interface Method for the Navier–Stokes Equations with Singular Forces. Journal of Computational Physics 171:2, pages 822-842.
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