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View all- Fullana TLe Chenadec VSayadi T(2023)Adjoint-based optimization of two-dimensional Stefan problemsJournal of Computational Physics10.1016/j.jcp.2022.111875475:COnline publication date: 15-Feb-2023
A sharp numerical method for the simulation of Stefan problems with convective effects
Authors: 
Elyce Bayat, Raphael Egan, Daniil Bochkov, Alban Sauret, Frederic GibouAuthors Info & Claims
References
[1]
Leif Ristroph, Matthew N.J. Moore, Stephen Childress, Michael J. Shelley, Jun Zhang, Sculpting of an erodible body by flowing water, Proc. Natl. Acad. Sci. 109 (48) (2012) 19606–19609.
[2]
Leif Ristroph, Sculpting with flow, J. Fluid Mech. 838 (2018) 1–4.
[3]
Jinzi Mac Huang, M. Nicholas J. Moore, Leif Ristroph, Shape dynamics and scaling laws for a body dissolving in fluid flow, J. Fluid Mech. 765 (2015).
[4]
Jinzi Mac Huang, Michael J. Shelley, David B. Stein, A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the immersed boundary smooth extension method, J. Comput. Phys. 432 (2021).
[5]
Ziqi Wang, Enrico Calzavarini, Chao Sun, Federico Toschi, How the growth of ice depends on the fluid dynamics underneath, Proc. Natl. Acad. Sci. USA 118 (10) (2021).
[6]
Michael Epstein, F.B. Cheung, Complex freezing-melting interfaces in fluid flow, Annu. Rev. Fluid Mech. 15 (1) (1983) 293–319.
[7]
Tetsuo Hirata, Koji Nagasaka, Masaaki Ishikawa, Crystal ice formation of solution and its removal phenomena at cooled horizontal solid surface. Part I: ice removal phenomena, Int. J. Heat Mass Transf. 43 (3) (2000) 333–339.
[8]
Blas Melissari, Stavros A. Argyropoulos, The identification of transition convective regimes in liquid metals using a computational approach, Prog. Comput. Fluid Dyn. 4 (2) (2004) 69–77.
[9]
Amitesh Kumar, Subhransu Roy, Heat transfer characteristics during melting of a metal spherical particle in its own liquid, Int. J. Therm. Sci. 49 (2) (2010) 397–408.
[10]
François Gallaire, P-T. Brun, Fluid dynamic instabilities: theory and application to pattern forming in complex media, Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 375 (2093) (2017).
[11]
M. Nicholas J. Moore, Riemann-Hilbert problems for the shapes formed by bodies dissolving, melting, and eroding in fluid flows, Commun. Pure Appl. Math. 70 (9) (2017) 1810–1831,. https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21689.
[12]
Shang-Huan Chiu, M. Nicholas J. Moore, Bryan Quaife, Viscous transport in eroding porous media, J. Fluid Mech. 893 (2020).
[13]
Ursula Telgmann, Harald Horn, Eberhard Morgenroth, Influence of growth history on sloughing and erosion from biofilms, Water Res. 38 (17) (2004) 3671–3684.
[14]
J. Langer, Instability and pattern formation in crystal growth, Rev. Mod. Phys. 52 (1980) 1–28.
[15]
A. Karma, W.-J. Rappel, Quantitative phase-field modeling of dendritic growth in two and three dimensions, Phys. Rev. E 57 (1997) 4323–4349.
[16]
B. Nestler, D. Danilov, P. Galenko, Crystal growth of pure substances: phase-field simulations in comparison with analytical and experimental results, J. Comput. Phys. 207 (2005) 221–239.
[17]
A. Karma, W.-J. Rappel, Phase-field modeling method for computationally efficient modeling of solidification with arbitrary interface kinetics, Phys. Rev. E 53 (1996).
[18]
K. Elder, M. Grant, N. Provatas, J. Kosterlitz, Sharp interface limits of phase-field models, SIAM J. Appl. Math. 64 (2001).
[19]
W.J. Boettinger, J.A. Warren, C. Beckermann, A. Karma, Phase-field simulations of solidification, Annu. Rev. Mater. Res. 32 (2002) 163–194.
[20]
D. Benson, Computational methods in Lagrangian and Eulerian hydrocodes, Comput. Methods Appl. Mech. Eng. 99 (1992) 235–394.
[21]
D. Benson, Volume of fluid interface reconstruction methods for multimaterial problems, Appl. Mech. Rev. 52 (2002) 151–165.
[22]
R. DeBar, Fundamentals of the KRAKEN code, Technical report, Lawrence Livermore National Laboratory (UCID-17366) 1974.
[23]
W. Noh, P. Woodward, SLIC (simple line interface calculation), in: 5th International Conference on Numerical Methods in Fluid Dynamics, 1976, pp. 330–340.
[24]
D. Youngs, An interface tracking method for a 3D Eulerian hydrodynamics code, Technical report, AWRE (44/92/35) 1984.
[25]
N. Al-Rawahi, Numerical simulation of dendritic solidification with convection: two-dimensional geometry, J. Comput. Phys. 180 (2) (August 2002) 471–496.
[26]
T.G. Myers, Sarah L. Mitchell, Application of the combined integral method to Stefan problems, Appl. Math. Model. 35 (9) (2011) 4281–4294.
[27]
G. Beckett, J.A. Mackenzie, M.L. Robertson, A moving mesh finite element method for the two-dimensional Stefan problems, J. Comput. Phys. 168 (2) (2001) 500–518.
[28]
E. Javierre, C. Vuik, F.J. Vermolen, S. van der Zwaag, A comparison of numerical models for one-dimensional Stefan problems, J. Comput. Appl. Math. 192 (2) (2006) 445–459.
[29]
Alexandre I. Fedoseyev, J. Iwan D. Alexander, An inverse finite element method for pure and binary solidification problems, J. Comput. Phys. 130 (2) (1997) 243–255.
[30]
Michael Le Bars, M. Grae Worster, Solidification of a binary alloy: finite-element, single-domain simulation and new benchmark solutions, J. Comput. Phys. 216 (1) (2006) 247–263.
[31]
S. Chen, B. Merriman, Smereka Osher, P. Smereka, A simple level set method for solving Stefan problems, J. Comput. Phys. 135 (1) (1997) 8–29.
[32]
Yi Yang, H.S. Udaykumar, Sharp interface Cartesian grid method iii: solidification of pure materials and binary solutions, J. Comput. Phys. 210 (1) (2005) 55–74.
[33]
Frédéric Gibou, Ronald Fedkiw, A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem, J. Comput. Phys. (ISSN ) 202 (2) (2005) 577–601,. http://www.sciencedirect.com/science/article/pii/S0021999104002980.
[34]
Frederic Gibou, Ronald Fedkiw, Russel Caflisch, Stanley Osher, A level set approach for the numerical simulation of dendritic growth, J. Sci. Comput. 19 (2003) 183–199.
[35]
Han Chen, Chohong Min, Frederic Gibou, A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate, J. Comput. Phys. 228 (16) (2009) 5803–5818.
[36]
Nicholas Zabaras, Baskar Ganapathysubramanian, Lijian Tan, Modelling dendritic solidification with melt convection using the extended finite element method, J. Comput. Phys. 218 (1) (October 2006) 200–227.
[37]
H.S. Udaykumar, S. Marella, S. Krishnan, Sharp-interface simulation of dendritic growth with convection: benchmarks, Int. J. Heat Mass Transf. 46 (14) (2003) 2615–2627.
[38]
Truong V. Vu, Anh V. Truong, Ngoc T.B. Hoang, Duong K. Tran, Numerical investigations of solidification around a circular cylinder under forced convection, J. Mech. Sci. Technol. 30 (11) (2016) 5019–5028.
[39]
Truong V. Vu, John C. Wells, Numerical simulations of solidification around two tandemly-arranged circular cylinders under forced convection, Int. J. Multiph. Flow 89 (2017) 331–344.
[40]
Truong V. Vu, Fully resolved simulations of drop solidification under forced convection, Int. J. Heat Mass Transf. 122 (2018) 252–263.
[41]
Frederic Gibou, Chohong Min, Ronald Fedkiw, High resolution sharp computational methods for elliptic and parabolic problems in complex geometries, J. Sci. Comput. 54 (2013) 369–413.
[42]
Ásdís Helgadóttir, Frederic Gibou, A Poisson–Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid, J. Comput. Phys. 230 (10) (May 2011) 3830–3848.
[43]
C. Min, F. Gibou, A second order accurate level set method on non-graded adaptive Cartesian grids, J. Comput. Phys. 225 (2007) 300–321.
[44]
Mohammad Mirzadeh, Maxime Theillard, Frederic Gibou, A second-order discretization of the nonlinear Poisson-Boltzmann equation over irregular geometries using non-graded adaptive Cartesian grids, J. Comput. Phys. 230 (5) (December 2010) 2125–2140.
[45]
M. Mirzadeh, F. Gibou, A conservative discretization of the Poisson–Nernst–Planck equations on adaptive Cartesian grids, J. Comput. Phys. 274 (2014) 633–653.
[46]
Frederic Gibou, Ronald P. Fedkiw, Li-Tien Cheng, Myungjoo Kang, A second-order-accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys. (ISSN ) 176 (1) (2002) 205–227,. http://www.sciencedirect.com/science/article/pii/S0021999101969773.
[47]
M. Theillard, F. Gibou, T. Pollock, A sharp computational method for the simulation of the solidification of binary alloys, J. Sci. Comput. (2014).
[48]
H. Chen, C. Min, F. Gibou, A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids, J. Sci. Comput. 31 (2007) 19–60.
[49]
Mohammad Mirzadeh, Maxime Theillard, Asdis Helgadottir, David Boy, Frédéric Gibou, An adaptive, finite difference solver for the nonlinear Poisson–Boltzmann equation with applications to biomolecular computations, Commun. Comput. Phys. 13 (1) (2012) 150–173.
[50]
Joseph Papac, Frederic Gibou, Christian Ratsch, Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions, J. Comput. Phys. 229 (3) (February 2010) 875–889.
[51]
Emmanuel Brun, Arthur Guittet, Frederic Gibou, A local level-set method using a hash table data structure, J. Comput. Phys. 231 (2012) 2528–2536.
[52]
Arthur Guittet, Maxime Theillard, Frédéric Gibou, A stable projection method for the incompressible Navier–Stokes equations on arbitrary geometries and adaptive quad/octrees, J. Comput. Phys. 292 (2015) 215–238.
[53]
Raphael Egan, Arthur Guittet, Fernando Temprano-Coleto, Tobin Isaac, François J. Peaudecerf, Julien R. Landel, Paolo Luzzatto-Fegiz, Carsten Burstedde, Frederic Gibou, Direct numerical simulation of incompressible flows on parallel octree grids, J. Comput. Phys. 428 (2021).
[54]
William M. Deen, Analysis of Transport Phenomena, 1998.
[55]
Jonathan A. Dantzig, Michel Rappaz, Solidification: -Revised & Expanded, EPFL Press, 2016.
[56]
Stanley Osher, James A. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1) (1988) 12–49.
[57]
Frederic Gibou, Ronald Fedkiw, Stanley Osher, A review of level-set methods and some recent applications, J. Comput. Phys. (ISSN ) 353 (Supplement C) (2018) 82–109,. http://www.sciencedirect.com/science/article/pii/S0021999117307441.
[58]
Mohammad Mirzadeh, Arthur Guittet, Carsten Burstedde, Frederic Gibou, Parallel level-set methods on adaptive tree-based grids, J. Comput. Phys. 322 (2016) 345–364.
[59]
Carsten Burstedde, Lucas C. Wilcox, Omar Ghattas, p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees, SIAM J. Sci. Comput. 33 (3) (2011) 1103–1133.
[60]
Mark Sussman, Peter Smereka, Stanley Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146–159.
[61]
Giovanni Russo, Peter Smereka, A remark on computing distance functions, J. Comput. Phys. 163 (1) (2000) 51–67.
[62]
Chohong Min, Frédéric Gibou, Hector D. Ceniceros, A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids, J. Comput. Phys. 218 (1) (2006) 123–140.
[63]
John Strain, A fast modular semi-Lagrangian method for moving interfaces, J. Comput. Phys. 161 (2) (2000) 512–536.
[64]
J. Strain, Tree methods for moving interfaces, J. Comput. Phys. (1999).
[65]
Chohong Min, Frédéric Gibou, A second order accurate level set method on non-graded adaptive Cartesian grids, J. Comput. Phys. 225 (1) (2007) 300–321.
[66]
Chohong Min, Frédéric Gibou, A second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive grids, J. Comput. Phys. 219 (2) (2006) 912–929.
[67]
Dongbin Xiu, George Em Karniadakis, A semi-Lagrangian high-order method for Navier–Stokes equations, J. Comput. Phys. 172 (2) (2001) 658–684.
[68]
George H. Shortley, Royal Weller, The numerical solution of Laplace's equation, J. Appl. Phys. 9 (5) (1938) 334–348.
[69]
Gangjoon Yoon, Chohong Min, Convergence analysis of the standard central finite difference method for Poisson equation, J. Sci. Comput. 67 (2) (2016) 602–617.
[70]
Alexandre Joel Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput. 22 (104) (1968) 745–762.
[71]
David Brown, Ricardo Cortez, Michael Minion, Accurate projection methods for the incompressible Navier–Stokes equations, J. Comput. Phys. 168 (2001) 464,.
[72]
John Kim, Parviz Moin, Application of a fractional-step method to incompressible Navier-Stokes equation, 1984.
[73]
Frank Losasso, Ron Fedkiw, Stanley Osher, Spatially adaptive techniques for level set methods and incompressible flow, Comput. Fluids 35 (2006) 995–1010.
[74]
Frank Losasso, Frederic Gibou, Ron Fedkiw, Simulating water and smoke with an octree data structure, ACM Trans. Graph. (SIGGRAPH Proc.) (2004) 457–462.
[75]
Bochkov, Daniil; Gibou, Frederic (2019): Multidimensional extrapolation over interfaces with kinks and regions of high curvatures. arXiv preprint arXiv:1912.09559.
[76]
Tariq D. Aslam, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys. 193 (1) (2004) 349–355.
[77]
Masashi Okada, Kozo Katayama, Kazuo Terasaki, Minoru Akimoto, Kyoichi Mabune, Freezing around a cooled pipe in crossflow, Bull. JSME 21 (160) (1978) 1514–1520.
[78]
K.C. Cheng, Hideo Inaba, R.R. Gilpin, An experimental investigation of ice formation around an isothermally cooled cylinder in crossflow, 1981.
[79]
H.C. Perkins Jr, G. Leppert, Local heat-transfer coefficients on a uniformly heated cylinder, Int. J. Heat Mass Transf. 7 (2) (1964) 143–158.
[80]
Mouna Laroussi, Mohamed Djebbi, Mahmoud Moussa, Triggering vortex shedding for flow past circular cylinder by acting on initial conditions: a numerical study, Comput. Fluids 101 (2014) 194–207.
[81]
Y.L. Hao, Y-X. Tao, Heat transfer characteristics of melting ice spheres under forced and mixed convection, J. Heat Transf. 124 (5) (2002) 891–903.
[82]
J. Hureau, E. Brunon, Ph Legallais, Ideal free streamline flow over a curved obstacle, J. Comput. Appl. Math. 72 (1) (1996) 193–214.
[83]
Silas Alben, Michael Shelley, Jun Zhang, How flexibility induces streamlining in a two-dimensional flow, Phys. Fluids 16 (5) (2004) 1694–1713.
[84]
Matthew N.J. Moore, Leif Ristroph, Stephen Childress, Jun Zhang, Michael J. Shelley, Self-similar evolution of a body eroding in a fluid flow, Phys. Fluids 25 (11) (2013).
[85]
Pietro de Anna, Bryan Quaife, George Biros, Ruben Juanes, Prediction of the low-velocity distribution from the pore structure in simple porous media, Phys. Rev. Fluids 2 (12) (2017).
[86]
Nicholas Zabaras, Deep Samanta, A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes, Int. J. Numer. Methods Eng. 60 (6) (2004) 1103–1138.
[87]
Balay, Satish; Abhyankar, Shrirang; Adams, Mark F.; Brown, Jed; Brune, Peter; Buschelman, Kris; Dalcin, Lisandro; Dener, Alp; Eijkhout, Victor; Gropp, William D.; Karpeyev, Dmitry; Kaushik, Dinesh; Knepley, Matthew G.; May, Dave A.; McInnes, Lois Curfman; Mills, Richard Tran; Munson, Todd; Rupp, Karl; Sanan, Patrick; Smith, Barry F.; Zampini, Stefano; Zhang, Hong; Zhang, Hong (2019): PETSc Web page. https://www.mcs.anl.gov/petsc.
[88]
Satish Balay, Shrirang Abhyankar, Mark F. Adams, Jed Brown, Peter Brune, Kris Buschelman, Lisandro Dalcin, Alp Dener, Victor Eijkhout, William D. Gropp, Dmitry Karpeyev, Dinesh Kaushik, Matthew G. Knepley, Dave A. May, Lois Curfman McInnes, Richard Tran Mills, Todd Munson, Karl Rupp, Patrick Sanan, Barry F. Smith, Stefano Zampini, Hong Zhang, Hong Zhang, PETSc users manual, Technical Report ANL-95/11 - Revision 3.13 Argonne National Laboratory, 2020, https://www.mcs.anl.gov/petsc.
[89]
Satish Balay, William D. Gropp, Lois Curfman McInnes, Barry F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in: E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.), Modern Software Tools in Scientific Computing, Birkhäuser Press, 1997, pp. 163–202.
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View all- Fullana TLe Chenadec VSayadi T(2023)Adjoint-based optimization of two-dimensional Stefan problemsJournal of Computational Physics10.1016/j.jcp.2022.111875475:COnline publication date: 15-Feb-2023