Liquid–vapor phase transition: Thermomechanical theory, entropy stable numerical formulation, and boiling simulations
Tài liệu tham khảo
Kuiper, 1981
Hirt, 1981, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201, 10.1016/0021-9991(81)90145-5
Osher, 1988, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12, 10.1016/0021-9991(88)90002-2
Anderson, 1998, Diffuse-interface methods in fluid mechanics, Annu. Rev. Fluid Mech., 30, 139, 10.1146/annurev.fluid.30.1.139
Rowlinson, 1979, Translation of J.D. van der Waals’ The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, J. Stat. Phys., 20, 200, 10.1007/BF01011513
Korteweg, 1901, Arch. Néerl., 6, 1
Truesdell, 1965
Dunn, 1985, On the thermomechanics of interstitial working, Arch. Ration. Mech. Anal., 88, 95, 10.1007/BF00250907
Cahn, 1958, Free energy of a non-uniform system. I. Interfacial free energy, J. Chem. Phys., 28, 258, 10.1063/1.1744102
Oden, 2010, General diffuse-interface theories and an approach to predictive tumor growth modeling, Math. Models Methods Appl. Sci., 20, 477, 10.1142/S0218202510004313
Liu, 2013, Isogeometric analysis of the advective Cahn-Hilliard equation: spinodal decomposition under shear flow, J. Comput. Phys., 242, 321, 10.1016/j.jcp.2013.02.008
Vilanova, 2014, Coupling of discrete random walks and continuous modeling for three-dimensional tumor-induced angiogenesis, Comput. Mech., 53, 449, 10.1007/s00466-013-0958-0
Gomez, 2013, Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium, J. Comput. Phys., 238, 217, 10.1016/j.jcp.2012.12.018
Dedè, 2012, Isogeometric analysis for topology optimization with a phase field model, Arch. Comput. Methods Eng., 19, 1, 10.1007/s11831-012-9075-z
Gurtin, 1996, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92, 178, 10.1016/0167-2789(95)00173-5
Gurtin, 2000, On the plasticity of single crystals: free energy, microforces, plastic-strain gradients, J. Mech. Phys. Solids, 48, 898, 10.1016/S0022-5096(99)00059-9
Wilson, 2013, A phase-field model for fracture in piezoelectric ceramics, Int. J. Fract, 183, 135, 10.1007/s10704-013-9881-9
Maraldi, 2011, Phase field model for coupled displacive and diffusive microstructural processes under thermal loading, J. Mech. Phys. Solids, 59, 1596, 10.1016/j.jmps.2011.04.017
Su, 2007, Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning, J. Mech. Phys. Solids, 55, 280, 10.1016/j.jmps.2006.07.006
Coleman, 1963, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Ration. Mech. Anal., 13, 167, 10.1007/BF01262690
Liu, 2014
Son, 2008, Numerical simulation of nucleate boiling on a horizontal surface at high heat fluxes, Int. J. Heat Mass Transfer, 51, 2566, 10.1016/j.ijheatmasstransfer.2007.07.046
Badillo, 2012, Quantitative phase-field modeling for boiling phenomena, Phys. Rev. E, 86, 10.1103/PhysRevE.86.041603
Dhir, 2013, Numerical simulation of pool boiling: a review, J. Heat Transfer, 135, 1, 10.1115/1.4023576
Juric, 1998, Computations of boiling flows, Int. J. Multiph. Flow, 24, 387, 10.1016/S0301-9322(97)00050-5
Onuki, 2007, Dynamic van der Waals theory, Phys. Rev. E, 75, 10.1103/PhysRevE.75.036304
Lakkaraju, 2013, Heat transport in bubbling turbulent convection, Proc. Natl. Acad. Sci. USA, 110, 9237, 10.1073/pnas.1217546110
Hughes, 1986, A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comput. Methods Appl. Mech. Engrg., 54, 223, 10.1016/0045-7825(86)90127-1
Shakib, 1991, A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., 89, 141, 10.1016/0045-7825(91)90041-4
Hughes, 2010, Stabilized methods for compressible flows, J. Sci. Comput., 43, 343, 10.1007/s10915-008-9233-5
Liu, 2013, Functional entropy variables: a new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier-Stokes-Korteweg equations, J. Comput. Phys., 248, 47, 10.1016/j.jcp.2013.04.005
Gomez, 2011, Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models, J. Comput. Phys., 230, 5310, 10.1016/j.jcp.2011.03.033
Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008
Dedè, 2015, Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation, Comput. Methods Appl. Mech. Engrg., 284, 320, 10.1016/j.cma.2014.09.013
Lipton, 2010, Robustness of isogeometric structural discretizations under severe mesh distortion, Comput. Methods Appl. Mech. Engrg., 199, 357, 10.1016/j.cma.2009.01.022
Evans, 2009, n-widths, sup-infs and optimality ratios for the k-version of the isogeometric finite element method, Comput. Methods Appl. Mech. Engrg., 198, 1726, 10.1016/j.cma.2009.01.021
Bueno, 2014, Interaction of complex fluids and solids: theory, algorithms and application to phase-change-driven implosion, Comput. Mech., 55, 1105, 10.1007/s00466-014-1098-x
Gomez, 2008, Isogeometric analysis of the Cahn-Hilliard phase-field model, Comput. Methods Appl. Mech. Engrg., 197, 4333, 10.1016/j.cma.2008.05.003
Gomez, 2010, Isogeometric anslysis of the isothermal Navier–Stokes-Korteweg equations, Comput. Methods Appl. Mech. Engrg., 199, 1828, 10.1016/j.cma.2010.02.010
Cottrell, 2009
Bazilevs, 2010, Isogeometric analysis using T-splines, Comput. Methods Appl. Mech. Engrg., 199, 229, 10.1016/j.cma.2009.02.036
Hsu, 2015, An interactive geometry modeling and parametric design platform for isogeometric analysis, Comput. Math. Appl., 10.1016/j.camwa.2015.04.002
Scott, 2012, Local refinement of analysis-suitable T-splines, Comput. Methods Appl. Mech. Engrg., 213, 206, 10.1016/j.cma.2011.11.022
Evans, 2013, Isogeometric divergence-conforming B-splines for the Darcy-Stokes-Brinkman equations, Math. Models Methods Appl. Sci., 23, 671, 10.1142/S0218202512500583
Evans, 2013, Isogeometric divergence-conforming B-splines for the steady Navier–Stokes equations, Math. Models Methods Appl. Sci., 23, 1421, 10.1142/S0218202513500139
Evans, 2013, Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations, J. Comput. Phys., 241, 141, 10.1016/j.jcp.2013.01.006
Casquero, 2015, A hybrid variational-collocation immersed method for fluid–structure interaction using unstructured T-splines, Internat. J. Numer. Methods Engrg.
Schillinger, 2013, Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations, Comput. Methods Appl. Mech. Engrg., 267, 170, 10.1016/j.cma.2013.07.017
Gomez, 2014, Accurate, efficient, and (iso) geometrically flexible collocation methods for phase-field models, J. Comput. Phys., 262, 153, 10.1016/j.jcp.2013.12.044
Schillinger, 2015, Isogeometric collocation for phase-field fracture models, Comput. Methods Appl. Mech. Engrg., 284, 583, 10.1016/j.cma.2014.09.032
Gurtin, 2009
Schroeder, 2000
Lowengrub, 1998, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, Proc. R. Soc. A, 454, 2617, 10.1098/rspa.1998.0273
Marsden, 1994
Panton, 2005
Kim, 2005, Phase field modeling and simulation of three-phase flows, Interfaces Free Bound., 7, 435, 10.4171/IFB/132
National Institute of Standards and Technology. Thermophysical Properties of Fluid Systems, 2012. http://webbook.nist.gov/chemistry/fluid/, (accessed 15.07.12).
Beattie, 1927, A new equation of state for fluids. I. Application to gaseous ethyl ether and carbon dioxide, J. Am. Chem. Soc., 49, 1665, 10.1021/ja01406a005
Benedict, 1940, An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures I. Methane, ethane, propane and n-butane, J. Chem. Phys., 8, 334, 10.1063/1.1750658
Serrin, 2008, The area rule for simple fluid phase transitions, J. Elasticity, 90, 129, 10.1007/s10659-007-9136-y
D.C. Johnson, Thermodynamic properties of the van der waals fluid, 2014. arXiv preprint arXiv:1402.1205.
Barth, 2006, On the role of involutions in the discontinuous galerkin discretization of maxwell and magnetohydrodynamic systems, 69
Bova, 1996, An entropy variable formulation and applications for the two-dimensional shallow water equations, Internat. J. Numer. Methods Fluids, 23, 29, 10.1002/(SICI)1097-0363(19960715)23:1<29::AID-FLD411>3.0.CO;2-U
Chalot, 1990, Symmetrization of conservation laws with entropy for high-temperature hypersonic computations, Comput. Syst. Eng, 1, 495, 10.1016/0956-0521(90)90032-G
Hughes, 1987
D.J. Eyre, An unconditionally stable one-step scheme for gradient systems. www.math.utah.edu/~eyre/research/methods/stable.ps.
Tierra, 2015, Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models, Arch. Comput. Methods Eng., 22, 269, 10.1007/s11831-014-9112-1
Wise, 2010, Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations, J. Sci. Comput., 44, 38, 10.1007/s10915-010-9363-4
Scriven, 1960, The Marangoni effects, Nature, 187, 186, 10.1038/187186a0
McGrew, 1966, Marangoni flow: an additional mechanism in boiling heat transfer, Science, 153, 1106, 10.1126/science.153.3740.1106
Mills, 1998, Marangoni effects in welding, Philos. Trans. R. Soc. Lond. Ser. A, 356, 911, 10.1098/rsta.1998.0196
Young, 1959, The motion of bubbles in a vertical temperature gradient, J. Fluid Mech., 6, 350, 10.1017/S0022112059000684
Antanovskii, 1995, A phase field model of capillarity, Phys. Fluids, 7, 747, 10.1063/1.868598
Haj-Hariri, 1997, Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers, Phys. Fluids, 9, 845, 10.1063/1.869182
Jasnow, 1996, Coarse-grained description of thermo-capillary flow, Phys. Fluids, 8, 660, 10.1063/1.868851
Tryggvason, 2001, A front-tracking method for the computations of multiphase flow, J. Comput. Phys., 169, 708, 10.1006/jcph.2001.6726
Onuki, 2005, Dynamic van der Waals theory of two-phase fluids in heat flow, Phys. Rev. Lett., 94, 10.1103/PhysRevLett.94.054501
Onuki, 2005, Droplet motion with phase change in a temperature gradient, Phys. Rev. E, 72, 10.1103/PhysRevE.72.066304
Dhir, 1998, Boiling heat transfer, Annu. Rev. Fluid Mech., 30, 365, 10.1146/annurev.fluid.30.1.365
Rohsenow, 1971, Boiling, Annu. Rev. Fluid Mech., 3, 211, 10.1146/annurev.fl.03.010171.001235
Son, 1997, Numerical simulation of saturated film boiling on a horizontal surface, J. Heat Transfer, 119, 525, 10.1115/1.2824132
Welch, 2000, A volume of fluid based method for fluid flows with phase change, J. Comput. Phys., 160, 662, 10.1006/jcph.2000.6481
Schillinger, 2012, An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces, Comput. Methods Appl. Mech. Engrg., 249–252, 116, 10.1016/j.cma.2012.03.017