Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

[1]  G. Sangalli,et al.  Isogeometric analysis in electromagnetics: B-splines approximation , 2010 .

[2]  John A. Evans,et al.  Robustness of isogeometric structural discretizations under severe mesh distortion , 2010 .

[3]  John A. Evans,et al.  Isogeometric analysis using T-splines , 2010 .

[4]  Ruben Juanes,et al.  A phase field model of unsaturated flow , 2009 .

[5]  Thomas J. R. Hughes,et al.  n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method , 2009 .

[6]  Victor M. Calo,et al.  Isogeometric Analysis of Phase-Field Models: Application to the Cahn-Hilliard Equation , 2009 .

[7]  V. Carey Liquid-Vapor Phase-Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment, Third Edition , 2020 .

[8]  Ruben Juanes,et al.  Nonlocal interface dynamics and pattern formation in gravity-driven unsaturated flow through porous media. , 2008, Physical review letters.

[9]  Bruce T. Murray,et al.  Approximation of Cahn–Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elements , 2008 .

[10]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[11]  Alessandro Reali,et al.  Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS , 2008 .

[12]  Thomas J. R. Hughes,et al.  NURBS-based isogeometric analysis for the computation of flows about rotating components , 2008 .

[13]  James Serrin,et al.  The Area Rule for Simple Fluid Phase Transitions , 2008 .

[14]  Philippe G. LeFloch,et al.  Why many theories of shock waves are necessary: Kinetic functions, equivalent equations, and fourth-order models , 2007, J. Comput. Phys..

[15]  H. Frieboes,et al.  Computer simulation of glioma growth and morphology , 2007, NeuroImage.

[16]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[17]  Victor M. Calo,et al.  The role of continuity in residual-based variational multiscale modeling of turbulence , 2007 .

[18]  Roy H. Stogner,et al.  C1 macroelements in adaptive finite element methods , 2007 .

[19]  I. Fonseca,et al.  Surfactants in Foam Stability: A Phase-Field Model , 2007 .

[20]  Alessandro Reali,et al.  Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) , 2007 .

[21]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[22]  B. Widom Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves , 2003 .

[23]  S. Tremaine,et al.  On the Origin of Irregular Structure in Saturn's Rings , 2002, astro-ph/0211149.

[24]  D. J. Torres,et al.  On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method , 2002 .

[25]  Long-Qing Chen Phase-Field Models for Microstructure Evolution , 2002 .

[26]  Chad M. Landis,et al.  Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics , 2002 .

[27]  O. Lebaigue,et al.  The second gradient method for the direct numerical simulation of liquid—vapor flows with phase change , 2001 .

[28]  N. Goldenfeld,et al.  Phase field model for three-dimensional dendritic growth with fluid flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Raphaël Danchin,et al.  Existence of solutions for compressible fluid models of Korteweg type , 2001 .

[30]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[31]  Harald Garcke,et al.  A mathematical model for grain growth in thin metallic films , 2000 .

[32]  Harald Garcke,et al.  A singular limit for a system of degenerate Cahn-Hilliard equations , 2000, Advances in Differential Equations.

[33]  Norman A. Fleck,et al.  A constitutive model for ferroelectric polycrystals , 1999 .

[34]  Il,et al.  Universal dynamics of phase-field models for dendritic growth , 1998, cond-mat/9810189.

[35]  B. Hayes,et al.  Nonclassical Shocks and Kinetic Relations: Finite Difference Schemes , 1998 .

[36]  J. Lowengrub,et al.  Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[37]  Harald Garcke,et al.  On anisotropic order parameter models for multi-phase system and their sharp interface limits , 1998 .

[38]  W. Craig Carter,et al.  Variational methods for microstructural-evolution theories , 1997 .

[39]  D. M. Anderson,et al.  DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS , 1997 .

[40]  Danan Fan,et al.  Diffuse-interface description of grain boundary motion , 1997 .

[41]  G. I. Barenblatt Scaling: Self-similarity and intermediate asymptotics , 1996 .

[42]  Morton E. Gurtin,et al.  Dynamic solid-solid transitions with phase characterized by an order parameter , 1994 .

[43]  Ryo Kobayashi,et al.  A Numerical Approach to Three-Dimensional Dendritic Solidification , 1994, Exp. Math..

[44]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[45]  A. Bray Theory of phase-ordering kinetics , 1993, cond-mat/9501089.

[46]  Paul C. Fife,et al.  Thermodynamically consistent models of phase-field type for the kinetics of phase transitions , 1990 .

[47]  G. Caginalp,et al.  Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. , 1989, Physical review. A, General physics.

[48]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[49]  J. E. Dunn,et al.  On the thermomechanics of interstitial working , 1985 .

[50]  J. Crank Free and moving boundary problems , 1984 .

[51]  C. J. Adkins Thermodynamics and statistical mechanics , 1972, Nature.

[52]  J. Waals The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density , 1979 .

[53]  J. S. Rowlinson,et al.  Translation of J. D. van der Waals' “The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density” , 1979 .

[54]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[55]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[56]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[57]  L. Landau,et al.  On the theory of superconductivity , 1955 .

[58]  K. Cheng Theory of Superconductivity , 1948, Nature.

[59]  J. Gibbs On the equilibrium of heterogeneous substances , 1878, American Journal of Science and Arts.