Diffuse-interface two-phase flow models with different densities: A new quasi-incompressible form and a linear energy-stable method

A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow

(2016) Harald Garcke et al.   APPLIED NUMERICAL MATHEMATICS

Phase-Field and Korteweg-Type Models for the Time-Dependent Flow of Compressible Two-Phase Fluids

(2016) Heinrich Freistühler et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Duality-based two-level error estimation for time-dependent PDEs: Application to linear and nonlinear parabolic equations

(2015) G. Şimşek et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

(2015) Jan Giesselmann et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn–Hilliard–Navier–Stokes equation

(2015) Daozhi Han et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows

(2015) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models

(2014) G. Tierra et al.   ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

(2014) Z. Guo et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements

(2014) Jessica Bosch et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models

(2013) X. Wu et al.   International Journal for Numerical Methods in Biomedical Engineering

Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

(2013) Ju Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A quasi-incompressible diffuse interface model with phase transition

(2013) Gonca L. Aki et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Phase-Field Models for Multi-Component Fluid Flows

(2012) Junseok Kim   Communications in Computational Physics

Mass and Volume Conservation in Phase Field Models for Binary Fluids

(2012) Jie Shen et al.   Communications in Computational Physics

An unconditionally stable uncoupled scheme for a triphasic Cahn-Hilliard/Navier-Stokes model

(2012) Sebastian Minjeaud   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models

(2011) Hector Gomez et al.   JOURNAL OF COMPUTATIONAL PHYSICS

THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

(2011) HELMUT ABELS et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem

(2011) M. Hintermüller et al.   OPTIMIZATION METHODS & SOFTWARE

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

(2011) Pengtao Yue et al.   PHYSICS OF FLUIDS

Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen–Cahn and Ginzburg–Landau Equations Past Topological Changes

(2011) Sören Bartels et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On compressible Korteweg fluid-like materials

(2010) Martin Heida et al.   INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING

(2010) J. TINSLEY ODEN et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition

(2010) Kristoffer G. van der Zee et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities

(2010) Jie Shen et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Existence of Weak Solutions for a Diffuse Interface Model for Viscous, Incompressible Fluids with General Densities

(2009) Helmut Abels   COMMUNICATIONS IN MATHEMATICAL PHYSICS

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation

(2009) Z. Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation

(2009) S. M. Wise et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Cahn–Hilliard/Navier–Stokes Model for the Simulation of Three-Phase Flows

(2009) F. Boyer et al.   TRANSPORT IN POROUS MEDIA