Conservative multigrid methods for Cahn-Hilliard fluids

By Junseok Kim, Kyungkeun Kang, John S. Lowengrub. 2004

339 citations recorded by the source corpus.

Subfields: Computational Mechanics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5077701dc976827ba168702f3f434bb063e241de

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In Computational Mechanics

In Materials Chemistry

Citations in the corpus

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation (2009, background): “[8] for uniform grids and extended by Wise et al.”
Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method. (2008, background): “See for example, Anderson and McFadden (1998), Lowengrub and Truskinovsky (1998), Kim et al. (2003), Badalessi et al. (2003), Yue et al. (2005) among many others for applications to multiphase flows.”
A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system (2012, background): “There are many numerical studies with the binary CH equation [4,9,13,28–40], ternary [20,28,41–52], and quaternary [53–57] CH systems.”
Trajectory attractors for binary fluid mixtures in 3D (2010, background): “Systems like (1.1)–(1.4) in the case K = CH have been investigated in a number of papers (see, for instance, [12, 13, 36, 39, 41 , 46] ). However, confining ourselves to the most theoretical aspects (i.e., well-posedness, regularity, asymptotic behavior), to the best of our knowledge the first resu”
Finite element approximation of a Cahn−Hilliard−Navier−Stokes system (2008, background): “The numerical simulation of these models is an area of research currently undergoing intense study (see for example [2, 9, 23, 26, 27]), with the majority of the work so far concentrating on finite difference discretisations.”
Isogeometric analysis of the Cahn–Hilliard phase-field model (2008, methodology): “(Another approach that has been used in the literature to speed up the solution is the use of multigrid methods [51,52], which is not pursued in this work.”
A continuous surface tension force formulation for diffuse-interface models (2005, methodology): “, merging or pinching off (see [4,17], and the references therein).”
A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant (2004, neutral): “[28–33]), volume-of-fluid (VOF) (e.”
Phase field modeling and simulation of three-phase flows (2005, methodology): “We find that the scheme presented here results in slightly be tter accuracy than that used in [30].”
The phase field method for geometric moving interfaces and their numerical approximations (2019, neutral): “On the algorithm development and numerical analysis side, more recent focus has been on effective linear and nonlinear solvers, including the development of various adaptive and multigrid techniques, see [286, 366, 424] and discussion in later sections.”