An application of the Cahn-Hilliard approach to smoothed particle hydrodynamics
type: Item
instance of: scholarly article
title: An application of the Cahn-Hilliard approach to smoothed particle hydrodynamics
zbMATH Open document ID: 1407.76120
DOI: 10.1155/2014/694894
author: W. Säckel
author: Manuel Hirschler
author: Manuel Accettulli Huber
author: Philip Kunz
author: Ulrich Nieken
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The development of a methodology for the simulation of structure forming processes is highly desirable. The smoothed particle hydrodynamics (SPH) approach provides a respective framework for modeling the self-structuring of complex geometries. In this paper, we describe a diffusion-controlled phase separation process based on the Cahn-Hilliard approach using the SPH method. As a novelty for SPH method, we derive an approximation for a fourth-order derivative and validate it. Since boundary conditions strongly affect the solution of the phase separation model, we apply boundary conditions at free surfaces and solid walls. The results are in good agreement with the universal power law of coarsening and physical theory. It is possible to combine the presented model with existing SPH models.
Mathematics Subject Classification ID: 76M28
Mathematics Subject Classification ID: 65M75
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 7017041
Wikidata QID: Q59069052
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/694894
OpenAlex ID: W2039925889
cites work: Free Energy of a Nonuniform System. I. Interfacial Free Energy
cites work: Quasi–incompressible Cahn–Hilliard fluids and topological transitions
cites work: Calculation of two-phase Navier-Stokes flows using phase-field modeling
cites work: Q4492806
cites work: Dynamic transitions for quasilinear systems and Cahn-Hilliard equation with Onsager mobility
cites work: Smoothed particle hydrodynamics: theory and application to non-spherical stars
cites work: Smoothed particle hydrodynamics and its diverse applications
cites work: Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives
cites work: Wall energy relaxation in the Cahn–Hilliard model for moving contact lines
cites work: A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh--Taylor instability
description: scientific article; zbMATH DE number 7017041