A pseudo-spectral based efficient volume penalization scheme for Cahn–Hilliard equation in complex geometries

Arijit Sinhababu and Anirban Bhattacharya

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 199, issue C, 1-24

Abstract: In this paper, we have developed an efficient volume penalization based diffuse-filtering scheme to solve variable mobility based Cahn–Hilliard equation in complex geometries. The main novelty of the work is that a dealiased pseudo-spectral scheme with immersed interface method (IIM) is proposed for solving any generalized concentration-dependent mobility function-based Cahn–Hilliard (CH) equation in complicated computational domains. An indicator function based mobility parameter is introduced to perform simulation of binary spinodal decomposition problem at a lower computational expense in complex geometries by solving a single phase field equation. Due to the smooth removal of high frequency Fourier components, the solution of the present RK4 based diffuse-filtering scheme does not display spurious currents when suitable low-pass filtering strategy and adequately resolved mobility indicator are incorporated. The traditional and memory optimized zero padding schemes are also implemented to show the comparative performance of different dealiasing schemes for the variable mobility based Cahn–Hilliard equation. It is found that the diffuse-filtering scheme displays reasonable accuracy similar to the zero padding based schemes but its average CPU time is significantly lower, which indicates better computational performance of the scheme for the variable mobility Cahn–Hilliard equation. Time variation of the characteristic length scale during spinodal decomposition of a binary mixture agrees well with the analytical prediction. The optimal three stage SSPRK3 temporal scheme is employed and it is found that time step size can be increased approximately 1.4 times than the classical RK4 scheme reducing total CPU time. Oscillation free numerical solution and conservation of order parameter are obtained for the complex geometry based spinodal decomposition problem. A radially-averaged structure factor is introduced to quantify resolution issues of the dealiasing schemes for the spinodal decomposition problem in different complex geometries.

Keywords: Phase field method; Cahn–Hilliard equation; Immersed interface method; Spinodal decomposition; Generalized mobility parameter; Pseudo-spectral method (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475422001148
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:199:y:2022:i:c:p:1-24

DOI: 10.1016/j.matcom.2022.03.015

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().