Efficient and Stable Time Integration of Cahn–Hilliard Equations: Explicit, Implicit, and Explicit Iterative Schemes

To solve the Cahn–Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the implicit system arising each time integration step. The proposed me...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 64; no. 8; pp. 1726 - 1746
Main Authors: Botchev, M. A., Fahurdinov, I. A., Savenkov, E. B.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.08.2024
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Energy
Finite volume method
General Numerical Methods
Interfaces
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear equations
Time integration
local iteration modified scheme
Eyre splitting
Cahn–Hilliard equation
gradient-stable schemes
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:To solve the Cahn–Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the implicit system arising each time integration step. The proposed method is gradient-stable and allows one to use large time steps, whereas, regarding its computational structure, it is an explicit time integration scheme. Numerical tests are presented to demonstrate abilities of the new method and compare it with other time integration methods for Cahn–Hilliard equation.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524700945