A conservative numerical method for solving the Cahn–Hilliard equation

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Аннотация

This paper presents a conservative numerical algorithm for solving the Cahn–Hillard equation. A method for linearizing the Cahn–Hillard equation is proposed, and a numerical scheme is constructed based on the control volume method. The implementation of the proposed numerical algorithm is described in detail. The conservativeness of the proposed discrete scheme is verified by numerical simulation. Numerical experiments were carried out.

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Авторлар туралы

D. Galeeva

Ufa University of Science and Technology

Хат алмасуға жауапты Автор.
Email: lara_wood@mail.ru
Ресей, Ufa

V. Kireev

Ufa University of Science and Technology

Email: lara_wood@mail.ru
Ресей, Ufa

L. Kovaleva

Ufa University of Science and Technology

Email: lara_wood@mail.ru
Ресей, Ufa

A. Musin

Ufa University of Science and Technology

Email: lara_wood@mail.ru
Ресей, Ufa

Әдебиет тізімі

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Әрекет
1. JATS XML
2. Fig. 1. Ginzburg–Landau double-well potential

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3. Fig. 2. Control volume on the (x, y) plane

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4. Fig. 3. Comparison of exact and approximate solutions for the one-dimensional case at time T = 10

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5. Fig. 4. Evolution of phase separation for Cahn numbers (a–c) , , at times T = 0.1, 1, 10

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6. Fig. 5. Dependence of total free energy on time for different Cahn numbers: 1–4: Cn = 10–4, 5⋅10–5, 3⋅10–5, 2⋅10–5

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7. Fig. 6. Evolution of phase separation of a) symmetric and b) asymmetric liquids at times T = 1, 3, 10

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8. Fig. 7. Evolution of phase separation for boundary conditions a) Neumann and b) Dirichlet at times T = 1, 3, 10

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