EFFICIENT AND STABLE TIME INTEGRATION OF THE CAHN-HILLARD EQUATIONS: EXPLICIT, IMPLICIT, AND EXPLICIT-ITERATIVE SCHEMES

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Abstract

The article proposes a new algorithm for numerical integration over time of the Cahn-Hilliard equation, based on the combined application of the Eyre splitting method and the local iteration modified (LIM) scheme for solving a finite-dimensional problem at each time step. The proposed method is gradient-stable and allows calculations with large time steps and has an explicit nature of calculations. The results of numerical calculations are presented, demonstrating the capabilities of the proposed method and its comparison with common methods of time integration of the Cahn– Hilliard equation.

About the authors

M. A Botchev

Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Email: botchev@kiam.ru
Moscow, Russia

I. A Fakhurdinov

Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences; National Research Nuclear University “Moscow Engineering Physics Institute”

Email: mv1451003@gmail.com
Moscow, Russia

E. B Savenkov

Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Email: savenkov@keldysh.ru
Moscow, Russia

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