An adaptive time‐stepping scheme for the numerical simulation of Cahn‐Hilliard equation with variable mobility. Issue 7 (26th April 2019)

• Record Type: Journal Article
• Authors: Shah, Abdullah; Sabir, Muhammad; Ayub, Sana
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 99:Issue 7(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-26
• Subjects: adaptive time‐stepping -- cahn‐hilliard equation -- diagonally implicit fractional step θ‐scheme -- DUNE‐PDELab -- spinodal decomposition -- 65M60; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201800246
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: In spinodal decomposition phenomena, the initial perturbations evolve at a faster time scale while there is a slower growth at a later time. Therefore, using uniform small time‐steps for tracking the fast dynamics is computationally expensive. On the other hand, uniform large time‐steps may overlook the rapid changes. In this article, we propose an adaptive time‐stepping scheme for faster time scale simulations of spinodal decomposition by solving the Cahn‐Hilliard equation numerically. We consider the double well potential having a polynomial of 6 th ‐order along with 4 th ‐order polynomial for the variable mobility. A diagonally implicit fractional step θ‐scheme(DIFSTS) for temporal discretization while conforming finite element method for spatial discretization is used. Accuracy and efficiency of the method are given and simulations of 2D spinodal decomposition are illustrated graphically. Abstract : In spinodal decomposition phenomena, the initial perturbations evolve at a faster time scale while there is a slower growth at a later time. Therefore, using uniform small time‐steps for tracking the fast dynamics is computationally expensive. On the other hand, uniform large time‐steps may overlook the rapid changes. In this article, we propose an adaptive time‐stepping scheme for faster time scale simulations of spinodal decomposition by solving the Cahn‐Hilliard equation numerically. We consider the double well potential having a polynomial of 6 th ‐order along with 4 th ‐order polynomial for the variable mobility. A diagonally implicit fractional step θ‐scheme(DIFSTS) for temporal discretization while conforming finite element method for spatial discretization is used. Accuracy and efficiency of the method are given and simulations of 2D spinodal decomposition are illustrated graphically.