An operator splitting scheme for numerical simulation of spinodal decomposition and microstructure evolution of binary alloys

Abdullah Shah; Sana Ayub; Muhammad Sohaib; Sadia Saeed; Saher Akmal Khan; Suhail Abbas; Said Karim Shah

doi:10.1016/j.heliyon.2023.e16597

An operator splitting scheme for numerical simulation of spinodal decomposition and microstructure evolution of binary alloys

Heliyon. 2023 May 26;9(6):e16597. doi: 10.1016/j.heliyon.2023.e16597. eCollection 2023 Jun.

Authors

Abdullah Shah¹, Sana Ayub², Muhammad Sohaib^{1

2

3}, Sadia Saeed⁴, Saher Akmal Khan², Suhail Abbas⁵, Said Karim Shah⁶

Affiliations

¹ Department of Mathematics, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia.
² Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad-45550, Pakistan.
³ Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24461, Pakistan.
⁴ Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan.
⁵ Department of Mathematics, Karakoram International University, Ghizer Campus, Ghizer 15200, Pakistan.
⁶ Department of Physics, Abdul Wali Khan University Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.

Abstract

This article compares the operator splitting scheme to linearly stabilized splitting and semi-implicit Euler's schemes for the numerical solution of the Cahn-Hilliard equation. For the purpose of validation, the spinodal decomposition phenomena have been simulated. The efficacy of the three schemes has been demonstrated through numerical experiments. The computed results show that the schemes are conditionally stable. It has been observed that the operator splitting scheme is computationally more efficient.

Keywords: Cahn-Hilliard equation; Linearly stabilized splitting scheme; Operator splitting scheme; Semi-implicit Euler's scheme; The spinodal decomposition.