Efficient numerical simulation of Cahn-Hilliard type models by a dimension splitting method. (15th April 2023)

• Record Type: Journal Article
• Authors: Xiao, Xufeng; Feng, Xinlong; Shi, Zuoqiang
• Is Part Of: Computers & mathematics with applications. Volume 136(2023)
• Page Start: 54
• Page End: 70
• Publication Date: 2023-04-15
• Subjects: Operator splitting method -- Cahn-Hilliard type equation -- Multi-thread computing -- High-order scheme -- Mass conservation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2023.01.037
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, an efficient dimension splitting method is applied to the two-dimensional (2D) and three-dimensional (3D) Cahn-Hilliard type equations with significant applications in physical, biological and computer science. The proposed method can greatly reduce the storage requirements and computational complexity in two and three dimensions, and preserve the high precision and mass conservation. The dimension splitting method is based on auxiliary variables for spatial derivative terms and the operator splitting approach. It converts the 2D or 3D problem into a series of one-dimensional (1D) problems which can be solved by using multi-thread. The stability and accuracy of the proposed method are improved by a local stabilizing approach and extrapolation. The analyses of discrete energy and discrete mass conservation property are shown. Numerical examples confirm the advantages of proposed method. And a variety of simulations, such as the phase separations, curvature driven flows, diblock copolymers, tumor growth and volume restoration, are performed with respect to practical applications. Highlights: Dimension splitting method for Cahn-Hilliard type equations. The global stability is achieved by the local stability of solving each sub-problem. Fourth-order mass conservative scheme based on the compact differencing and extrapolation. A large number of numerical examples for practical applications.