An energy-stable scheme for a 2D simple fluid-particle interaction problem

JOURNAL OF COMPUTATIONAL PHYSICS

卷:424

Article

Li, Xiang^1,2  Du, Qiang^3,4  Luo, Li⁵  Wang, Xiao-Ping² 

[1] Beijing Computat Sci Res Ctr, Appl & Computat Math Div, Beijing, Peoples R China

[2] Hong Kong Univ Sci & Technol, Dept Math, Hong Kong, Peoples R China

[3] Columbia Univ, Dept Appl Phys, New York, NY 10027 USA

[4] Columbia Univ, Appl Math & Data Sci Inst, New York, NY 10027 USA

[5] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen 518055, Peoples R China

关键词: Fluid-particle interaction;    Energy-stable scheme;    Temporary arbitrary Lagrangian-Eulerian;    Extended finite element method;   

DOI  :  10.1016/j.jcp.2020.109850

来源: Elsevier

【 摘 要 】

We develop an energy-stable scheme for simulating fluid-particle interaction problems governed by a coupled system consisting of the incompressible Navier-Stokes (NS) equations defined in a time-dependent fluid domain and Newton's second law for particle motion. A modified temporary arbitrary Lagrangian-Eulerian (tALE) method is designed based on a bijective mapping between the fluid regions at different time steps. In the proposed numerical scheme, the tALE mesh velocity, the incompressible NS equations, and Newton's second law are solved simultaneously. We prove that under certain conditions, the new time discretization scheme satisfies an energy law. For the space discretization, the extended finite element method (XFEM) is used to solve the problem on a fixed Cartesian mesh. The developed method is first-order accurate in time and space without being momentum conservative. To verify the accuracy and stability of our numerical scheme, we present numerical experiments including the fitting of the Jeffery orbit by rotating of an ellipse and the free-falling of an elliptic particle in water. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free