论文|Rong Zhang, Qiaolin He,：The least–square/fictitious domain method based on Navier slip boundary condition for simulation of flow–particle interaction

本文（The least–square/fictitious domain method based on Navier slip boundary condition for simulation of flow–particle interaction）原载 Applied Mathematics and Computation，由四川大学数学学院贺巧琳教授等科研人员创作，系四川大学智慧法治超前部署学科系列学术成果。后续会持续分享四川大学智慧法治超前部署学科系列学术成果，欢迎大家阅读。

Abstract:In this article, we develop a least–squares/fictitious domain method for direct simulation of fluid particle motion with Navier slip boundary condition at the fluid–particle interface. Let Ω and B be two bounded domains of Rd such that B¯⊂Ω. The motion of solid particle B is governed by Newton’s equations. Our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full Ω, followed by a well–chosen correction over B and corrections related to translation velocity and angular velocity of the particle. This method is of the virtual control type and relies on a least–squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Since the fully explicit scheme to update the particle motion using Newton’s equation is unstable, we propose and implement an explicit–implicit scheme in which, at each time step, the position of the particle is updated explicitly, and the solution of Navier-Stokes equations and particle velocities are solved by the least–squares/fictitious domain method implicitly. Numerical results are given to verify our numerical method.

Rong Zhang, Qiaolin He, The least–square/fictitious domain method based on Navier slip boundary condition for simulation of flow–particle interaction, Applied Mathematics and Computation, 2022(415), 126687.（论文下载）