An Interface-Fitted Fictitious Domain Finite Element Method for the Simulation of Neutrally Buoyant Particles in Plane Shear Flow

Abstract

In this paper, an interface-fitted fictitious domain finite element method is developed for the simulation of fluid–rigid particle interaction problems in cases of rotated particles with small displacement, where an interface-fitted mesh is employed for the discrete scheme to capture the fluid–rigid particle interface accurately, thereby improving the solution accuracy near the interface. Moreover, a linearization and decoupling process is presented to release the constraint between velocities of fluid and rigid particles in the finite element space, and to make the developed numerical method easy to be implemented. Our numerical experiments are carried out using two different moving interface-fitted meshes; one is obtained by a rotational arbitrary Lagrangian–Eulerian (ALE) mapping, and the other one through a local smoothing process among interface-cut elements. A unified velocity is defined in the entire domain based on the fictitious domain method, making it easier to develop an interface-fitted mesh generation algorithm in a fixed domain. Both show that the proposed method has a good performance in accuracy for simulating a neutrally buoyant particle in plane shear flow. This approach can be easily extended to fluid–structure interaction problems involving fluids in different states and structures in different shapes with large displacements or deformations.