We present a novel computational modeling framework to numerically investigate fluid-structure interaction in viscous fluids using the phase field embedding method. Each rigid body or elastic structure immersed in the incompressible viscous fluid matrix, grossly referred to as the particle in this paper, is identified by a volume preserving phase field. The motion of the particle is driven by the fluid velocity in the matrix for passive particles or combined with its self-propelling velocity for active particles. The excluded volume effect between a pair of particles or between a particle and the boundary is modeled by a repulsive potential force. The drag exerted to the fluid by a particle is assumed proportional to its velocity. When the particle is rigid, its state is described by a zero velocity gradient tensor within the nonzero phase field that defines its profile and a constraining stress exists therein. While the particle is elastic, a linear constitutive equation for the elastic stress is provided within the particle domain. A hybrid, thermodynamically consistent hydrodynamic model valid in the entire computational domain is then derived for the fluid-particle ensemble using the generalized Onsager principle accounting for both rigid and elastic particles. Structure-preserving numerical algorithms are subsequently developed for the thermodynamically consistent model. Numerical tests in 2D and 3D space are carried out to verify the rate of convergence and numerical examples are given to demonstrate the usefulness of the computational framework for simulating fluid-structure interactions for passive as well as self-propelling active particles in a viscous fluid matrix.

中文翻译：

---

粘性流体中流固耦合的混合相场法

我们提出了一种新的计算建模框架，使用相场嵌入方法对粘性流体中的流固耦合进行数值研究。浸入不可压缩粘性流体基质中的每个刚体或弹性结构，在本文中统称为粒子，由体积保持相场识别。对于被动粒子，粒子的运动是由基质中的流体速度驱动的，或者对于主动粒子是由其自推进速度驱动的。一对粒子之间或粒子与边界之间的排除体积效应由排斥势力建模。假设粒子对流体施加的阻力与其速度成正比。当粒子是刚性的时，它的状态由定义其轮廓的非零相场内的零速度梯度张量描述，其中存在约束应力。虽然粒子是弹性的，但在粒子域内提供了弹性应力的线性本构方程。然后使用广义的 Onsager 原理，同时考虑刚性和弹性粒子，推导出在整个计算域中有效的混合热力学一致流体动力学模型，用于流体粒子系综。随后为热力学一致模型开发了结构保持数值算法。