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A unified Eulerian variational framework for multiphase fluid-structure interaction Mao, Xiaoyu


Multiphase fluid-structure interaction (FSI) involving multiphase flow and contact between immersed solids is omnipresent in numerous processes in nature, biology, and engineering applications. Examples include bio-inspired avian-aquatic vehicles, aneurysm and cardiovascular diseases in biomedical engineering, and marine vessels in ocean engineering. Of particular interest to the present study is the ice-going ships in the Arctic environment. Numerical simulation of this complex system involves modeling dynamics of disparate materials, evolving multiphase interfaces, and collisions between solids. The development of a novel three-dimensional multiphase and multiphysics computational framework based on unified continuum mechanics laws is the focus of the present dissertation. In the proposed numerical framework, we employ a fully Eulerian description for the continua of different phases, which facilitates topological changes of their interfaces during the evolution and contact processes. The interfaces and phase components are captured by the phase-field-based diffuse interface description. While the diffuse interface description circumvents the complexity of explicit interface reconstruction, it poses challenges in consistent interface transition and accurate geometric representation. To address these challenges, we developed an interface and geometry preserving phase-field method, which is the key contribution of this dissertation and lays the foundation for the success of the current framework in handling multiphase interfaces. With the phase components, we unify the mass and momentum conservations by phase-dependent interpolation. The kinematics of solid phases in an Eulerian frame of reference is resolved by evolving the left Cauchy-Green tensor. The unified Eulerian framework for two-phase and multiphase FSI is implemented in a partitioned-block iterative manner within the in-house 3D parallel variational multiphysics solver. The solver is systematically explored for a variety of cases of two-phase flow with surface tension effect, single-phase FSI, multiphase FSI, and contact of immersed deformable solids. The study is concluded by a 3D demonstration of ice-going ships sailing across floating ice floes. The unified Eulerian variational framework with a parallel implementation based on the novel interface and geometry preserving phase-field method provides a general and robust approach for investigating a wide range of multiphase FSI problems.

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