Three-phase Model of Visco-elastic Incompressible Fluid Flow and its Computational Implementation.
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2019-01
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Energetic Variational Approach is used to derive a novel thermodynamically consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model which automatically satisfies the energy dissipation law and is Galilean invariant, consists of coupled Navier-Stokes and Cahn-Hilliard equations. Modified General Navier Boundary Condition with fluid elasticity taken into account is also introduced for using the model to study moving contact line problems. Energy stable numerical scheme is developed to solve system of model equations efficiently. Convergence of the numerical scheme is verified by simulating a droplet sliding on an inclined plane under gravity. The model can be applied for studying various biological or biophysical problems. Predictive abilities of the model are demonstrated by simulating deformation of venous blood clots with different visco-elastic properties and experimentally observed internal structures under different biologically relevant shear blood flow conditions.
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Xu, Shixin, Mark Alber and Zhiliang Xu (2019). Three-phase Model of Visco-elastic Incompressible Fluid Flow and its Computational Implementation. Communications in computational physics, 25(2). pp. 586–624. 10.4208/cicp.oa-2017-0167 Retrieved from https://hdl.handle.net/10161/27450.
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Shixin Xu
Shixin Xu is an Assistant Professor of Mathematics whose research spans several dynamic and interconnected fields. His primary interests include machine learning and data-driven models for disease prediction, multiscale modeling of complex fluids, neurovascular coupling, homogenization theory, and numerical analysis. His current projects reflect a diverse and impactful portfolio:
- Developing predictive models based on image data to identify hemorrhagic transformation in acute ischemic stroke.
- Conducting electrodynamics modeling of saltatory conduction along myelinated axons to understand nerve impulse transmission.
- Engaging in electrochemical modeling to explore the interactions between electric fields and chemical processes.
- Investigating fluid-structure interactions with mass transport and reactions, crucial for understanding physiological and engineering systems.
These projects demonstrate his commitment to addressing complex problems through interdisciplinary approaches that bridge mathematics with biological and physical sciences.
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