A phase field model for compressible immiscible fluids with a new equation of state
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2022-04-01
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In this paper, we propose a new compressible phase field model of two different immiscible fluid components, in which the density of each phase is variable. In order to establish the compressible phase field model, a new P-V-T equation of state is introduced to solve the pressure. The new model is derived by the physics law of conservation, and conforms to the second law of thermodynamics. The model adopts an innovative expression of Helmholtz free energy, taking into account the new state equation of pressure and the varying material properties of each phase. A high-order accurate numerical scheme is introduced to solve the model equations. The convection terms of the governing equations are discretized by the fifth-order WENO scheme, and the residual terms are discretized by the Lax–Friedrichs method. Finally, the reliability and validity of the compressible two-phase model are verified by numerical simulations.
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Dai, H, S Xu, Z Xu, N Zhao, CX Zhu and C Zhu (2022). A phase field model for compressible immiscible fluids with a new equation of state. International Journal of Multiphase Flow, 149. pp. 103937–103937. 10.1016/j.ijmultiphaseflow.2021.103937 Retrieved from https://hdl.handle.net/10161/27444.
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Scholars@Duke
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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