**报告人：**刘巨博士（斯坦福大学博士后）

**邀请人：**郑海标

**报告时间地点：**2019年11月11日, 下午14:00-15:00. 数学楼401.

**报告摘要：**

Modern computational science and engineering are faced with problems coupled with different physics at disparate scales. Representative examples include fluid-structure interaction (FSI) and liquid-vapor phase transition. Due to the disparity of spatiotemporal scales and the elusive nature of the coupled physics, challenges remain in research and practice. In this work, I will first systematically derive a rational modeling framework for multiphase continua, using the celebrated microforce theory initially proposed by M.E. Gurtin. This framework provides an elegant approach of incorporating the essential physics of microscopic processes in the continuum setting without upsetting the second law of thermodynamics. In the meantime, with a proper choice of the thermodynamic potential, this framework unifies the description of solids and fluids. The unified modeling framework offers a fresh perspective on addressing FSI problems [1]. It naturally allows one to apply a computational fluid dynamics algorithm to solid dynamics, or vice versa. As an example, the variational multiscale formulation (VMS) can be generalized to the continuum body. It recovers a large eddy simulation formulation for the Navier-Stokes equations on one hand and provides a mechanism to circumvent the mesh locking of low-order elements for hyperelasticity on the other hand. The framework enjoys a Hamiltonian structure that naturally leads to a superior dynamic formulation. More importantly, the resulting FSI formulation eases the implementation and allows a robust and efficient solution strategy based on block factorization and the algebraic multigrid method. A general-purpose parallel finite element code, PERIGEE, has been developed to provide an object-oriented implementation platform for multiphysics problems. These attributes and numerical evidence indicate the promising potential of the proposed methodology for a wide range of problems. I will discuss several ongoing research projects that apply the technologies to cardiovascular biomedical applications. In the second part of this talk, I will discuss the Navier-Stokes-Korteweg equations, which is another specialized model derived from the aforementioned framework [2]. In this model, the description of liquid-vapor interface is embedded in the constitutive law, and it gives an elegant approach for describing liquid-vapor phase transition. I will discuss a suite of numerical technique that preserves the second law of thermodynamics at the fully discrete level. The capability of this model is demonstrated by the simulations of nucleate and film boiling. This new modeling framework is expected to provide a new way of understanding the multiphase phenomena, including boiling heat transfer and cavitating flows. I will conclude my talk by discussing future research directions.

References

[1] J. Liu and A.L. Marsden. A unified continuum and variational multiscale formulation for fluids, solids, and fluidstructure interaction. Computer Methods in Applied Mechanics and Engineering, 337:549-597, 2018.

[2] J. Liu, C.M. Landis, H. Gomez, and T.J.R. Hughes. Liquid-Vapor Phase Transition: Thermomechanical Theory, Entropy Stable Numerical Formulation, and Boiling Simulations. Computer Methods in Applied Mechanics and Engineering, 297:476-553, 2015.

**报告人个人简介：**刘巨，西安交通大学本科，美国德克萨斯大学奥斯丁分校博士，师从 TJR Hughes，斯坦福大学博士后。