Numerical methods for nonequilibrium models derived from the generalized Onsager principle
主 题: Numerical methods for nonequilibrium models derived from the generalized Onsager principle
报告人: Prof. Qi Wang (Beijing Computational Science Research Center/University of South Carolina)
时 间: 2016-09-21 10:30-11:30
地 点: 理科一号楼1303(科学与工程计算系列讨论班(Scientific and Engineering Computing Seminar)
Equilibrium thermodynamics is a well-established discipline. However, theories for nonequilibrium phenomena are far from settled. There have not been well-established physical laws like the three fundamental thermodynamical laws for nonequilibrium phenomena. To established baseline principles for developing theories for nonequilibrium phenomena, ones have resorted to extend the equilibrium thermodynamic laws, especially, the second law to near equilibrium phenomena or tried to set up prototypical mathematical structures for admissible nonequilibrium thermodynamic theories. These include the GENERIC and Poisson Bracket formulation of nonequilibrium theories or the generalized Onsager principle. In this talk, I will first discuss briefly what is the generalized Onsager principle and its applicability to developing nonequilibrium theories for physical systems. Then, I will discuss how numerical analysts can exploit the mathematical structure in the models derived using the generalized Onsager principle systematically. A new technique termed the energy quadratization (EQ) will be introduced. I will illustrate the idea using a few well-known models for multi-phase materials and generalized hydrodynamics for complex fluid flows.