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Applied and Computational Math Seminar

Energy quadratization strategy for numerical approximations of nonequilibrium models

Qi Wang, University of South Carolina 

Location:  Hill 423
Date & time: Friday, 22 September 2017 at 12:00PM - 1:00PM

Abstract: There are three fundamental laws in equilibrium thermodynamics. But, what are the laws in nonequilibrium thermodynamics that guides the development of theories/models to describe nonequilibrium phenomena? Continued efforts have been invested in the past on developing a general framework for nonequilibrium thermodynamic models, which include Onsager's maximum entropy theory, Prigogine's minimum entropy production rate theory, Poisson bracket formulation of Beris and Edwards, as well as the GENERIC formalism promoted by Ottinger and Grmela. To some extent, they are equivalent and all give practical means to develop nonequilibrium dynamic models. In this talk, I will focus on the Onsager approach, termed the Generalized Onsager Principle (GOP). I will review how one can derive thermodynamic and generalized hydrodynamic models using the generalized Onsager principle coupled with the variational principle. Then, I will discuss how we can exploit the mathematical structure of the models derived using GOP to design structure and property preserving numerical approximations to the governing system of partial differential equations. Since the approach is valid near equilibrium as pointed it out by Onsager, an energy quadratization strategy is proposed to arrive linear numerical schemes. This approach is so general that in principle we can use it to any nonequilibrium model so long as it has the desired variational and dissipative structure. Some numerical examples will be given to illustrate the usefulness of this approach.

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