All nonequilibrium dynamical models for materials systems should be derived from thermodynamical principles, which include the first and second law of thermodynamics. Model derived this way possess certain mathematical structures that warrant well-posedness of the governing partial differential equations and can guide the development of structure-preserving numerical approximations. In this talk, I will give a rudimentary discussion on the model derivation via the so-called generalized Onsager principle and present a simple paradigm for designing thermodynamically consistent numerical approximations. The new method is coined energy quadratization method (EQ). Applications of the EQ approach to various model problems will be discussed. Applications to soft matter physics and bioscience will be presented as well.

海报