Kinetic model for the phase transition of the van der Waals fluid

Abstract

This is a continuation of previous works [S. Takata and T. Noguchi, J. Stat. Phys. 172, 880 (2018); S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, Phys. Rev. E 98, 052123 (2018)]. The simple model proposed in the previous works is extended to be free from the isothermal assumption. The new model conserves the total mass, momentum, and energy in the periodic domain. A monotone functional is found, assuring the H theorem for the new model. Different approaches are taken to tell apart the stable, the metastable, and the unstable uniform equilibrium state. Numerical simulations are also conducted for spatially one-dimensional cases to demonstrate various features occurring in the time evolution process. A prediction method for the profile at the stationary state is discussed as well.