Hydrodynamic computational models for nonequilibrium fluid dynamics and issues of projecting their solutions into phase space

There exist growing interests in developing proper mathematical models of the physical process in the mesoscopic regime. Notable examples can be found in micro- and nano-scale fluid flows and rarefied hypersonic gas flows. In this work, a method to derive high-order hydrodynamic equations for nonequilibrium fluid dynamics is presented. In addition, a slip model based on Langmuir's theory of adsorption of gases on solids is developed in order to describe the gas-surface molecular interaction in micro- and nano-scale system. Finally, issues of reconstructing a solution in phase space from information available in thermodynamic space will be discussed through the investigation of a one-dimensional shock wave flow of monatomic gases.