Properties and Characteristics of the Fluid Flow Model With Non-Equilibrium Thermodynamic Pressure

Abstract

The paper presents a model of fluid flow with non-equilibrium pressure and the pressure evolution equation. The equation takes into account the dynamics of pressure changes caused by the difference between hydrodynamic and thermodynamic pressure as well as bulk viscosity effects. For the model of one-dimensional fluid flow, consisting of the conservation equations and the pressure evolution equation, the disturbances velocity was determined using the method of characteristics. Even though there occurs viscosity in the equations, the perturbation velocities are finite. The evolution equation for pressure makes it possible to understand pressure as an independent component of a vector of unknowns, similarly to density, velocity and internal energy. Thanks to this, the integration of the non-equilibrium pressure over time is performed as it is an other unknown. The fluid flow solution is controlled by the presence of thermodynamic pressure in the form of an equilibrium equation of state.