Interpreting pressure and viscous effects in Gas Kinetic Simulations of non- equilibrium flows

Gas Kinetic Scheme (GKS) is used to compute non-equilibrium flows, especially for high-speed and rarefied flow applications. In this approach, equations for mass and momentum are solved directly, but the fluxes are computed using a non-equilibrium particle distribution function (pdf). The flux computed from the pdf combines the effects of advection (A), pressure (P) and viscosity (V). To understand the flow mechanisms, it is often necessary to separate the individual effects. In current practice, the advection term is computed using the equilibrium distribution function taking advantage of the conservation of momentum statement. The pressure and the viscous terms are then estimated from constitutive relations. In this work, we develop the framework necessary for direct computation of pressure and viscous effects from the non-equilibrium distribution which leads to a more accurate assessment. A comparison between the two approaches is also presented at various departures from the equilibrium state.