Abstract
Numerical simulations are an important tool for the design and optimization of gas flow equipment in many areas of science and technology. Most gas flows can be simulated using the continuum transport equations (Navier-Stokes), which describe the transport of mass, momentum and energy. These equations are based on the hypothesis that the mean free path length λ of the gas molecules is very small in comparison to a characteristic dimension L of the flow. This dimension can be either a physical dimension, e.g. a pipe diameter, or a flow dimension, e.g. the gradient length scale \( \frac{1}{\phi }\frac{{\partial \phi }}{{\partial x}} \) on which some flow property φ changes significantly. The dimensionless Knudsen number Kn can be used to describe this situation:
When Kn < 0.01, gas molecules travel only a small distance (compared to the geometry and flow dimensions) between collisions. For internal flows this means that molecules only very rarely collide with walls, and the flow is dominated by the characteristics of the inter-molecular collisions. As a result, the gas will be in local equilibrium and the velocity distribution of its molecules will be Maxwellian.
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Abbate, G., Thijsse, B.J., Kleijn, C.R. (2009). Hybrid Navier-Stokes/DSMC Simulations of Gas Flows with Rarefied-Continuum Transitions. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_14
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