Macroscopic Transport Equations for Rarefied Gas Flows
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Cites background or methods from "Macroscopic Transport Equations for..."
...We refer to Struchtrup (2005) for alternative approaches that avoid some of the shortcomings of the classical high-order closures....
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...The problem of finding high-order closures to the moment system for small and moderate Knudsen numbers has been tackled by several authors with the goal of avoiding the expensive solution of the kinetic equation (Müller and Ruggeri 1993, Struchtrup 2005)....
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...H. Struchtrup (2005), Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory, Interaction of Mechanics and Mathematics, Springer....
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...Higher-order fluid models, such as the compressible Navier– Stokes model, can be derived using the expansions due to Chapman–Enskog and to Grad (Müller and Ruggeri 1993, Struchtrup 2005)....
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220 citations
Cites background or methods from "Macroscopic Transport Equations for..."
...In most applications we are not interested in knowing the exact form of the velocity distribution function, rather knowledge of its lower-order moments is sufficient [70]....
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...The BGK model does not provide the correct value of Pr, which should be 2/3 for a mono-atomic gas [70]....
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...Note that most moment methods are designed to work for systems near equilibrium where the collisions are dominant [41,52,70,71] (i....
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...For inelastic hard-sphere collisions, a kinetic model can be used to approximate the Boltzmann collision integral in terms of a closed set of lower-order moments [10,70]....
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...The advantage of using the BGK approximation is that the moment equations derived from the collision term are closed [70]....
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197 citations
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Cites background or methods from "Macroscopic Transport Equations for..."
...The small parameter ε usually denotes Kn number (the ratio of mean free path to the characteristic size of fluid system) in classical hydrodynamics [154,155]....
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...Velocity slip boundary in microscale gas flow Inmicroscale gas flow, theKnudsennumber (Kn) is defined as the ratio ofmolecularmean free pathΛ to the characteristic dimension L of gas flow (such as the height of a channel, or the diameter of a pipe) [154]: Kn = Λ/L....
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...In addition, the firstorder Chapman–Enskog expansion to Boltzmann transport equation can also yield the Navier–Stokes equation [154]; the entropy balance equation and expressions of entropy flux in CIT can be derived from the kinetic theory of gases [40,219]....
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...Finally, an interesting aspect is noted that nine-moment phonon hydrodynamic model corresponds to the classical thirteen-moment model in hydrodynamics [153,154]....
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