Optimal Hydrodynamic Closure for Linear Boltzmann equations

Abstract:

We present a novel set of non-local linear hydrodynamic equations describing rarefied gas flow for all Knudsen numbers. Our results are based on dynamically optimal spectral closures, which are derived from the theory of slow manifolds and a detailed spectral analysis. We discuss the physical properties of these new rarefied hydrodynamics, including criticality as well as entropy-dissipation balance, and illustrate their accuracy on classical examples, such as the Knudsen minimum in pipe flows. Furthermore, we present a learning scheme to obtain the spectrally closed generalised transport coefficients from DSMC data. This gives a new direction for the solution of Hilbert’s Sixth Problem.