We analyze a large number of high-order discrete velocity models for solving the Boltzmann-BGK equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.

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Lattice-Boltzmann simulations of the turbulent flow around a surface-mounted circular cylinder at the height-to-diameter ratio of 1 are performed in order to assess the capability to capture the highly unsteady flow field. The Reynolds number based on the freestream velocity and cylinder diameter is 32 000 and the boundary layer thickness of the approach flow is equal to the cylinder height. We use two different formulations of the entropic multi-relaxation time model and the standard Bhatnagar-Gross-Krook model equipped with the Smagorinsky subgrid model. The unsteady flow behavior including the vortex structures are analyzed and both pressure coefficients and velocity profiles are evaluated. While the results of all Lattice-Boltzmann models are in good agreement with reference data, the entropic multi-relaxation time model based on central moments show the best predictive accuracy.

The efficiency of filter media can be improved by applying nanofibers to the surface of the microstructure. In order to gain a deeper insight into the influence of the nanofiber geometry on filtration efficiency in terms of pressure loss, separation efficiency, and dust holding capacity, the microstructure is analyzed by geometrical pore space characteristics such as the degree of vertices function, the spherical contact distribution function, and the pore size distribution function. The pore space characteristics are investigated by using a distance transform and a 3D pore space graph generated by the Ma‐Sonka‐Algorithm with the P‐simple‐points extension.