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# Lattice Boltzmann approach to rarefied gas flows using half-range Gauss-Hermite quadratures: Comparison to DSMC results based on ab initio potentials

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### Abstract

In this paper, we employ the lattice Boltzmann method to solve the Boltzmann equation with the Shakhov model for the collision integral in the context of the 3D planar Couette flows to demonstrate the dramatic increase in simulation efficiency when the momentum space is discretised using the half-range Gauss-Hermite quadrature to account for the discontinuity in the distribution function induced by the walls. The lattice Boltzmann simulation results are compared with direct simulation Monte Carlo (DSMC) results for $${}^3{\rm He}$$ and $${}^4{\rm He}$$ atoms interacting via ab initio potentials, at various values of the rarefaction parameter $$\delta$$, where the temperature of the plates varies from $$1\ {\rm K}$$ up to $$3000\ {\rm K}$$. Good agreement is observed between the results obtained using the Shakhov model and the DSMC data at large values of the rarefaction parameter. The agreement deteriorates as the rarefaction parameter is decreased, however we highlight that the relative errors in the non-diagonal component of the shear stress do not exceed $$2.5\%$$.

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###### Journal
11 October 2018
1810.07803