Two-dimensional simulation of rarefied gas flows using quadrature-based moment equations

The recent development of the quadrature-based moment equations (QBME) for the simulation of rarefied gases using the Boltzmann equation led to a promising hyperbolic moment model. This paper deals with the two-dimensional QBME model, presents its derivation based on different possible expansions, and gives explicit equations for the QBME model and related models before describing a numerical method to solve the nonconservative PDE system on two-dimensional, unstructured grids. The first simulations using the two-dimensional QBME are shown in this paper using the flow past a cylinder and a forward facing step test case. The results indicate the applicability of the QBME models for rarefied gas flows as well as convergence to the Euler solution in the case of vanishing Knudsen number.