Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities

The computational efficiency of the integro-moment method for solving steady-state two-dimensional rarefied gas flows is investigated. The two-dimensional boundary driven flow of a single gas in a cavity is used as a model problem, because the kinetic equations and the boundary conditions describing this flow contain most of the terms and features, which might appear in problems modeled by kinetic equations. Following a detailed quantitative comparison with the discrete velocity method, it is concluded that the integro-moment method may be considered as a alternative reliable and efficient computational scheme for solving rarefied (or non-equilibrium) flows in the whole range of the Knudsen number. Even more, it is shown that by implementing the integro-moment method the propagation of any discontinuities, which may exist at the boundaries, inside the computational domain and the production of an unphysical oscillatory behavior in the macroscopic quantities, are completely eliminated. The proposed integro-moment methodology is general and may be applied to any multidimensional non-equilibrium flow described by linear kinetic model equations.