A Survey of Deterministic Solvers for Rarefied Flows

Numerical simulations of rarefied gas flows are generally made with DSMC methods. Up to a recent period, deterministic numerical methods based on a discretization of the Boltzmann equation were restricted to simple problems (1D), linearized flows, or simple geometries, for instance). in the last decade, several deterministic solvers have been developed in different teams to tackle more complex problems like 2D and 3D flows. Some of them are based on the full Boltzmann equation. Solving this equation numerically is still very challenging, and 3D solvers are still restricted to monoatomic gases, even if recent works have proved it was possible to simulate simple flows for polyatomic gases. Other solvers are based on simpler BGK like models: they allow for much more intensive simulations on 3D flows for realistic geometries, but treating complex gases requires extended BGK models that are still under development. In this paper, we discuss the main features of these existing solvers, and we focus on their strengths and inefficiencies. We will also review some recent results that show how these solvers can be improved: - higher accuracy (higher order finite volume methods, discontinuous Galerkin approaches) - lower memory and CPU costs with special velocity discretization (adaptive grids, spectral methods) - multi-scale simulations by using hybrid and asymptotic preserving schemes - efficient implementation on high performance computers (parallel computing, hybrid parallelization) Finally, we propose some perspectives to make these solvers more efficient and more popular.