On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime

•Analyzed fluid dynamic behavior of the SG methods for Boltzmann equation.•AP schemed for deterministic and uncertain Boltzmann equation.•Proved leading order weak hyperbolicity of SG methods for uncertain Boltzmann in fluid regime. The Boltzmann equation may contain uncertainties in initial/boundary data or collision kernel. To study the impact of these uncertainties, a stochastic Galerkin (sG) method was proposed in [18] and studied in the kinetic regime. When the system is close to the fluid regime (the Knudsen number is small), the method would become prohibitively expensive due to the stiff collision term. In this work, we develop efficient sG methods for the Boltzmann equation that work for a wide range of Knudsen numbers, and investigate, in particular, their behavior in the fluid regime.