Uncertainty Quantification for the BGK Model of Boltzmann Equation Using Multilevel Variance Reduced Monte Carlo Methods

In this paper, a gas kinetic solver is developed for the Reynolds Average Navier-Stokes (RANS) equations in two-space dimensions. To our best knowledge, this is the first attempt to extend the application of the BGK (Bhatnagaar-Gross-Krook) scheme to solve RANS equations with a turbulence model using finite difference method. The convection flux terms which appear on the left hand side of the R...

In this paper, we develop a family of third order asymptotic-preserving (AP) and asymptotically accurate (AA) diagonally implicit Runge–Kutta (DIRK) time discretization methods for the stiff hyperbolic relaxation systems kinetic Bhatnagar–Gross–Krook (BGK) model in semi-Lagrangian (SL) setting. The are constructed based on an accuracy analysis SL scheme BGK limiting fluid regime when Knudsen nu...

1 The BGK model 3 1.1 Basic Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Hydrodynamic limit of the BGKW Model . . . . . . . . . . . . . . . . . . 5 1.3 BGKW Model Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Normal shock profiles in a hard sphere gas . . . . . . . . . . . . . . 7 1.3.2 1-D heat flow in a rarefied hard sphere gas . ...

An analytical solution of the matrix Riemann-Hilbert problem relevant to the BGK modelin the field of rarefied-gas dynamics is used to deduce the partial indices basic to a canonicalsolution of the considered Riemann-Hilbert problem. SommarioSi fa uso di una soluzione analitica del problema di Riemann-Hilbert che origina dalmodello BGK nel campo della dinamica dei gas rarefa...