Дискретизация уравнения Больцмана при помощи метода конечных объемов и явно-неявных схем

The features of discretization of the Boltzmann equation using the finite volume method are considered. Finite-difference schemes for calculation of fluxes and finite-difference schemes for discretization in time are discussed. A TVD-type scheme is used for flux discretization, and an explicit-implicit scheme is applied to time discretization. The results of numerical simulation of rarefied gas flow in a shock tube for various Knudsen numbers are presented. For small Knudsen numbers, the solution of the Boltzmann equation is compared with the solution obtained from the Euler equation.