General synthetic iterative scheme for polyatomic rarefied gas flows

Recently, the general synthetic iterative scheme (GSIS) has been proposed to solve the Boltzmann equation efficiently and accurately in the whole range of gas rarefaction. Here, the GSIS is extended and further improved to find the steady-state solutions in nonlinear polyatomic gas flows. The numerical method is developed within the unstructured finite volume framework, where the kinetic equation and synthetic equations are solved alternately. The synthetic equations, which are derived from the modified Rykov kinetic model, reduce to the two-temperature (translational and rotational) Navier–Stokes–Fourier equations in the continuum flow regime, and include high-order constitutive relations for rarefaction effects in other flow regimes. These high-order terms are obtained by solving the kinetic model with the discrete velocity method. When the synthetic equations are solved, their macroscopic quantities are used to guide the evolution of velocity distribution functions in the kinetic model. As a consequence of this two-way coupling, GSIS not only finds steady-state solutions quickly but also relieves the constraints on spatial cell size. Furthermore, the robustness of GSIS is improved by modifying the boundary macroscopic fluxes in the macroscopic implicit iteration. The efficiency and multiscale property of GSIS is demonstrated through several challenging test cases, including the one-dimensional normal shock wave with large internal-translational relaxation times, the two-dimensional hypersonic flow passing a cylinder, and the pump-driven flow in Europe’s demonstration fusion power plant. •Fast convergence of GSIS for nonlinear polyatomic gas in all flow regimes.•New boundary flux modification in the macroscopic implicit solver.•Implicit treatment of source terms in two temperature NS equations.