An implicit adaptive unified gas-kinetic scheme for steady-state solutions of nonequilibrium flows

In recent years, nonequilibrium flows have been frequently encountered in various aerospace engineering and micro-electro-mechanical systems applications. To understand nonequilibrium physics, multiscale effects, and the dynamics in these applications, a reliable multiscale scheme for all flow regimes is required. Following the direct modeling methodology, the adaptive unified gas-kinetic scheme employs discrete velocity space to accurately capture the nonequilibrium physics, recovering the original unified gas-kinetic scheme (UGKS). By adaptively employing continuous distribution functions based on the Chapman–Enskog expansion, it efficiently handles near-equilibrium flow regions. The two regions are dynamically coupled at the cell interface through the fluxes from the discrete and continuous gas distribution functions, thereby avoiding any buffer zone between them. In this study, an implicit adaptive unified gas-kinetic scheme (IAUGKS) is constructed to further enhance the efficiency of steady-state solutions. The current scheme employs implicit macroscopic governing equations and couples them with implicit microscopic governing equations within the nonequilibrium region, resulting in high convergence efficiency in all flow regimes. To validate the efficiency and robustness of the IAUGKS, a series of numerical tests were conducted for high Mach number flows around diverse geometries. The current scheme can capture the nonequilibrium physics and provide accurate predictions of surface quantities. In comparison with the original UGKS, the velocity space adaptation, unstructured discrete velocity space, and implicit iteration significantly improve the efficiency by one or two orders of magnitude. Given its exceptional efficiency and accuracy, the IAUGKS serves as an effective tool for nonequilibrium flow simulations.