Implicit simplified unified gas-kinetic scheme for diatomic rarefied flows based on OpenFOAM

An implicit simplified unified gas-kinetic scheme (ISUGKS) for diatomic rarefied flows is developed and implemented within the OpenFOAM framework. The solver incorporates the Rykov kinetic model to capture translational–rotational energy exchange and employs an implicit macro–micro coupling strategy with matrix-free PR-SGS iteration to remove the time-step constraints inherent to explicit formulations. A dual-time-stepping formulation and an error-compensation technique are introduced to preserve multiscale fidelity and suppress velocity-space discretization errors, respectively. The solver is validated on four representative benchmark cases spanning supersonic rarefied flow over a flat plate, three-dimensional sphere flow, an Apollo re-entry capsule, and a lifting-body vehicle, with results showing good agreement with experimental data and reference implicit UGKS and DSMC solutions. Compared with its explicit counterpart, the solver achieves a speedup exceeding one order of magnitude, and a hybrid physical–velocity parallel decomposition further yields a 4.0 × speedup when scaling from 512 to 1024 cores. These results demonstrate the extension of fully coupled implicit multiscale kinetic solvers to diatomic gases within the OpenFOAM ecosystem.