Implicit Simplified Unified Gas-Kinetic Scheme for Diatomic Rarefied Flows Based on OpenFOAM

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Abstract
An implicit simplified unified gas-kinetic scheme (ISUGKS) for diatomic gas flows is developed and implemented within the OpenFOAM framework. The solver integrates the Rykov kinetic model to characterize translational–rotational energy exchange and nonequilibrium effects, adopting an implicit macro–micro coupling strategy to eliminate the time-step limitation of explicit schemes. The macroscopic conservation equations are discretized using vector flux splitting, while the microscopic distribution function is solved with a first-order upwind scheme. Both systems are solved by a matrix-free point-relaxation symmetric Gauss–Seidel (PR-SGS) method for low cost and fast convergence. A dual-time-stepping approach is employed to preserve multiscale flow characteristics and accelerate steady-state convergence, and an error compensation technique is introduced to suppress conservation errors caused by velocity-space discretization. The interface flux is reconstructed via the right rectangular integration rule to simplify computation and improve efficiency. Validations are conducted through benchmark cases including a supersonic rarefied flow over a flat plate, a 3D supersonic/hypersonic flow over a sphere, an Apollo re-entry capsule, and a lifting-body vehicle, covering supersonic to hypersonic rarefied flow regimes. Numerical results show good agreement with experimental data, implicit UGKS, and DSMC solutions. Compared with the explicit counterpart, the proposed solver achieves more than one order of magnitude speedup under the same parallel configuration, demonstrating significantly improved efficiency for large-scale engineering simulations. The developed ISUGKS solver fills the gap of implicit multiscale kinetic solvers for diatomic gases in OpenFOAM and provides a reliable tool for hypersonic rarefied aerothermodynamic predictions.

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