Study of simplified conservation flux scheme for gas kinetics based on OpenFOAM framework II: Rykov model

Abstract

We present a computational fluid dynamics solver for diatomic gases, meticulously developed within the dugksFOAM framework. This solver is built upon a conservative gas kinetic scheme with simplified interface flux evaluations, enabling efficient and accurate solutions of the Rykov model equation. An unstructured discrete velocity space is introduced, in which the velocity points are strategically distributed to balance computational efficiency and numerical accuracy. A sophisticated hybrid parallelization strategy, referred to as X-space parallelization, has also been introduced. It integrates domain decomposition in both physical and velocity spaces, significantly enhancing computational efficiency in large-scale simulations. We further compare the computational efficiency between the structured and unstructured velocity space approaches, demonstrating that the unstructured configuration achieves notable reductions in computational cost without compromising accuracy. Moreover, the parallel performance of the solver is systematically evaluated under both small- and large-scale settings, showcasing excellent scalability and robustness. The accuracy and reliability of the solver are validated against a comprehensive set of benchmark cases, including shock structure problems, lid-driven cavity flow, supersonic flows past a flat plate, cylindrical blunt body, and sphere. These results convincingly confirm the solver's capability to capture a wide range of rarefied flow phenomena in diatomic gases, from one-dimensional to three-dimensional flows.