The application of the implicit scheme of the multiscale discrete velocity method for three-dimensional flows of diatomic gas in all flow regimes

This paper presents the development of an implicit multiscale discrete velocity method, which is applicable to three-dimensional flows of diatomic gas in all flow regimes. The Boltzmann-Rykov model equation serves as the fundamental governing equation for this implicit method. By implicitly solving this equation along with its corresponding macroscopic adjoint equations, the efficiency in addressing problems across all flow regimes is significantly enhanced. To reduce the additional memory consumption associated with implicit solutions, this paper utilizes point-relaxation symmetric Gauss-Seidel iteration to solve the governing equations. Moreover, inspired by the construction philosophy of the discrete unified gas kinetic scheme, a multiscale interface flux is formulated, and the macroscopic flux is decomposed into equilibrium and non-equilibrium components, thereby enhancing the stability of the algorithm. Through a series of three-dimensional flow cases, including lid-driven cavity flow, flow around a sphere, flow around an Apollo 6 capsule, flow around a blunted-cone, and flow around an X-38 vehicle, this paper comprehensively validates the accuracy of the proposed implicit algorithm in managing all flow regime problems and demonstrates an efficiency improvement of one to two orders of magnitude compared to the corresponding explicit algorithm.