An efficiency and memory-saving programming paradigm for the unified gas-kinetic scheme

In recent years, non-equilibrium flows have gained significant attention in aerospace engineering and micro-electro-mechanical systems. The unified gas-kinetic scheme (UGKS) follows the methodology of direct modeling to couple particle collisions and free transport during gas evolution. However, like other discrete-velocity-based methods, the UGKS faces challenges related to high memory requirements and computational costs, such as the possible consumption of 1.32 TB of memory when using 512 cores for the simulations of the hypersonic flow around an X38-like space vehicle. This paper introduces a new UGKS programming paradigm for unstructured grids, focusing on reducing memory usage and improving parallel efficiency. By optimizing the computational sequence, the current method enables each cell in physical space to store only the distribution function for the discretized velocity space, eliminating the need to retain the entire velocity space for slopes and residuals. Additionally, the parallel communication is enhanced through the use of non-blocking MPI. Numerical experiments demonstrate that the new strategy in the programming effectively simulates non-equilibrium problems while achieving high computational efficiency and low memory consumption. For the hypersonic flow around an X38-like space vehicle, the simulation, which utilizes $1,058,685$ physical mesh cells and $4,548$ discrete velocity space mesh cells, requires only 99.30 GB for 32 cores and 168.12 GB for 512 cores of memory when executed on 512 CPU cores. This indicates that memory consumption in the UGKS is much reduced. This new programming paradigm can serve as a reference for discrete velocity methods for solving kinetic equations.