  Recently, successes have been achieved for the high-order gas-kinetic schemes
(HGKS) on unstructured meshes for compressible flows. In this paper, to
accelerate the computation, HGKS is implemented with the graphical processing
unit (GPU) using the compute unified device architecture (CUDA). HGKS on
unstructured meshes is a fully explicit scheme, and the acceleration framework
can be developed based on the cell-level parallelism. For single-GPU
computation, the connectivity of geometric information is generated for the
requirement of data localization and independence. Based on such data
structure, the kernels and corresponding girds of CUDA are set. With the
one-to-one mapping between the indices of cells and CUDA threads, the
single-GPU computation using CUDA can be implemented for HGKS. For multiple-GPU
computation, the domain decomposition and data exchange need to be taken into
account. The domain is decomposed into subdomains by METIS, and the MPI
processes are created for the control of each process and communication among
GPUs. With reconstruction of connectivity and adding ghost cells, the main
configuration of CUDA for single-GPU can be inherited by each GPU. The
benchmark cases for compressible flows, including accuracy test and flow
passing through a sphere, are presented to assess the numerical performance of
HGKS with Nvidia RTX A5000 and Tesla V100 GPUs. For single-GPU computation,
compared with the parallel central processing unit (CPU) code running on the
Intel Xeon Gold 5120 CPU with open multi-processing (OpenMP) directives, 5x
speedup is achieved by RTX A5000 and 9x speedup is achieved by Tesla V100. For
multiple-GPU computation, HGKS code scales properly with the increasing number
of GPU. Numerical results confirm the excellent performance of multiple-GPU
accelerated HGKS on unstructured meshes.
