Heterogeneous CPU-GPU parallelization for nonlinear coupled constitutive relations in hypersonic rarefied non-equilibrium flows

The nonlinear coupled constitutive relations (NCCR) have been proven to be a promising tool for rarefied non-equilibrium flows. To further optimize the efficiency of the NCCR solution in hypersonic complex flows, the first migration of the NCCR method to a graphics processing unit (GPU) platform is conducted in this study, with the application of compute unified device architecture (CUDA) and message passing interface (MPI) models. Concurrently, the data parallel lower upper relaxation (DPLUR) implicit scheme is applied to avoid data dependence during the computational processes. After a code validation, three numerical cases, i.e., hypersonic flows around a blunt cylinder with varying mesh sizes, a circular cylinder with different Knudsen numbers, and a hypersonic technology vehicle (HTV)-type flying vehicle with various Mach numbers, were investigated for assessing the performance improvement of GPU-NCCR solver on a CPU-GPU heterogeneous parallel computing platform. The results in this work show that the proposed GPU-accelerated NCCR solver on a single NVIDIA GeForce RTX 4090 GPU can achieve one or two orders of magnitude speedups, ranging from 54.5 to 179.3, in comparison to the CPU-only NCCR solution on a single AMD EPYC 7T83 CPU core. Within the computing power capabilities, the GPU-NCCR algorithm's performance gain is greater with a larger mesh size, and slightly affected by the incoming flow conditions. More importantly, the GPU-accelerated NCCR solution attains more speedups than the GPU-NS solver in hypersonic non-equilibrium flows. These superior advantages of the proposed GPU-accelerated computational strategy are expected to render the NCCR method a fairly efficient engineering approach for modelling rarefied non-equilibrium flows around hypersonic vehicles.