A comparison of CPU and GPU performance for high-order finite-volume methods for simulating hypersonic transition

Abstract: , Here is the text you provided, displayed exactly as it is:, , The location of transition from laminar to turbulent flow on hypersonic accelerator vehicles is a key influence on their design. To aid our understanding of hypersonic transition, Direct Numerical Simulation (DNS) can be applied to investigate the underlying physics. Compared to Reynolds-Averaged Navier Stokes (RANS) and Large Eddy Simulations (LES), DNS is the most computationally expensive turbulence simulation technique, but it captures the highest physical fidelity. The computational efficiency and trustability of DNS, in a finite-volume (FV) setting, can be improved by algorithm enhancement (such as using higher-order methods), hardware advancements (to compute with more cells), or a combination of both. This paper describes a compressible flow solver in which both strategies are combined by finding and developing fluid algorithms that are best suited to Graphics Processing Units (GPUs) as hardware accelerators. To provide an assessment of how much performance benefit there is for DNS on GPUs as compared to CPUs, a FV flow solver is written in the C language for CPUs and with CUDA for GPUs. The same computational gas-dynamic algorithms are implemented on CPUs and on GPUs to compare simulation run-times between the two architectures. Proof-of-concept results were generated in a one-dimensional algorithm and showed an execution speed-up of 59 times for the GPU version compared to the CPU version. In this paper, we extend the flow solver to multiple spatial dimensions (2D/3D) and investigate the performance benefit of GPUs for compressible flow algorithms. Results will be obtained by run-time tests on an isentropic vortex test case, multi-dimensional Riemann problems, and a high-speed laminar boundary-layer. To show an application of the multi-dimensional solver, the hypersonic flow over a flat plate is considered for the same flow conditions as used in T4 shock tunnel experiments. A heating investigation is conducted where an unheated flat plate transitional area is compared to the same area but for different heated cases. In one configuration, the whole flat plate is heated, in the next case the heating starts at 70mm and 120mm along the plate, and in another setup a heated strip is implemented at the beginning of the plate. Keywords: Direct numerical simulation, Boundary layer transition, Graphics processing units, Hypersonic flows