Thesis title: A Numerical investigation of surface roughness effects in supersonic turbulent channel flows
The thesis sets out to achieve two main objectives. The first objective is to perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers M_b = 0.3–4, both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature–velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating.
The second objective of thesis is directed mainly on the software development aspects of the direct numerical simulation solver used in the first objective. Exascale High Performance Computing represents a tremendous opportunity to push the boundaries of Computational Fluid Dynamics, but despite the consolidated trend towards the use of Graphics Processing Units (GPUs), programmability is still an issue. The solver used in this work, STREAmS-2 is a compressible flow code for canonical wall-bounded turbulent flows capable of harvesting the potential of NVIDIA GPUs. In this thesis, we extend the already available CUDA Fortran backend with a novel HIPFort backend targeting AMD GPU architectures. The main implementation strategies are discussed along with a novel Python tool that can generate the HIPFort and CPU code versions allowing developers to focus their attention only on the CUDA Fortran backend. Single GPU performance is analysed focusing on NVIDIA A100 and AMD MI250x cards which are currently at the core of several HPC clusters. The gap between peak GPU performance and STREAmS-2 performance is found to be generally smaller for NVIDIA cards. Roofline analysis allows tracing this behavior to unexpectedly different computational intensities of the same kernel using the two cards. Additional single-GPU comparisons are performed to assess the impact of grid size, number of parallelised loops, thread masking and thread divergence. Parallel performance is measured on the two largest EuroHPC pre- exascale systems, LUMI (AMD GPUs) and Leonardo (NVIDIA GPUs). Strong scalability reveals more than 80% efficiency up to 16 nodes for Leonardo and up to 32 for LUMI. Weak scalability shows an impressive efficiency of over 95% up to the maximum number of nodes tested (256 for LUMI and 512 for Leonardo). This analysis shows that STREAmS-2 is the perfect candidate to fully exploit the power of current pre-exascale HPC systems in Europe, allowing users to simulate flows with over a trillion mesh points, thus reducing the gap between the Reynolds numbers achievable in high-fidelity simulations and those of real engineering applications. Additionally, the computational techniques employed allows us to efficiently perform complex simulations similar to the first objective.