No area of computing is hungrier for performance than High Performance Computing (HPC), the demands of which continue to be a major driver for processor performance and adoption of accelerators, and also advances in memory, storage, and networking technologies. A key feature of the Intel processor domination of the past decade has been the extensive adoption of GPUs as coprocessors, whilst more recent developments have seen the increased availability of a number of CPU processors, including the novel ARM-based chips. This paper analyses the performance and scalability of a state-of-the-art Computational Fluid Dynamics (CFD) code on three HPC cluster systems equipped with AMD EPYC-Rome (EPYC, 4096 cores), ARM-based Marvell ThunderX2 (TX2, 8192 cores) and Intel Skylake (SKL, 8000 cores) processors. Three benchmark cases are designed with increasing computation-to-communication ratio and numerical complexity, namely lid-driven cavity flow, Taylor-Green vortex and a travelling solitary wave using the level-set method, adopted with 4 th -order central-differences or a 5 th -order WENO scheme. Our results show that the EPYC cluster de-