First- and second-order accurate numerical methods, implemented for
CPUs, underpin the majority of industrial CFD solvers. Whilst this technology
has proven very successful at solving steady-state problems via a
Reynolds Averaged Navier-Stokes approach, its utility for undertaking scaleresolving
simulations of unsteady flows is less clear. High-order methods for
unstructured grids and GPU accelerators have been proposed as an enabling
technology for unsteady scale-resolving simulations of flow over complex
geometries. In this study we systematically compare accuracy and cost of
the high-order Flux Reconstruction solver PyFR running on GPUs and the
industry-standard solver STAR-CCM+ running on CPUs when applied to a
range of unsteady flow problems. Specifically, we perform comparisons of
accuracy and cost for isentropic vortex advection (EV), decay of the Taylor-
Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow
over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a
second-order configuration, and a third-order configuration, where the latter
was recommended by CD-Adapco for more effective computation of unsteady
flow problems. Results from both PyFR and Star-CCM+ demonstrate that
third-order schemes can be more accurate than second-order schemes for a
given cost e.g. going from second- to third-order, the PyFR simulations of the
EV and TGV achieve 75x and 3x error reduction respectively for the same or
reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake
statistics significantly more accurately for only twice the cost. Moreover,
advancing to higher-order schemes on GPUs with PyFR was found to offer
even further accuracy vs. cost benefits relative to industry-standard tools.