Impact of number representation for high-order implicit large-eddy simulations

Abstract

High-order numerical methods for unstructured grids combine the superior accuracy of high-order spectral or finite difference methods with the geometric flexibility of low-order finite volume or finite element schemes. Over the past few years, they have shown promise in enabling implicit large-eddy simulations within the vicinity of complex geometrical configurations. However, the cost of such simulations remains prohibitive. In this paper, the impact of number representation on the efficiency and efficacy of these methods is considered. Theoretical performance models are derived and assessed. Specifically, four test cases are considered: 1) the viscous Taylor–Green vortex, 2) flow over a circular cylinder, 3) flow through a T106c low-pressure turbine cascade, and 4) flow around a NACA 0021 in deep stall. It is found that the use of single (in lieu of double) precision arithmetic does not have a significant impact on accuracy. The performance of the resulting simulations was found to improve between 1.4 and 2.9 times.