Abstract
In this paper the assessment and the enhancement of the computational performance of a high-order finite volume CFD code is presented. Weighted Essentially Non-Oscillatory (WENO) schemes are considered to be from the most computationally expensive numerical frameworks, in the context of high-resolution schemes particularly on hybrid unstructured grids. The focus of this study is to assess the computational bottlenecks of the solver for the WENO schemes for Implicit Large Eddy Simulation (ILES) and optimise the performance and efficiency through a series of code modifications e.g. formula rewriting, reduction of number operations, inclusion of linear systems libraries, non-blocking communications amongst others. The code is assessed on five different HPC systems; significant speed-up is achieved ranging from 1.5 to 8.5, with very high-order schemes benefiting the most. Good scalability is also obtained up to 104 number of cores, demonstrating viability and affordability of WENO type schemes for scale resolving simulations.
Highlights
IntroductionNumerical methods of the high-order family were prohibited a decade ago in terms of great computational effort for large scale, moderate to high -Reynolds number cases; these methods are being increasingly adopted for various industrial applications e.g. acoustics, combustion, rotating wings and turbo machinery and are available in commercial solver packages
Numerical methods of the high-order family were prohibited a decade ago in terms of great computational effort for large scale, moderate to high -Reynolds number cases; these methods are being increasingly adopted for various industrial applications e.g. acoustics, combustion, rotating wings and turbo machinery and are available in commercial solver packages.High-order numerical methods can provide improved accuracy at a reduced computational cost for transient CFD applications compared to second-order schemes
There is a wealth of high-order numerical methods for unstructured meshes developed across different frameworks including the finite volume (FV) [1,2,3,4,5,6,7,8,9,10], the Discontinuous Galerkin (DG) [11,12,13,14,15,16], the Spectral Finite Volume (SFV) methods [17,18,19,20,21,22] and the flux reconstruction scheme (FR) [23,24,25,26,27,28]
Summary
Numerical methods of the high-order family were prohibited a decade ago in terms of great computational effort for large scale, moderate to high -Reynolds number cases; these methods are being increasingly adopted for various industrial applications e.g. acoustics, combustion, rotating wings and turbo machinery and are available in commercial solver packages. In this study we are interested in reducing the computational cost of WENO schemes, other techniques for improving their compactness could be explored to Dumbser et al [31], we are pursuing this through a series of enhancements in the execution of the algorithms and operations rather altering the numerical methodology These enhancements are tested across five different HPC architectures including a Intel Xeon Phi KnightsLanding manycore processor, and to the best of our knowledge this is the first time that very high-order finite volume WENO schemes for unstructured meshes, have been assessed, optimised and deployed for ILES of turbulent flows in this type of manycore architectures. The conclusions of the present study are outlined in the last section
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