Towards p-Adaptive Spectral/hp Element Methods for Modelling Industrial Flows
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There is an increasing requirement from both academia and industry for high-fidelity flow simulations that are able to accurately capture complicated and transient flow dynamics in complex geometries. Coupled with the growing availability of high-performance, highly parallel computing resources, there is therefore a demand for scalable numerical methods and corresponding software frameworks which can deliver the next-generation of complex and detailed fluid simulations to scientists and engineers in an efficient way. In this article we discuss recent and upcoming advances in the use of the spectral/hp element method for addressing these modelling challenges. To use these methods efficiently for such applications, is critical that computational resolution is placed in the regions of the flow where it is needed most, which is often not known a priori. We propose the use of spatially and temporally varying polynomial order, coupled with appropriate error estimators, as key requirements in permitting these methods to achieve computationally efficient high-fidelity solutions to complex flow problems in the fluid dynamics community.
D.M. acknowledges support from the EU Horizon 2020 project ExaFLOW (grant 671571) and the PRISM project under EPSRC grant EP/L000407/1. D.S. is grateful for the support received from CNPq (grant 231787/2013–8) and FAPESP (grant 2012/23493-0). D.E. acknowledges support from the EU ITN project ANADE (grant PITN-GA-289428). S.J.S. acknowledges Royal Academy of Engineering support under their research chair scheme. R.M.K. acknowledges support from the US Army Research Office under W911NF1510222 (overseen by Dr. M. Coyle). Computing resources supported by the UK Turbulence Consortium (EPSRC grant EP/L000261/1) and the Imperial College HPC service.
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