Towards p-adaptive spectral/hp element methods for modelling industrial flows
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, pp. 63-79 (2017)
@inproceedings{moxey-2017a,
title = {Towards $p$-adaptive spectral/$hp$ element methods for modelling industrial flows},
author = {Moxey, D. and Cantwell, C. D. and Mengaldo, G. and Serson, D. and Ekelschot, D. and Peir\'o, J. and Sherwin, S. J. and Kirby, R. M.},
booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016},
pages = {63-79},
year = {2017},
doi = {10.1007/978-3-319-65870-4_4},
url = {https://davidmoxey.uk/assets/pubs/2017-icosahom16.pdf},
abstract = {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 \emph{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 \emph{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.}
}
High-fidelity simulation is only affordable if resolution goes where it is needed, and where that is usually cannot be known in advance. This paper makes the case for polynomial order that varies in space and time, coupled with suitable error estimators, as the requirement for applying spectral/hp element methods to complex industrial flow problems.
Abstract
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.