Spectral Properties of High-Order Element Types for Implicit Large Eddy Simulation
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Spectral Properties of High-Order Element Types for Implicit Large Eddy Simulation Carlos A. Pereira1
· Brian C. Vermeire1
Received: 25 November 2019 / Revised: 13 May 2020 / Accepted: 1 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The use of high-order schemes continues to increase, with current methods becoming more robust and reliable. The resolution of complex turbulent flows using Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) can be computed more efficiently with high-order methods such as the Flux Reconstruction approach. We make use of the implicit form of LES, referred to as ILES, in which the numerical dissipation of the spatial scheme passively filters high-frequency modes, and no subgrid-scale turbulence model is explicitly implemented. Therefore, given the inherent three-dimensional behaviour of turbulent flows, it is important to understand the spectral characteristics of spatial discretizations in three dimensions. The dispersion and dissipative properties of hexahedra, prismatic and tetrahedral element types are compared using Von Neumann analysis. This comparison is performed on a per degree of freedom basis to assess their suitability for ILES in terms of computational cost. We observe dispersion relations that display non-smooth behaviour for tetrahedral and prismatic elements. In addition, the periodicity of the dispersion relations in one dimension is generally not observed in three-dimensional configurations. Semilogarithmic plots of the numerical error are presented. We observe that the amount of numerical dissipation and dispersion added by hexahedral elements is the least, followed by prisms and finally tetrahedra. We validate our analysis comparing results obtained on computational domains with comparable computational cost against DNS data. Hexahedral elements have the best agreement with the reference data, followed by prismatic and finally tetrahedral elements, which is consistent with the spectral analysis. Keywords High-order methods · Flux reconstruction · Von Neumann analysis · Element types
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Carlos A. Pereira [email protected] Brian C. Vermeire [email protected]
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Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QC, Canada 0123456789().: V,-vol
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48
Page 2 of 38
Journal of Scientific Computing
(2020) 85:48
1 Introduction Advances in high-order methods continue to enable accurate and robust simulations of turbulent flows. Complex phenomena can be more efficiently captured with high accuracy compared to current industry-adopted low-order schemes, which often fail to accurately model complex turbulent flows due to their relatively high numerical error. Hence, highorder schemes are often more suitable for Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). They can be applied to a wide range of fields of importance, such as computational fluid dynamics, aeroacoustics and other wave propagation phenomena. Some schemes current
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