Performance and accuracy of hybridized flux reconstruction schemes

Pereira, Carlos A.; Vermeire, Brian C.

doi:10.1016/j.jcp.2022.111039

Cited by 4 publications

(4 citation statements)

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“…, where we have computed t pFR /t pHFR and t pFR /t pEFR , and p FR , p HFR and p EFR are the polynomial degrees of a given FR, HFR and EFR scheme. Consistent with previous observations [7], hybridized methods show increased performance benefits at higher polynomial degrees. However, by looking at the diagonals of these tables, where we compare equal polynomial degrees for the hybridized and standard formulations, we see that at least 1.26 faster simulations were achieved at p = 1.…”

Section: A Cylinder At Re=150supporting

confidence: 89%

“…with n k,f the physical outward unit normal vector and s a stabilization parameter [7], [11]. In contrast to standard FR formulations, where neighboring element information is used in the numerical flux, we have here introduced the so-called trace variable.…”

Section: The Hybridized Flux Reconstruction Schemementioning

confidence: 99%

“…Previous work on p-adaptive hybridizable methods [8]- [10] has focused on the HDG method where the trace variable is allowed to be globally discontinuous. In our previous work [7], we have shown that the EFR method is in fact competitive in terms of efficiency. The objective of this paper is to introduce p-adaptation in the context of hybridized flux reconstruction schemes and to compare their performance against p-uniform and p-adaptive standard FR discretizations.…”

Section: Introductionmentioning

confidence: 95%

“…The scaling of the hybridized global system is (p + 1) d−1 . The hybridization approach has been recently extended to the family of Flux Reconstruction schemes by Pereira et al [7]. Specifically, the hybridized flux reconstruction (HFR) method and embedded flux reconstruction (EFR) method have been shown to significantly speed up numerical computations for a series of conservation laws.…”

Section: Introductionmentioning

confidence: 99%

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Hybridization of a polynomial adaptive high-order solver for unsteady compressible flows

Pereira,

Vermeire

2023

Progress in Canadian Mechanical Engineering. Volume 6

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We present p-adaptive hybridized flux reconstruction schemes to reduce the computational cost of implicit discretizations using a nondimensional vorticity indicator. At each adaptation level, we apply a projection operation to the new space based on the element-wise projected solution and the transmission conditions. We validate our implementation and analyze performance via numerical examples. Specifically, we show that p-adaptation of hybridizable flux reconstruction (HFR) methods results in comparable numerical error to standard p-adaptive and p-uniform standard flux reconstruction (FR) discretizations with a fraction of degrees of freedom. Performance results for a cylinder at Re = 150 showcase speedup factors in excess of 6 for hybridized methods in comparison with p-adaptive standard FR schemes, and up to 40 compared to p-uniform FR discretizations. Similarly, results for a NACA 0012 airfoil at Re = 10, 000 demonstrate speedup factors close to 6 compared to p-adaptive FR discretizations, and up to 33 compared to p-uniform conventional FR. Hence, combinining hybridization with adaptation yields a significant reduction in computatonal cost compared to conventional implicit discretizations.

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Section: A Cylinder At Re=150supporting

confidence: 89%

Section: The Hybridized Flux Reconstruction Schemementioning

confidence: 99%