Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes

Cox, Christopher; Trojak, Will; Dzanic, Tarik; Witherden, Freddie D.; Jameson, Antony

doi:10.1016/j.compfluid.2021.104922

Cited by 29 publications

(32 citation statements)

References 59 publications

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“…When switching to the high-order method, the results of the URDNS approach degraded, with large oscillations observed in the variance profiles. This effect can likely be attributed to aliasing-driven instabilities evident in high-order approximations of under-resolved turbulent flows, which can introduce spurious high-frequency oscillations in the flow that are more evident in higher-order statistics [30]. When using the high-order method for the PANS approach, this effect was not seen, likely due to the suppression of aliasing errors as a result of the introduction of a physically appropriate eddy viscosity.…”

Section: Periodic Hillmentioning

confidence: 99%

Partially-Averaged Navier-Stokes Simulations of Turbulence Within a High-Order Flux Reconstruction Framework

Dzanic,

Girimaji,

Witherden

2021

Preprint

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High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this work is to develop the combination of these methods and analyze the effects of high-order discretizations on hybrid turbulence models, particularly with respect the optimal model parameters and the relative accuracy benefits compared to approaches such as under-resolved direct numerical simulation (URDNS). We employ the Partially-Averaged Navier-Stokes (PANS) approach using the flux reconstruction scheme on the flow around a periodic hill and the wake flow of a circular cylinder at a Reynolds number of 3900, the latter of which we provide direct numerical simulation results and novel statistical analysis. By increasing the order of the discretization while fixing the total degrees of freedom, it was observed that larger improvements in the prediction of the statistics and flow physics were generally seen with PANS than URDNS. Furthermore, less sensitivity to the resolution-control parameter was observed with a high-order discretization, indicating that high-order discretizations may be an effective approach for increasing the accuracy and reliability of hybrid turbulence models for scale-resolving simulations without a significant increase in computational effort.

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Section: Periodic Hillmentioning

confidence: 99%

Partially-Averaged Navier-Stokes Simulations of Turbulence Within a High-Order Flux Reconstruction Framework

Dzanic,

Girimaji,

Witherden

2021

Preprint

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“…In Eqs. (34)(35)(36), P U is the transformation matrix from conservative to characteristic variables usually expressed following:…”

Section: Wave Equationmentioning

confidence: 99%

“…Actually, in Liang et al [35], it was shown that FR is most efficient and DG is the slowest but in terms of accuracy DG is the best and FR is the worst. For both efficiency and accuracy the SD method stands in between whereas in a more recent study, Cox et al [36] stated that the SD method is more robust and accurate than FR. This is very encouraging for pursuing the development of the SD method to simulate complex flows.…”

Section: Introductionmentioning

confidence: 95%

Extension of the Spectral Difference method to combustion

Marchal¹,

Deniau²,

Boussuge³

et al. 2021

Preprint

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A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier-Stokes equations (NSE) is presented. The classical SD algorithm is shown to be unstable when a multispecies gas where thermodynamic properties depend on temperature and species mass fractions is considered. In that case, a modification of the classical algorithm was successfully employed making it stable. It uses the fact that it is better for the multispecies case to compute primitive variables from conservative variables at solution points and then extrapolate them at flux points rather than extrapolating conservative variables at flux points and reconstruct primitive variables on these points. Characteristic, wall and symmetry boundary conditions for reactive flows in the SD framework are also introduced. They all use the polynomial form of the variables and of the fluxes to impose the correct boundary condition at a boundary flux point. Validation test cases on one-dimensional and two-dimensional laminar flames have been performed using both global chemistry and Analytically Reduced Chemistry (ARC). Results show excellent agreement with the reference combustion code AVBP validating the implementation of this SD method on laminar combustion.

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“…This method has become increasingly popular over the past decade, spawning further research in discontinuous high-order schemes. [39][40][41][42][43][44][45][46] Details on the current flow solver are provided in Cox et al [47][48][49] and Cox. 50 A grid spacing h and polynomial p convergence study was performed 12 where we found that a mesh containing a total of 69 888 hexahedral elements and a p = 4 Lagrange polynomial used to approximate the solution in each element provide ample spatial resolution (∼8.7M degrees of freedom) to converge the L 2 -norm of the error in the wall shear stress to within 0.78% and the velocity magnitude to within 0.25%.…”

Section: B Numerical Schemementioning

confidence: 99%

The effect of entrance flow development on vortex formation and wall shear stress in a curved artery model

Cox,

Plesniak

2021

Preprint

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We numerically investigate the effect of entrance condition on the spatial and temporal evolution of multiple threedimensional vortex pairs and wall shear stress distribution in a curved artery model. We perform this study using a Newtonian blood-analog fluid subjected to a pulsatile flow with two inflow conditions. The first flow condition is fully developed while the second condition is undeveloped (i.e. uniform). We discuss the connection along the axial direction between regions of organized vorticity observed at various cross-sections of the model and compare results between the different entrance conditions. We model a human artery with a simple, rigid 180 • curved pipe with circular cross-section and constant curvature, neglecting effects of taper, torsion and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver. The flow rate used in this study is physiological. We observe differences in secondary flow patterns, especially during the deceleration phase of the physiological waveform where multiple vortical structures of both Dean-type and Lyne-type coexist. We highlight the effect of the entrance condition on the formation of these structures and subsequent appearance of abnormal inner wall shear stresses-a potentially significant correlation since cardiovascular disease is known to progress along the inner wall of curved arteries under varying degrees of flow development.

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Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes

Cited by 29 publications

References 59 publications

Partially-Averaged Navier-Stokes Simulations of Turbulence Within a High-Order Flux Reconstruction Framework

Partially-Averaged Navier-Stokes Simulations of Turbulence Within a High-Order Flux Reconstruction Framework

Extension of the Spectral Difference method to combustion

The effect of entrance flow development on vortex formation and wall shear stress in a curved artery model

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