Comparison of artificial-dissipation and solution-filtering stabilization schemes for time-accurate simulations

Edoh, Ayaboe; Mundis, Nathan L.; Merkle, Charles L.; Karagozian, Ann; Sankaran, Venkateswaran

doi:10.1016/j.jcp.2018.08.019

Cited by 21 publications

(9 citation statements)

References 29 publications

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“…with = 1 recovering the divergence (Div) representation and = 1∕2 giving the quasi skew-symmetric (SS) form of Feiereisen et al 27 (which also yields discretely consistent spatial representations for the transport of secondary conservation quantities, 15,16 2 ). Meanwhile the tunable attenuation is employed as filter-based AD 12 in order to achieve temporally consistent numerical damping (note: temporally-consistent solution filtering procedures would also be appropriate 12,28,29 ). The numerical dissipation then contributes to the original residual equation as…”

Section: Computational Resultsmentioning

confidence: 99%

“…The convective terms are considered in a quadratically split form

\begin{align} \partial_{x_{j}} ρ u_{j} ϕ prefix\approx α \cdot δ_{x_{j}} ρ u_{j} ϕ + false(1 prefix- α false) \cdot ((), ρ u_{j} δ_{x_{j}} ϕ + ϕ δ_{x_{j}} ρ u_{j}), \end{align}

with α=1 recovering the divergence (Div) representation and α=1/2 giving the quasi skew‐symmetric (SS) form of Feiereisen et al 27 (which also yields discretely consistent spatial representations for the transport of secondary conservation quantities, 15,16 ρ ϕ 2 ). Meanwhile the tunable attenuation is employed as filter‐based AD 12 in order to achieve temporally consistent numerical damping (note: temporally‐consistent solution filtering procedures would also be appropriate 12,28,29 ). The numerical dissipation then contributes to the original residual equation as

\begin{align} \partial_{t} boldQ = R_{o} false(boldQ false) + true \sum_{i}^{n D i m} R_{i, AD} false(boldQ false), \end{align}

where the directional damping is scaled by an appropriate velocity scale (eg, the acoustic speed) for dimensional consistency with the equations:

\begin{align} R_{i, AD} false(boldQ false) = {boldQ}_{i}^{''} such that ([], 1 + true \sum_{ℓ = 1}^{L} ϵ_{IF, 2 ℓ} false(Δ x_{i} fal...) \end{align}

…”

Section: Computational Resultsmentioning

confidence: 99%

“…It may be possible to tune the response without affecting a baseline conditioning by simply rescaling the dissipative component of the filter. 12 This results in employing ′ EF,2r = ⋅ EF,2r + (1 − ) ⋅ IF,2 , with ≤ 1 for monotonically increasing dissipation. This choice, however, will impact the amount of attenuation administered at the smallest scales, as is typically the case when tuning explicit filters.…”

Section: A Concerted Assembly Of Scheme Componentsmentioning

confidence: 99%

“…The construction of dissipative schemes with customizable attenuation is well understood within the context of discrete filters 11 and has previously been extended to artificial dissipation (AD) and temporally consistent solution filtering frameworks for time-accurate use. 12 By selecting formulations that are tunable and scale-discriminant, it is possible to effectively restrict the numerical dissipation to the high-wavenumber range of aliased modes-thus hindering the possibility of such errors being reflected back into the range of nonaliased content. Such selective attenuation could simultaneously be used to reduce the presence of linear phase errors, which are typically more pronounced at smaller scales (ie, high wavenumbers).…”

Section: Introductionmentioning

confidence: 99%

“…The ability to maintain a strict segregation of aliased content as initially proposed by Orszag requires spectrally sharp filtering, which then calls for proper numerical damping procedures in the case of nodal‐based methods. The construction of dissipative schemes with customizable attenuation is well understood within the context of discrete filters 11 and has previously been extended to artificial dissipation (AD) and temporally consistent solution filtering frameworks for time‐accurate use 12 . By selecting formulations that are tunable and scale‐discriminant, it is possible to effectively restrict the numerical dissipation to the high‐wavenumber range of aliased modes—thus hindering the possibility of such errors being reflected back into the range of nonaliased content.…”

Section: Introductionmentioning

confidence: 99%

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Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations

Edoh

Mundis

Karagozian

et al. 2020

Numerical Methods in Fluids

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The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.

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