Conjugate filters with spectral-like resolution for 2D incompressible flows

Gu, Yun; Zhou, Y. C.; Wei, Guannan

doi:10.1016/s0045-7930(02)00066-x

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…In this section, we solve a variety of benchmark problems 46‐52 to study the numerical accuracy and efficiency of the newly designed RK4‐based RPSM scheme. In the first subsection, we provide validation and comparison of different dealiasing schemes using the 2D Taylor Green (TG) vortex problem.…”

Section: Resultsmentioning

confidence: 99%

“…The shear layer between the vortical structures gradually stretches and turn into thinner flow structures as time progresses which is a challenge for any numerical scheme. The initial conditions for the quad shear layer problem are given as 49

u false(x, y false) = \{\begin{matrix} \tanh {(y prefix- π false/ 4) false/ ρ}, & y \leq π false/ 2, \\ \tanh {(3 π false/ 4 prefix- y) false/ ρ}, & π false/ 2 < y \leq π, \\ \tanh {(y prefix- 5 π false/ 4) false/ ρ}, & π < y \leq 3 π false/ 2, \\ \tanh {(7 π false/ 4 prefix- y) false/ ρ}, & y > 3 π false/ 2, \end{matrix}

v false(x, y false) = δ \sin false(2 x false)

Here,

ρ

and

δ

denote the shear layer thickness and perturbation amplitude, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…The 2D Euler equations are studied using a doubly periodic domain

x, y \in false[0, 2 π false] \times false[0, 2 π false]

with sharply varying hyperbolic tangent initial conditions in the velocity field as mentioned in the previous studies 1,47‐49,55,56 for different spatial resolutions

false(N = 32, 64, 128, 256, 512, 1024 & 2048 false)

. It is the only test case where the effect of spatial resolution is explored in conjunction with various dealiasing schemes.…”

Section: Resultsmentioning

confidence: 99%

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An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

Sinhababu

Ayyalasomayajula

2020

Numerical Methods in Fluids

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Summary In this paper, the Random Phase Shift Method (RPSM) dealiasing scheme has been developed with the classical fourth‐order explicit Runge‐Kutta (RK4) method. This scheme is implemented in different benchmark problems to verify its numerical accuracy and computational efficiency where strong gradients are present in the solution. The propagation of aliasing errors through the substeps of RK4 is derived to show the existence of the residual aliasing error terms which results in mild smoothing effect without dissipating the small‐scale flow structures. Smoothness and numerical stability in the solutions obtained from the RPSM scheme also remain well preserved even at under‐resolved conditions. Numerical results agree well with the analytical and the computed solutions from previous studies. RPSM scheme shows a slight delay in the formation of numerical singularity for the inviscid flows but the filtering‐based schemes suffer from early blow‐up problem. We observe that this scheme displays better resolving ability than higher‐order exponential smoothing spectral filter scheme in capturing the strong fronts accurately even at just resolved spatial grid resolutions. Three‐dimensional truncation‐based dealiasing scheme, spherical truncation (SPT) shows vortices generated due to the parasitic currents in the solution of the inviscid three‐dimensional Taylor Green (TG) vortex flows. RPSM displays only the accurate isocontours of vortical field at nearly same computational expenses as the SPT scheme.

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Section: Resultsmentioning

confidence: 99%

u false(x, y false) = \{\begin{matrix} \tanh {(y prefix- π false/ 4) false/ ρ}, & y \leq π false/ 2, \\ \tanh {(3 π false/ 4 prefix- y) false/ ρ}, & π false/ 2 < y \leq π, \\ \tanh {(y prefix- 5 π false/ 4) false/ ρ}, & π < y \leq 3 π false/ 2, \\ \tanh {(7 π false/ 4 prefix- y) false/ ρ}, & y > 3 π false/ 2, \end{matrix}

v false(x, y false) = δ \sin false(2 x false)

Here,

ρ

and

δ

denote the shear layer thickness and perturbation amplitude, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…The 2D Euler equations are studied using a doubly periodic domain

x, y \in false[0, 2 π false] \times false[0, 2 π false]

with sharply varying hyperbolic tangent initial conditions in the velocity field as mentioned in the previous studies 1,47‐49,55,56 for different spatial resolutions

false(N = 32, 64, 128, 256, 512, 1024 & 2048 false)

. It is the only test case where the effect of spatial resolution is explored in conjunction with various dealiasing schemes.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

Sinhababu

Ayyalasomayajula

2020

Numerical Methods in Fluids

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show abstract

Accuracy and computational efficiency of dealiasing schemes for the DNS of under resolved flows with strong gradients

Sinhababu

Ayyalasomayajula

2021

Mathematics and Computers in Simulation

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Simulation of Inviscid Compressible Flows Using PDE Transform

Yang

Guo³

2014

Commun. comput. phys.

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The solution of systems of hyperbolic conservation laws remains an interesting and challenging task due to the diversity of physical origins and complexity of the physical situations. The present work introduces the use of the partial differential equation (PDE) transform, paired with the Fourier pseudospectral method (FPM), as a new approach for hyperbolic conservation law problems. The PDE transform, based on the scheme of adaptive high order evolution PDEs, has recently been applied to decompose signals, images, surfaces and data to various target functional mode functions such as trend, edge, texture, feature, trait, noise, etc. Like wavelet transform, the PDE transform has controllable time-frequency localization and perfect reconstruction. A fast PDE transform implemented by the fast Fourier Transform (FFT) is introduced to avoid stability constraint of integrating high order PDEs. The parameters of the PDE transform are adaptively computed to optimize the weighted total variation during the time integration of conservation law equations. A variety of standard benchmark problems of hyperbolic conservation laws is employed to systematically validate the performance of the present PDE transform based FPM. The impact of two PDE transform parameters, i.e., the highest order and the propagation time, is carefully studied to deliver the best effect of suppressing Gibbs’ oscillations. The PDE orders of 2-6 are used for hyperbolic conservation laws of low oscillatory solutions, while the PDE orders of 8-12 are often required for problems involving highly oscillatory solutions, such as shock-entropy wave interactions. The present results are compared with those in the literature. It is found that the present approach not only works well for problems that favor low order shock capturing schemes, but also exhibits superb behavior for problems that require the use of high order shock capturing methods.

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Conjugate filters with spectral-like resolution for 2D incompressible flows

Cited by 3 publications

References 17 publications

An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

An improved dealiasing scheme for the fourth‐order Runge‐Kutta method: Formulation, accuracy and efficiency analysis

Accuracy and computational efficiency of dealiasing schemes for the DNS of under resolved flows with strong gradients

Simulation of Inviscid Compressible Flows Using PDE Transform

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