Comparison of the convergence rates between Fourier pseudo-spectral and finite volume method using Taylor-Green vortex problem

Nascimento, Andreia Aoyagui; Mariano, Felipe Pamplona; Padilla, Elie Luis Martínez; Neto, Aristeu da Silveira

doi:10.1007/s40430-020-02570-5

Cited by 7 publications

(8 citation statements)

References 22 publications

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“…A synthesised or manufactured solution was used to determine a source term, thereby giving an analytical solution to the velocity and pressure fields. This source term, which has dimensions of [N/m 3 ] , is added to the Navier-Stokes equations, which has a numerical solution that can be compared with the synthesised solution [20]. The following equations, proposed by [35], are used in the present work:…”

Section: Manufactured Solutionmentioning

confidence: 99%

“…The listed works that have the purpose of evaluating some specific numerical and/or computational aspect in IMERSPEC methodology [20] are compared the analysis of convergence orders and computational times between the pseudo-spectral Fourier method and the finite volume method. In [21,22] is presented the development of the insertion of three different boundary conditions, using the immersed boundary method, particularly to thermal flow problems.…”

Section: Introductionmentioning

confidence: 99%

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An improved immersed boundary method by coupling of the multi-direct forcing and Fourier pseudo-spectral methods

Mariano

Moreira

Nascimento

et al. 2022

J Braz. Soc. Mech. Sci. Eng.

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The present paper aims to report an improve on the development of the IMERSPEC methodology, which is a methodology that couples the Fourier pseudo-spectral and immersed boundary methods, which can now solve flows over complex geometries. In the present work, the Lagrangian mesh that represents the immersed body inside the flow does not have to coincide with the Eulerian mesh. Furthermore, a high accuracy for the resultant methodology is achieved. These two important improvements arise from the development of the multi-direct forcing method and used to calculate the force field of the immersed boundary method. In order to verify the IMERSPEC methodology, a manufactured solution technique was used. The results of a refined mesh were employed, and different distribution and interpolation functions were used and analysed. Finally, flows over a backward-facing step geometry were simulated in two dimensions. This type of flow presents several physical features, for example, detachment and reattachment of the boundary layer and vortex generation, which are difficult to capture using numerical solutions. A comparison with the experimental data is presented and shows that the IMERSPEC methodology is promising for computational fluid dynamics applications and its analysis.

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Section: Manufactured Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An improved immersed boundary method by coupling of the multi-direct forcing and Fourier pseudo-spectral methods

Mariano

Moreira

Nascimento

et al. 2022

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

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“…[17,18] f i x ! , t is the external force exerted on the flow field due to the mutual interaction force between the fluid and the immersed boundaryexpressed as follows [20][21][22] :…”

Section: Mathematical Modelmentioning

confidence: 99%

Large‐eddy simulation of downhole flow: The effects of flow and rotation rates

et al. 2021

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The present paper concerns large-eddy simulations of turbulent downhole flow for six Reynolds numbers and five Taylor numbers. Swirl parameter within the range (0-0.98), which compares the effects of the rotation and the flow rates, was evaluated. In this work, the fluid is injected through the drill pipe and then accelerated by the nozzle. As the fluid discharges from the nozzle, a high speed jet is generated in the downhole region, the fluid then impinges the bottomhole surface and finally flows out the downhole region through the annulus. The nozzle is represented by a sudden contraction. The dynamic subgrid scale model has been used to calculate the turbulent viscosity. The immersed boundary method is employed to represent the solid walls of the proposed geometry. Coherent structures appear as spiral rolls into the nozzle and their inclination angles depend on the rotational speed. When the rotational speed increases, these structures are more aligned with the tangential direction. Due to the geometry of the problem, a toroidal vortex takes place and it grows as the Reynolds number increases. The magnitude of the velocity fluctuations increase in the jet region and near the sidewall with increasing flow rate; it also increased in the jet region with increasing rotational speeds.The impact force and the peak pressure on the impacted surface increases with increasing flow rates. Good agreement of the impact force with other works supports the present work methodology.

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“…In this work, IBM is also utilized to model the structure of the cylinder immersed in the flow, enabling the representation of its structural movement. In [36] the authors presented the verification of the IMERSPEC using the multi-direct forcing [59], by using the manufactured solution proposed by Taylor and Green [56]. In aforementioned study, the authors note the high accuracy of the spectral method and address the influence when using the coupling with the IBM with two different interpolation and distribution functions.…”

Section: Introductionmentioning

confidence: 99%

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

Nascimento,

Mariano,

da Silveira Neto

et al. 2024

J Braz. Soc. Mech. Sci. Eng.

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The current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E($$-9$$ - 9 ) to 1E($$-3$$ - 3 ). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.

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Comparison of the convergence rates between Fourier pseudo-spectral and finite volume method using Taylor-Green vortex problem

Cited by 7 publications

References 22 publications

An improved immersed boundary method by coupling of the multi-direct forcing and Fourier pseudo-spectral methods

An improved immersed boundary method by coupling of the multi-direct forcing and Fourier pseudo-spectral methods

Large‐eddy simulation of downhole flow: The effects of flow and rotation rates

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

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