A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

Merrill, Brandon; Peet, Yulia; Lottes, James

doi:10.1016/j.jcp.2015.11.057

Cited by 34 publications

(39 citation statements)

References 72 publications

(161 reference statements)

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“…Typically three to five subiterations (κ iter ) are needed per timestep to ensure stability [24] for mthorder extrapolation of the interface boundary data, when m > 1. Using this approach, Merrill et al [21] demonstrated exponential convergence in space and up to third-order accuracy in time for Schwarz-SEM flow applications.…”

Section: Sem-schwarz For Navier-stokesmentioning

confidence: 99%

Nonconforming Schwarz-spectral element methods for incompressible flow

2019

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We present scalable implementations of spectral-element-based Schwarz overlapping (overset) methods for the incompressible Navier-Stokes (NS) equations. Our SEM-based overset grid method is implemented at the level of the NS equations, which are advanced independently within separate subdomains using interdomain velocity and pressure boundarydata exchanges at each timestep or sub-timestep. Central to this implementation is a general, robust, and scalable interpolation routine, gslib-findpts, that rapidly determines the computational coordinates (processor p, element number e, and local coordinates (r, s, t) ∈Ω := [−1, 1] 3 ) for any arbitrary point x * = (x * , y * , z * ) ∈ Ω ⊂ lR 3 . The communication kernels in gslib execute with at most log P complexity for P MPI ranks, have scaled to P > 10 6 , and obviate the need for development of any additional MPI-based code for the Schwarz implementation. The original interpolation routine has been extended to account for multiple overlapping domains. The new implementation discriminates the possessing subdomain by distance to the domain boundary, such that the interface boundary data is taken from the inner-most interior points. We present application of this approach to several heat transfer and fluid dynamic problems, discuss the computation/communication complexity and accuracy of the approach, and present performance measurements for P > 12, 000.

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Section: Sem-schwarz For Navier-stokesmentioning

confidence: 99%

Nonconforming Schwarz-spectral element methods for incompressible flow

2019

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“…To avoid the aforementioned deficiencies associated with synthetic or recycling turbulence generation approaches, we, as in experimental study of Chen and Choa [29], place a small cylinder upstream of a pitching airfoil and directly compute the turbulent wake shed by the cylinder, in a fully coupled manner with the pitching airfoil simulations. These novel simulations are possible due to our recently developed moving overlapping grid methodology in a spectral-element method that features spectral accuracy in space and high-order accuracy in time and is well suited for high-fidelity simulations on moving domains [44][45][46].…”

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confidence: 99%

Effect of Impinging Wake Turbulence on the Dynamic Stall of a Pitching Airfoil

Merrill

Peet

2017

AIAA Journal

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Dynamically moving airfoils are encountered in helicopter rotors, wind-turbine blades, and maneuvering aircraft. A clearer understanding of how freestream disturbances affect the aerodynamic forces on pitching airfoils leads to improved designs. In the present study, the authors' recently validated spectrally accurate moving overlapping mesh methodology is used to perform a direct numerical simulation of a NACA 0012 airfoil pitching with oscillatory motion in the presence of a turbulent wake created by an upstream solid cylinder. The global computational domain is decomposed into a stationary background mesh, which contains the solid cylinder, and a mesh constructed around the airfoil that is constrained to pitch with predetermined reduced frequency k 0.16. Present simulations are performed with chord-based Reynolds number Re c 44;000. Aerodynamic forces and vortex-shedding properties are compared between the pitching airfoil simulations with and without upstream disturbances. Power spectral density functions of the aerodynamic forces and moments are investigated to further determine the effect of a turbulent wake on a pitching airfoil.

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“…The variation in the wind direction (wind veering -geophysical effect) can also be incorporated quite easily during the spectral interpolation of the inflow condition using stationary overlapping mesh methodology. 24 Ideally, variation in the wind direction should be incorporated by rotating the whole precursor simulation domain; however, since variation of wind direction from LIDAR scans is within ±6 • (See Figure 4d), we rotate only the inflow vector (u, v velocities) instead of rotating the whole precursor domain. This allows us to save significantly on the computational cost that would be associated with remeshing and interpolation at every timestep, in the setting of the moving domain of the precursor simulation.…”

Section: Iiib a Splitting Scheme For Incorporation Of Geophysical Ementioning

confidence: 99%

Incorporating realistic geophysical effects of mean wind from LIDAR measurements in Large Eddy Simulation of Wind Turbine Arrays

Chatterjee

Cherukuru

Peet³

et al. 2017

35th Wind Energy Symposium

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The present paper aims at performing Large Eddy Simulation of a 3 × 3 wind turbine array in atmospheric boundary layer, by incorporating realistic large scale geophysical effects, such as the variation in mean wind flux (gusts) and wind direction (wind veer) from the data obtained by field measurements. The purpose of this study is to understand the effect of realistic winds on turbulence and wake interactions, and also on the power generated by the wind turbines. The wind turbines are modelled using a state-of-theart reduced order actuator line (AL) model, which is computationally more efficient than resolving the blades of the turbine. The inflow conditions are generated by spectrally interpolating the data from a precursor Atmospheric Boundary Layer (ABL) simulation and incorporating the geophysical effects obtained from LIDAR scans to adjust the wind flux and wind direction from the precursor simulations, as appropriate. Additionally, we also present a comparison of the above approach with an LES performed with a standard turbulent inflow to further understand the influence of the geophysical effects on large-scale coherence and subsequently on wind power. Furthermore, the knowledge of the influence of geophysical effects in a long term is expected to improve decision making capabilities in wind farm optimization algorithms and contribute to the design and validation of data assimilation algorithms.

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A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

Cited by 34 publications

References 72 publications

Nonconforming Schwarz-spectral element methods for incompressible flow

Nonconforming Schwarz-spectral element methods for incompressible flow

Effect of Impinging Wake Turbulence on the Dynamic Stall of a Pitching Airfoil

Incorporating realistic geophysical effects of mean wind from LIDAR measurements in Large Eddy Simulation of Wind Turbine Arrays

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