Time-Spectral Rotorcraft Simulations on Overset Grids

Leffell, Joshua I.; Murman, Scott M.; Pulliam, Thomas H.

doi:10.2514/6.2014-3258

Cited by 6 publications

(5 citation statements)

References 38 publications

(45 reference statements)

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“…with y = y initial + ∆y (27) Here [DD T S ] and [D T S ] are the matrices containing the time-spectral coefficients for the second and firstorder derivative terms of y, respectively, and y initial is the initial value for y. Applying the same idea used previously in the approximate factorization algorithm, ∆y can be found by taking equation (26) to the frequency domain. Therefore the system of coupled equations changes to N decoupled equations since the spectral matrices are strictly diagonal in the frequency domain.…”

Section: Iiib Second-order Derivative Problem Resultsmentioning

confidence: 99%

“…Here ∆τ denotes the pseudo-time step, J refers to the Jacobian of the spatial discretization, and [D T S ] corresponds to the matrix of the time-spectral coefficients d j n as defined in equation (12). Approximate factorization is an efficient algorithm that factors the Jacobian into the following form: 4,12,25,26 [A]…”

Section: Iid Approximate Factorization Algorithmmentioning

confidence: 99%

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An Order N log ₂(N) Parallel Solver for Time Spectral Problems

Ramezanian

Mavriplis

2017

55th AIAA Aerospace Sciences Meeting

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The time-spectral (TS) method is a fast and efficient scheme for computing the solution to temporal periodic problems. Compared to traditional backward difference timeimplicit methods, time-spectral methods incur significant computational savings by taking advantage of the temporal Fourier representation of the time discretization. However, the computational cost for current time-spectral solver implementations, which are based on the discrete Fourier transform (DFT), scales as O(N 2) where N represents the number of time instances. For parallel implementations, where each time instance is assigned to an individual processor, the wall clock time necessary to converge time-spectral solutions is of order O(N), whereas, the wall clock time for an optimal solver in this weak scaling approach is expected to be on the order of O(1). The present paper is focused on making the current TS method more efficient by reducing the computational cost to O(N log 2 N) for even and O(2N log 3 N) for odd numbers of samples (where N is a power of 3) and hence for parallel implementations, achieving a wall clock time on the order of O(log 2 N) for even and O(log 3 N) for odd numbers of samples. This is achieved by developing a parallel fast Fourier transform (FFT) implementation instead of the current discrete Fourier transform approach for evaluating and solving the temporal derivative terms, which significantly decreases the computational cost and results in notably shorter wall clock time.

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Section: Iiib Second-order Derivative Problem Resultsmentioning

confidence: 99%

Section: Iid Approximate Factorization Algorithmmentioning

confidence: 99%

An Order N log ₂(N) Parallel Solver for Time Spectral Problems

Ramezanian

Mavriplis

2017

55th AIAA Aerospace Sciences Meeting

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“…The TS operator is purely imaginary so we have focused initially on undamped central difference operators; it has been shown that temporal dissipation has been successful for TS applications [44][45][46] so finitedifference-based temporal artificial dissipation will be explored as part of future work in addition to one-sided circulant differentiation operators (e.g. BDF2).…”

Section: Finite Difference Methods In Time (Fdmt)mentioning

confidence: 99%

“…In the current work, this involves wrapping the spatial residual evaluation routines (solver.rhs()) and implicit inversion operation (solver.lhs()) that can be called from the high-level Python controller. The space-time approximate factorization approach [45][46][47][55][56][57] effectively decouples the implicit solutions of the spatial and temporal systems providing a straightforward implementation of the standalone PinT module; the spatial residual is passed from the flow solver(s) to the PinT module, which performs the necessary temporal coupling (e.g.…”

Section: Vb Python-based Infrastructurementioning

confidence: 99%

“…Figure 4 plots instantaneous streamwise momentum, ρu, computed with the BDF2 scheme in addition to the discrete solution values of Time-Spectral calculations for N ∈ {3, 5, 9, 17, 33}; reconstructions of the TS solutions are plotted as curves in the corresponding color. The high-frequency signal transferred from the blade passages poses resolution problems for the TS calculations, as discussed in [45,46], including the N = 33 case that exhibits significant Gibbs' phenomenon. This is demonstrated further in Fig.…”

Section: Via Nrel Phase VI Wind Turbinementioning

confidence: 99%

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Towards Efficient Parallel-in-Time Simulation of Periodic Flows

Leffell

Sitaraman

Lakshminarayan

et al. 2016

54th AIAA Aerospace Sciences Meeting

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In response to the stagnation of computer microprocessor speeds over the past decade, the design emphasis of novel supercomputing architectures has focused primarily on increasing the overall number of available cores and reducing communication bottlenecks. Typically, flow solvers have been able to achieve parallel efficiency using domain decomposition, but this approach has the natural limitation that saturation will manifest itself on a finite number of cores at which point parallel speedup stalls and eventually deteriorates. In order to improve parallel scalability we seek to leverage the existing knowledge base on spatial decomposition, while attempting to exploit additional parallelism in the temporal dimension. Specifically, we explore the case of time periodic flows using Parallel-in-Time (PinT) variants of the Time-Spectral (TS) method. A framework employing a Pythonbased infrastructure is described including a standalone library that can be coupled to existing flow solvers in order to facilitate PinT calculations. A model problem of a periodic density pulse is used to examine the different discretization options. Implications for application to wind turbines and rotors are addressed.

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