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Parallel Spectral Computations of Complex Engineering Flows
Published in Hojjat Adeli, Supercomputing in Engineering Analysis, 2020
George Em Karniadakis, Steven A. Orszag
Parallel implementation of monodomain spectral methods reduces to the problem of efficient implementation of a fast Fourier transform (FFT) if Fourier or Chebyshev expansion series are employed in the discretization. There have been many studies of parallel implementation of the multidimensional FFT especially due to its importance also in other areas such as image and signal processing (Champerlain, 1988). While it is possible in principle to rearrange the data so that all operations in the transforms being performed locally (Chu, 1987), in practice an alternative approach is taken where one or two dimensions are handled in parallel for vectors distributed across processors while serial FFTs are performed for the nondistributed data. Preliminary results of a Fourier pseudospectral discretization implemented on a 1024-node hypercube for a 1283 direct simulation of homogeneous turbulence were obtained at an efficiency of about 80% (Pelz, 1990a). Similar performances can be achieved also for the Chebyshev pseudospectral method employing FFTs and efficient recursive relations (Pelz, 1990b).
A multidomain multigrid pseudospectral method for incompressible flows
Published in Numerical Heat Transfer, Part B: Fundamentals, 2018
Wenqian Chen, Yaping Ju, Chuhua Zhang
As a kind of collocation method, the Chebyshev pseudospectral method forces the numerical solution to satisfy the governing equations exactly at collocation points. Therefore, by substituting Eqs. (7)–(12) into Eq. (2), we have the semi-discretized equations for Eq. (2) and denote them as: where, is the residual of Eq. (2).
Environmental benefits in terms of fuel efficiency and noise when introducing continuous climb operations as part of terminal airspace operation
Published in International Journal of Sustainable Transportation, 2020
Manuel Villegas Díaz, Victor Fernando Gómez Comendador, Javier García-Heras Carretero, Rosa María Arnaldo Valdés
The previously described trajectory optimization problem has been solved through Chebyshev Pseudospectral method. This method has been hand-tailored and implemented in AMPL Modeling Language (2013), for an Airbus A330 aircraft using IPOPT as NLP solver. AMPL is an algebraic modeling system for mathematical programing of large-scale optimization problems. A solver is defined as the number-crunching algorithm that computes optimal solutions.