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Paredes Gonzalez
Pedro

Hermanns Navarro
Miguel

Le Clainche Martínez
Soledad

Theofilis
Vassilios
Order 10 4 speedup in global linear instability analysis using matrix formation
pub
 mecanica
Global linear flow instability analysis Highorder finitedifferences Largescale eigenvalue problems Sparse linear algebra
A unified solution framework is presented for one, two or threedimensional complex nonsymmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the ChebyshevGaussLobatto (CGL) points and a suite of highorder finitedifference methods comprising the previously employed for this type of work DispersionRelationPreserving (DRP) and Padé finitedifference schemes, as well as the Summationby parts (SBP) and the new highorder finitedifference scheme of order q (FDq) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FDq method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FDq spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the threedimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.
201301
published
Elsevier
http://www.sciencedirect.com/science/article/pii/S0045782512002964
10.1016/j.cma.2012.09.014
public
Computer Methods in Applied Mechanics and Engineering
253
287304
Aeronauticos
Motopropulsion
TRUE
00457825
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