%0 Conference Paper
%A Paredes Gonzalez, Pedro
%A Theofilis, Vassilios
%A Rodríguez Álvarez, Daniel
%A Tendero Ventanas, Juan Angel
%B 6th AIAA Theoretical Fluid Mechanics Conference
%C Honolulu, Hawaii, USA
%D 2011
%F upm:13082
%I AIAA
%P 0-0
%T The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension
%U http://oa.upm.es/13082/
%X The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order ﬁnitediﬀerence-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of eﬃciency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity oﬀered by the ﬁnite-diﬀerence scheme and, as expected, is shown to perform substantially more eﬃciently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the ﬂow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic ﬂow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional ﬂow composed of a counter-rotating pair of nonparallel Batchelor vortices.