TY - JOUR
EP - 304
KW - Global linear flow instability analysis High-order finite-differences Large-scale eigenvalue problems Sparse linear algebra
SP - 287
JF - Computer Methods in Applied Mechanics and Engineering
UR - http://www.sciencedirect.com/science/article/pii/S0045782512002964
VL - 253
AV - public
A1 - Paredes Gonzalez, Pedro
A1 - Hermanns Navarro, Miguel
A1 - Le Clainche Martínez, Soledad
A1 - Theofilis, Vassilios
Y1 - 2013/01//
SN - 0045-7825
TI - Order 10 4 speedup in global linear instability analysis using matrix formation
N2 - A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric 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 Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q 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, FD-q spatial discretization delivering a speedup of đ (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.
ID - upm19104
PB - Elsevier
ER -