Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 253, Issue -, Pages 287-304Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2012.09.014
Keywords
Global linear flow instability analysis; High-order finite-differences; Large-scale eigenvalue problems; Sparse linear algebra
Funding
- Spanish Ministry of Science and Innovation [MICINN-TRA2009-13648]
- Air Force Office of Scientific Research, Air Force Material Command, USAF [FA8655-12-1-2004]
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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 Pade finite-difference schemes, as well as the Summation-by-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 O(10(4)). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort. (C) 2012 Elsevier B.V. All rights reserved.
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