Matrix extraction technique for global stability of compressible flows and applications

The derivation of the linearized operator for large-scale flow problems is a cumbersome and error-prone task, especially regarding the adjoint. The complexity of compressible direct numerical simulations and the use of high-order discretizations complicate the application of efficient procedures. Nevertheless, both operators are at the core of numerous algorithms for quantitative flow analysis; thus providing access to them is of great practical interest. A novel algorithm based on a divide and conquer strategy for the extraction and evaluation of the linearized operators, from a nonlinear flow solver, is presented. This technique is demonstrated on an existing compressible flow solver and validated by the computation of global modes in a spatially developing boundary layer. Finally, potential applications will be illustrated by the computation of the most unstable direct and adjoint global modes in the flow around an airfoil. Copyright © 2011 by the author(s).