An Algorithm for the Recovery of 2- and 3-D BiGlobal Instabilities of Compressible Flow Over 2-D Open Cavities

Abstract

The identification of numerical residuals from direct numerical simulations (DNS) with the least-damped BiGlobal eigenmodes of an underlying steady-state permits extraction of both the steady-state and amplitude functions of the BiGlobal eigenmodes from simple algebraic operations. Algorithms for the calculation of the basic state and the spatial structure of the related BiGlobal eigenmodes from transient DNS data have been constructed and presented. Here we extend initial calculations for the (closed) incompressible lid-driven cavity to the related (compressible) open-cavity flow. Order-of-magnitude savings are demonstrated when using of the discussed algorithm for the calculation of the basic state, compared with straightforward time-integration of the equations of motion until convergence in time. Further, employing this algorithm, different classes of instabilities in the open cavity are unified in the framework of BiGlobal instability analysis.

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