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Direct optimal growth analysis for timesteppers. (English) Zbl 1144.76044
Summary: Methods are described for transient growth analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to vary slowly in the streamwise direction. Emphasis is on capturing the global effects arising from localized convective stability in streamwise-varying flows. The methods employ the ‘timestepper’s approach’ in which a nonlinear Navier-Stokes code is modified to provide evolution operators for both the forward and adjoint linearized equations. First, the underlying mathematical treatment in primitive flow variables is presented. Then, details are given for the inner level code modifications and outer level eigenvalue and SVD algorithms in the timestepper’s approach. Finally, some examples are shown, and guidance is provided on practical aspects of this type of large-scale stability analysis.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F10 Iterative numerical methods for linear systems
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