Linear stability of flow in a differentially heated cavity via large-scale eigenvalue calculations
نویسندگان
چکیده
We locate the onset of oscillatory instability in the flow in a differentially heated cavity of aspect ratio 2 by computing a steady state and analyzing the stability of the system via eigenvalue approximation. We discuss the choosing of parameters for the Cayley transformation so that the calculation of selected eigenvalues of the transformed system will most reliably answer the question of stability. We also present an argument that due to the symmetry of the problem, the first two unstable modes will have eigenvalues that are nearly identical, and our numerical experiments confirm this. We also locate a codimension 2 bifurcation signifying where there is a switch in the mode of initial instability. The results were obtained using a parallel finite element CFD code (MPSalsa) along with an Arnoldi-based eigensolver (ARPACK), a preconditioned Krylov method code for the necessary linear solves (Aztec), and a stability analysis library (LOCA).
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