Understanding the 8: 1 cavity problem via scalable stability analysis algorithms

Stability analysis algorithms coupled with a robust steady state solver are used to understand the behavior of the 2D model problem of thermal convection in a 8 : 1 differentially heated cavity. The system is discretized using a Galerkin=Least Squares Finite Element formulation, and solved to steady state on parallel computers using a fully coupled Newton method and iterative linear solvers. An eigenvalue capability is used to probe the stability of the solutions, and the neutral stability curves are tracked directly using a Hopf tracking algorithm.

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