Computational bifurcation and stability studies of the 8: 1 thermal cavity problem

摘要: Stability analysis algorithms coupled with a robust Newton-Krylov steady-state iterative solver are used to understand the behavior of 2D model problem thermal convection in 8:1 differentially heated cavity. Parameter continuation methods along bifurcation and linear stability study transition from steady transient flow as function Rayleigh number. To carry out this form governing PDEs is discretized using Galerkin/least-squares finite element formulation, solved on parallel computers fully Newton method preconditioned Krylov solvers. Linear employing large-scale eigenvalue capability determine solutions. The boundary between time-dependent flows determined by Hopf tracking that directly track instability respect aspect ratio system mesh resolution. effect upwinding stabilization terms formulation computed value critical number investigated