Abstract
A new reduced-order model is applied to study bifurcations in a Rayleigh–Bénard convection problem, using as bifurcation parameter the Rayleigh number. The problem is modeled in a rectangular domain with the incompressible Navier–Stokes equations and the heat equation. The reduced-order model is based on proper orthogonal decomposition and Galerkin projection. The snapshots are eigenfunctions from a linear stability analysis of transient Newton iterations produced by a run of a high-fidelity solver at a single value of the bifurcation parameter. The symmetry properties of the equations have been used to enrich the proper orthogonal decomposition bases. The reduced-order method allows computing the whole bifurcation diagram in an interval of values of the Rayleigh number. Four types of solutions and three bifurcation points are computed with small errors. The results have been validated with the high-fidelity solver. The computational time is reduced with this methodology.
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