A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem

Abstract

A Galerkin/POD reduced-order model from eigenfunctions of non-converged time evolution transitory states in a problem of Rayleigh–Bénard is presented. The problem is modeled in a rectangular box with the incompressible momentum equations coupled with an energy equation depending on the Rayleigh number R as a bifurcation parameter. From the numerical solution and stability analysis of the system for a single value of the bifurcation parameter, the whole bifurcation diagram in an interval of values of R is obtained. Three different bifurcation points and four types of solutions are obtained with small errors. The computing time is drastically reduced with this methodology.

Keywords

• reduced-order models
• proper orthogonal decomposition
• spectral methods
• Rayleigh–Bénard instability
• geophysical flows