Non-incremental transient solution of the Rayleigh–Bénard convection model by using the PGD

Abstract

This paper focuses on the non-incremental solution of transient coupled non-linear models, in particular the one related to the Rayleigh–Bénard flow problem that models natural thermal convection. For this purpose we are applying the so-called Proper Generalized Decomposition that proceeds by performing space-time separated representations of the different unknown fields involved by the flow model. This non-incremental solution strategy allows significant computational time savings and opens new perspectives for introducing some flow and/or fluid parameters as extra-coordinates.