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.
Highlights
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
If instead of the separated representation just discussed, one performs a standard incremental solution, P dD models, d = 1, 2, 3, must be solved (P being the number of time steps, i.e. P = tmax/ Dt, where the time step Dt must be chosen for ensuring the stability conditions)
We consider the dimensionless form of the Rayleigh–Bénard model: 8 >>>>
Summary
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. Several systems and industrial processes are based on natural convection, justifying the impressive volume of work devoted to its understanding and efficient solution during more than one century This model, quite simple in appearance, deserves many surprises related to its intricate nature and many issues concerning its numerical solution, mainly in the case of nonNewtonian fluids and/or when the Rayleigh number is large enough to induce the transition to the turbulence. Models coming from the physics of materials and processes are in general non-linear and strongly coupled It was in this scenario that Pierre Ladeveze proposed in the 1980s a new powerful simulation paradigm, the LATIN method [15] that combines two key ingredients: (i) an efficient non-linear treatment and (ii) a space-time separated representation.
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