|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article forum
| |
|
|
Heat transport bounds for a truncated model of Rayleigh-B'enard convection via polynomial optimization | | Matthew L. Olson
; David Goluskin
; William W. Schultz
; Charles R. Doering
; | | Date: |
15 Apr 2020 | | Abstract: | Upper bounds on time-averaged heat transport are obtained for an eight-mode
Galerkin truncation of Rayleigh’s 1916 model of thermal convection. Bounds for
the ODE model---an extension of Lorenz’s three-mode model---are derived by
constructing auxiliary functions that satisfy sufficient conditions wherein
certain polynomial expressions must be nonnegative. This nonnegativity is
enforced by requiring these expressions to admit sum-of-squares
representations. Polynomial auxiliary functions subject to such constraints can
be optimized computationally using semidefinite programming, minimizing the
resulting bound. Sharp or nearly sharp bounds on mean heat transport are
computed numerically for numerous values of the model parameters, the Rayleigh
and Prandtl numbers and the domain aspect ratio. In all cases where the
Rayleigh number is small enough for the ODE model to be quantitatively close to
the PDE model, mean heat transport is maximized by steady states. In some cases
at larger Rayleigh numbers, time-periodic states maximize heat transport in the
truncated model. Analytical parameter-dependent bounds are derived using
quadratic auxiliary functions, and they are sharp for sufficiently small
Rayleigh numbers. | | Source: | arXiv, 2004.7204 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No message found in this article forum.
You have a question or message about this article?
Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..
To add a message in the forum, you need to login or register first. (free): registration page
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER