A spectral/hp element method for thermal convection
File(s)
Published version
Author(s)
Hossain, Mohammad Z
Cantwell, Chris D
Sherwin, Spencer J
Type
Journal Article
Abstract
We report on a high‐fidelity, spectral/hp element algorithm developed for the direct numerical simulation of thermal convection problems. We consider the incompressible Navier–Stokes (NS) and advection–diffusion equations coupled through a thermal body‐forcing term. The flow is driven by a prescribed flowrate forcing with explicit treatment of the nonlinear advection terms. The explicit treatment of the body‐force term also decouples both the NS and the advection–diffusion equations. The problem is then temporally discretized using an implicit–explicit scheme in conjunction with a velocity‐correction splitting scheme to decouple the velocity and pressure fields in the momentum equation. Although not unique, this type of discretization has not been widely applied to thermal convection problems and we therefore provide a comprehensive overview of the algorithm and implementation which is available through the open‐source package Nektar++. After verifying the algorithm on a number of illustrative problems we then apply the code to investigate flow in a channel with uniform or streamwise sinusoidal lower wall, in addition to a patterned sinusoidal heating. We verify the solver against previously published two‐dimensional results. Finally, for the first time we consider a three‐dimensional problem with a streamwise sinusoidal lower wall and sinusoidal heating which, for the chosen parameter, leads to the unusual dynamics of an initially unsteady two‐dimensional instability leading to a steady three‐dimensional nonlinear saturated state.
Date Issued
2021-07
Date Acceptance
2021-03-07
Citation
International Journal for Numerical Methods in Fluids, 2021, 93 (7), pp.2380-2395
ISSN
0271-2091
Publisher
John Wiley and Sons
Start Page
2380
End Page
2395
Journal / Book Title
International Journal for Numerical Methods in Fluids
Volume
93
Issue
7
Copyright Statement
© 2021 The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons Ltd.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000633529600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Mathematics, Interdisciplinary Applications
Mechanics
Physics, Fluids & Plasmas
Computer Science
Mathematics
Physics
incompressible Navier–
Stokes
spectral
hp element method
thermal convection
Publication Status
Published
Date Publish Online
2021-03-14