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A spectral/hp element method for thermal convection

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Title: A spectral/hp element method for thermal convection
Authors: Hossain, MZ
Cantwell, CD
Sherwin, SJ
Item 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.
Issue Date: Jul-2021
Date of Acceptance: 7-Mar-2021
URI: http://hdl.handle.net/10044/1/88083
DOI: 10.1002/fld.4978
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.
Keywords: 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
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
Applied Mathematics
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published
Open Access location: https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.4978
Online Publication Date: 2021-03-14
Appears in Collections:Aeronautics
Faculty of Engineering



This item is licensed under a Creative Commons License Creative Commons