Computation of incompressible thermal flows using Hermite finite elements |
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| Authors: | Jonas T Holdeman Jin Whan Kim |
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| Affiliation: | 1. 1056 Lovell Road, Knoxville, Tennessee 37932, USA;2. Department of Mechanical Engineering, Dong-Eui University, Busanjin-Gu, Busan 614-714, South Korea;1. Department of Mathematics, University College London, London, UK-WC1E 6BT, United Kingdom;2. Department of Mechanical Engineering, Jönköping University, SE-55111 Jönköping, Sweden;3. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;1. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK;2. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;3. Department of Mechanical Engineering, Jönköping University, SE-551 11 Jönköping, Sweden;1. Department of Mechanical Engineering, Jönköping University, SE-551 11 Jönköping, Sweden;2. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;3. Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden;1. Department of Bioengineering, University of California San Diego, La Jolla, CA, USA;2. Carl E. Ravin Advanced Imaging Laboratories, Duke University, Durham, NC, USA;3. Simula Research Laboratory, Center for Biomedical Computing, Lysaker, Norway;4. Cardiothoracic Radiology, Veterans Administration Healthcare System, San Diego, CA, USA;5. Department of Physics, University of California San Diego, La Jolla, CA, USA;6. Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA, USA;7. Department of Medicine (Cardiology), University of California San Diego, La Jolla, CA, USA;8. Division of Cardiology, Veterans Administration Healthcare System, San Diego, CA, USA;9. Cardiac Biomedical Science and Engineering Center, University of California San Diego, La Jolla, CA, USA;10. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA |
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| Abstract: | Using Hermit basis functions with the finite element method offers a remarkably simple way to compute non-isothermal buoyancy-driven incompressible flow. The Hermite bases we use simplify the governing equation and strongly enforce the continuity equation. For this problem, we use a fourth-order C1 stream function defined on rectangles here, but other higher and lower-order Hermite elements on rectangles and triangles can easily be derived or modified from elements found in the plate-bending literature. Hermite elements are also used for the temperature and pressure. We conclude with results from application of the method to the square thermal cavity at moderate to high Rayleigh numbers. |
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