Volume 15, Issue 4-5
Ensemble Timestepping Algorithms for Natural Convection

Joseph Anthony Fiordilino & Sarah Khankan

Int. J. Numer. Anal. Mod., 15 (2018), pp. 524-551.

Published online: 2018-04

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  • Abstract

This paper presents two algorithms for calculating an ensemble of solutions to laminar natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability. Solutions are calculated by solving two coupled linear systems, each involving a shared coefficient matrix, for multiple right-hand sides at each timestep. Storage requirements and computational costs to solve the system are thereby reduced. Stability and convergence of the method are proven under a timestep condition involving fluctuations. A series of numerical tests, including predictability horizons, are provided which confirm the theoretical analyses and illustrate uses of ensemble simulations.

  • Keywords

Natural convection, Ensemble calculation, Uncertainty quantification, Finite element method.

  • AMS Subject Headings

65M12, 65M60, 76D05, 76R10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

JAF150@pitt.edu (Joseph Anthony Fiordilino)

sarah.khankan@gmail.com (Sarah Khankan)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-524, author = {Fiordilino , Joseph Anthony and Khankan , Sarah}, title = {Ensemble Timestepping Algorithms for Natural Convection}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {524--551}, abstract = {

This paper presents two algorithms for calculating an ensemble of solutions to laminar natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability. Solutions are calculated by solving two coupled linear systems, each involving a shared coefficient matrix, for multiple right-hand sides at each timestep. Storage requirements and computational costs to solve the system are thereby reduced. Stability and convergence of the method are proven under a timestep condition involving fluctuations. A series of numerical tests, including predictability horizons, are provided which confirm the theoretical analyses and illustrate uses of ensemble simulations.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12529.html} }
TY - JOUR T1 - Ensemble Timestepping Algorithms for Natural Convection AU - Fiordilino , Joseph Anthony AU - Khankan , Sarah JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 524 EP - 551 PY - 2018 DA - 2018/04 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12529.html KW - Natural convection, Ensemble calculation, Uncertainty quantification, Finite element method. AB -

This paper presents two algorithms for calculating an ensemble of solutions to laminar natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction reliability. Solutions are calculated by solving two coupled linear systems, each involving a shared coefficient matrix, for multiple right-hand sides at each timestep. Storage requirements and computational costs to solve the system are thereby reduced. Stability and convergence of the method are proven under a timestep condition involving fluctuations. A series of numerical tests, including predictability horizons, are provided which confirm the theoretical analyses and illustrate uses of ensemble simulations.

Joseph Anthony Fiordilino & Sarah Khankan. (2020). Ensemble Timestepping Algorithms for Natural Convection. International Journal of Numerical Analysis and Modeling. 15 (4-5). 524-551. doi:
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