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 - <p style="text-align: justify;">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.</p>