Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 231, Issue 23, Pages 7851-7867Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.07.028
Keywords
Time parallelization; Parareal algorithm; Turbulent transport; Plasma turbulence; Magnetically confined plasmas
Funding
- Postdoctoral Mobility Program of the National Plan of Scientific Research, Development and Technological Innovation of the Spanish Ministry of Investigation and Science I+D+i
- Spanish National Project [ENE2009-12213-C03-03]
- DOE Office of Science [DE-FG02-04ER54741]
- U.S. Department of Energy (DOE) [DE-FG02-04ER54741] Funding Source: U.S. Department of Energy (DOE)
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Parareal is a recent algorithm able to parallelize the time dimension in spite of its sequential nature. It has been applied to several linear and nonlinear problems and, very recently, to a simulation of fully-developed, two-dimensional drift wave turbulence. The mere fact that parareal works in such a turbulent regime is in itself somewhat unexpected, due to the characteristic sensitivity of turbulence to any change in initial conditions. This fundamental property of any turbulent system should render the iterative correction procedure characteristic of the parareal method inoperative, but this seems not to be the case. In addition, the choices that must be made to implement parareal (division of the temporal domain, election of the coarse solver and so on) are currently made using trial-and-error approaches. Here, we identify the mechanisms responsible for the convergence of parareal of these simulations of drift wave turbulence. We also investigate which conditions these mechanisms impose on any successful parareal implementation. The results reported here should be useful to guide future implementations of parareal within the much wider context of fully-developed fluid and plasma turbulent simulations. (C) 2012 Elsevier Inc. All rights reserved.
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