Parallel Computation of Reliable Chaotic Solutions of Saltzman’s Equations by Means of the Clean Numerical Simulation
DOI:
https://doi.org/10.5890/DNC.2013.11.004Abstract
The method of the so-called “Clean Numerical Simulation” (CNS) is applied to gain reliable chaotic solutions of Saltzman’s dynamic system, a simplified model for convection flows of fluid. Based on the high-order Taylor series method with data in multiple precision library and a validation check of global reliability of result, the CNS provides us a practical way to gain reliable, accurate enough solutions of chaotic dynamic systems in a finite but long enough time interval. The parallel computation is used to greatly increase the computational efficiency. The numerical noises of the CNS can be controlled to be so small that even the influence of the micro-level inherent uncertainty of initial conditions can be investigated in details. It is found that the micro-level inherent physical uncertainty (i.e. the unavoidable statistical fluctuation of temperature and velocity of fluid) of initial conditions of chaotic Saltzman’s system transfers into macroscopic randomness. This suggests that chaos might be a bridge between micro-level inherent physical uncertainty and macroscopic randomness. The current work illustrates that the above conclusion holds not only for Lorenz equation with three ODEs but also for Saltzman’s equation with up-to nine ODEs, and thus has general meanings.References
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