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Hierarchical Cascade Model Leading to 7-Th Order Initial Value Problem by Akram, Ghazala; Beck, Christian is a scholarly article available to read on EtoBox.

What is Hierarchical Cascade Model Leading to 7-Th Order Initial Value Problem about?

In turbulent flows, local velocity differences often obey a cascade-like hierarchical dynamics, in the sense that local velocity differences at a given scale k are driven by deterministic and random forces from the next-higher scale k-1. Here we consider such a hierarchically coupled model with periodic boundary conditions, and show that it leads to an N-th order initial value problem, where N is the number of cascade steps. We deal in detail with the case N=7 and introduce a non-polynomial spline method that solves the problem for arbitrary driving forces. Several examples of driving forces are considered, and estimates of the numerical precision of our method are given. We show how to optimize the numerical method to obtain a truncation error of order O(h^5) rather than O(h^2), where h is the discretization step.

Author

Akram, Ghazala; Beck, Christian

Published

2012

Language

EN