Computational coarse graining of a randomly forced 1-D Burgers equation

Details Computational coarse graining of a randomly forced 1-D Burgers equation Computational coarse graining of a randomly forced 1-D Burgers equation

2007-07-03

arxiv.org/abs/0707.0510v1

Physics

Computational Physics

21 pages, 7 figures

Scientific paper

10.1063/1.2856212

We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in time. We demonstrate coarse projective integration and coarse dynamic renormalization as tools that accelerate the extraction of macroscopic information (integration in time, self-similar shapes, and nontrivial dynamic exponents) from short bursts of appropriately initialized direct simulation. These procedures solve numerically an effective evolution equation for the energy spectrum without ever deriving this equation in closed form.

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