## Abstract

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, 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.

Original language | English (US) |
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Article number | 035111 |

Journal | Physics of Fluids |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2008 |

## All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

## Keywords

- Computational fluid dynamics
- Differential equations
- Turbulence