Computational coarse graining of a randomly forced one-dimensional Burgers equation

Sunil Ahuja; Victor Yakhot; Ioannis G. Kevrekidis

doi:10.1063/1.2856212

Computational coarse graining of a randomly forced one-dimensional Burgers equation

Sunil Ahuja, Victor Yakhot, Ioannis G. Kevrekidis

Chemical & Biological Engineering

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5 Scopus citations

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)
Article number	035111
Journal	Physics of Fluids
Volume	20
Issue number	3
DOIs	https://doi.org/10.1063/1.2856212
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

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10.1063/1.2856212

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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.",

keywords = "Computational fluid dynamics, Differential equations, Turbulence",

author = "Sunil Ahuja and Victor Yakhot and Kevrekidis, {Ioannis G.}",

note = "Funding Information: This work was partially supported by DARPA and the U.S. DOE (CMPD). The use of computer resources at the Boston University Scientific Computing and Visualization Group (SCV) is gratefully acknowledged. The authors would also like to thank John Wanderer for his help in developing the numerical simulator.",

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AU - Ahuja, Sunil

AU - Yakhot, Victor

AU - Kevrekidis, Ioannis G.

N1 - Funding Information: This work was partially supported by DARPA and the U.S. DOE (CMPD). The use of computer resources at the Boston University Scientific Computing and Visualization Group (SCV) is gratefully acknowledged. The authors would also like to thank John Wanderer for his help in developing the numerical simulator.

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N2 - 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.

AB - 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.

KW - Computational fluid dynamics

KW - Differential equations

KW - Turbulence

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Computational coarse graining of a randomly forced one-dimensional Burgers equation

Abstract

All Science Journal Classification (ASJC) codes

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