Coarse graining, dynamic renormalization and the kinetic theory of shock clustering

Xingjie Li; Matthew O. Williams; Ioannis G. Kevrekidis; Govind Menon

doi:10.1088/0951-7715/29/3/947

Coarse graining, dynamic renormalization and the kinetic theory of shock clustering

Xingjie Li, Matthew O. Williams, Ioannis G. Kevrekidis, Govind Menon

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We demonstrate the utility of the equation-free methodology developed by one of the authors (IGK) for the study of scalar conservation laws with disordered initial conditions. The numerical scheme is benchmarked on exact solutions in Burgers turbulence corresponding to Lévy process initial data. For these initial data, the kinetics of shock clustering is described by Smoluchowski's coagulation equation with additive kernel. The equation-free methodology is used to develop a particle scheme that computes self-similar solutions to the coagulation equation, including those with fat tails.

Original language	English (US)
Article number	947
Pages (from-to)	947-961
Number of pages	15
Journal	Nonlinearity
Volume	29
Issue number	3
DOIs	https://doi.org/10.1088/0951-7715/29/3/947
State	Published - Feb 4 2016

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

Keywords

Burgers turbulence
Smoluchowski's coagulation equation
dynamic scaling
equation free method
sticky particles

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10.1088/0951-7715/29/3/947

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title = "Coarse graining, dynamic renormalization and the kinetic theory of shock clustering",

abstract = "We demonstrate the utility of the equation-free methodology developed by one of the authors (IGK) for the study of scalar conservation laws with disordered initial conditions. The numerical scheme is benchmarked on exact solutions in Burgers turbulence corresponding to L{\'e}vy process initial data. For these initial data, the kinetics of shock clustering is described by Smoluchowski's coagulation equation with additive kernel. The equation-free methodology is used to develop a particle scheme that computes self-similar solutions to the coagulation equation, including those with fat tails.",

keywords = "Burgers turbulence, Smoluchowski's coagulation equation, dynamic scaling, equation free method, sticky particles",

author = "Xingjie Li and Williams, {Matthew O.} and Kevrekidis, {Ioannis G.} and Govind Menon",

note = "Funding Information: One of the authors (IGK) would like to remember here S A Orszag, who suggested this very problem as a challenge for equation free methods a decade ago. The authors also acknowledge support from the following funding agencies. MOW acknowledges support from NSF DMS 1204783. IGK acknowledges partial support from US-AFOSR through grant number FA9550-12-1-0332 and NSF grant CDSE 1310173. GM acknowledges partial support from NSF DMS 1411278. Publisher Copyright: {\textcopyright} 2016 IOP Publishing Ltd & London Mathematical Society.",

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doi = "10.1088/0951-7715/29/3/947",

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AU - Li, Xingjie

AU - Williams, Matthew O.

AU - Kevrekidis, Ioannis G.

AU - Menon, Govind

N1 - Funding Information: One of the authors (IGK) would like to remember here S A Orszag, who suggested this very problem as a challenge for equation free methods a decade ago. The authors also acknowledge support from the following funding agencies. MOW acknowledges support from NSF DMS 1204783. IGK acknowledges partial support from US-AFOSR through grant number FA9550-12-1-0332 and NSF grant CDSE 1310173. GM acknowledges partial support from NSF DMS 1411278. Publisher Copyright: © 2016 IOP Publishing Ltd & London Mathematical Society.

PY - 2016/2/4

Y1 - 2016/2/4

N2 - We demonstrate the utility of the equation-free methodology developed by one of the authors (IGK) for the study of scalar conservation laws with disordered initial conditions. The numerical scheme is benchmarked on exact solutions in Burgers turbulence corresponding to Lévy process initial data. For these initial data, the kinetics of shock clustering is described by Smoluchowski's coagulation equation with additive kernel. The equation-free methodology is used to develop a particle scheme that computes self-similar solutions to the coagulation equation, including those with fat tails.

AB - We demonstrate the utility of the equation-free methodology developed by one of the authors (IGK) for the study of scalar conservation laws with disordered initial conditions. The numerical scheme is benchmarked on exact solutions in Burgers turbulence corresponding to Lévy process initial data. For these initial data, the kinetics of shock clustering is described by Smoluchowski's coagulation equation with additive kernel. The equation-free methodology is used to develop a particle scheme that computes self-similar solutions to the coagulation equation, including those with fat tails.

KW - Burgers turbulence

KW - Smoluchowski's coagulation equation

KW - dynamic scaling

KW - equation free method

KW - sticky particles

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Coarse graining, dynamic renormalization and the kinetic theory of shock clustering

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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