Volume 18, Issue 3
Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing

Tobias Grafke, Rainer Grauer & Stephan Schindel

Commun. Comput. Phys., 18 (2015), pp. 577-592.

Published online: 2018-04

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  • Abstract

Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action functional. Due to the high number of degrees of freedom in multi-dimensional fluid flows, traditional global minimization techniques quickly become prohibitive in their memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamical system is a non-gradient, non-linear partial differential equation, and the forcing is restricted to a limited length scale. We demonstrate the efficiency of the algorithm in terms of performance and memory by computing high resolution instanton field configurations corresponding to viscous shocks for 1D and 2D compressible flows.

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@Article{CiCP-18-577, author = {}, title = {Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {3}, pages = {577--592}, abstract = {

Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action functional. Due to the high number of degrees of freedom in multi-dimensional fluid flows, traditional global minimization techniques quickly become prohibitive in their memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamical system is a non-gradient, non-linear partial differential equation, and the forcing is restricted to a limited length scale. We demonstrate the efficiency of the algorithm in terms of performance and memory by computing high resolution instanton field configurations corresponding to viscous shocks for 1D and 2D compressible flows.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.031214.200415a}, url = {http://global-sci.org/intro/article_detail/cicp/11041.html} }
TY - JOUR T1 - Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing JO - Communications in Computational Physics VL - 3 SP - 577 EP - 592 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.031214.200415a UR - https://global-sci.org/intro/article_detail/cicp/11041.html KW - AB -

Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action functional. Due to the high number of degrees of freedom in multi-dimensional fluid flows, traditional global minimization techniques quickly become prohibitive in their memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamical system is a non-gradient, non-linear partial differential equation, and the forcing is restricted to a limited length scale. We demonstrate the efficiency of the algorithm in terms of performance and memory by computing high resolution instanton field configurations corresponding to viscous shocks for 1D and 2D compressible flows.

Tobias Grafke, Rainer Grauer & Stephan Schindel. (2020). Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing. Communications in Computational Physics. 18 (3). 577-592. doi:10.4208/cicp.031214.200415a
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