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Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing

Published online by Cambridge University Press:  14 September 2015

Tobias Grafke ,
Rainer Grauer  and
Stephan Schindel
Tobias Grafke*
Affiliation:
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
Rainer Grauer
Affiliation:
Theoretische Physik I, Ruhr-Universität Bochum, Universitätsstr. 150, D44780 Bochum, Germany
Stephan Schindel
Affiliation:
Theoretische Physik I, Ruhr-Universität Bochum, Universitätsstr. 150, D44780 Bochum, Germany
*
*Corresponding author. Email addresses: tobias.grafke@weizmann.ac.il (T. Grafke), grauer@tp1.rub.de (R. Grauer), sts@tp1.rub.de (S. Schindel)
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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.

Keywords

47.11.-j47.27.ef05.10.-a47.40.-xInstanton formalismminimizing trajectorynumerical minimizationGPU programmingCUDA
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 3 , September 2015 , pp. 577 - 592
Copyright
Copyright © Global-Science Press 2015 

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