T. Grafke, R. Grauer, and S. Schindel, Commun. Comp. Phys 18 (2015) 577
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 because of their memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in the turbulence setup, where the underlying dynamical system is a non-gradient, non-linear partial differential equation. 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 turbulent flows.