Prediction of the spatiotemporal dynamics of von Kármán Vortices by ANFIS

Abstract

Wakes and vortices are commonly observed in fluid flows around bluff bodies, a phenomenon which is called vortex shedding. Such vortices are named as von Kármán vortices since their first investigation is performed by the leading fluid dynamicist Theodore von Kármán. Although initially observed in the studies of fluid flows, the same phenomenon can also be observed in different branches of mediums such as condensates. It is possible to model these vortices using numerical techniques that solve the Navier-Stokes equations, however, some dynamic equations such as the complex Ginzburg-Landau (GL) equation is another frequently used model for these purposes. In this paper, we solve the GL equation using a spectral scheme and Runge-Kutta time integrator to simulate the dynamics of von Kármán vortices around a cylinder. The prediction of temporal dynamics is of crucial importance to avoid excessive shedding, resonance, and structural damage of the engineering structures. With this motivation, here we examine the predictability of the von Kármán vortices using the adaptive neuro-fuzzy inference system (ANFIS) which relies on a rule-based relationship between input values and output values that are learned adaptively by being trained with the data set analyzed. We show that the temporal dynamics of the von Kármán vortices can be adequately performed by ANFIS and we report the prediction success of the ANFIS in the solution of this complex prediction problem measured by the coefficient of determination (𝑅) and the root mean square error (𝑅𝑀𝑆𝐸) values. Our results can be used for predicting, interpolating, and extrapolating vortex data to analyze fluid dynamics problems and to develop control strategies for avoiding structural failures.