Vortex core detection in turbulent simulations based on machine learning approaches

The identification of vortex cores in fluid mechanics is a challenging task that re- quires sophisticated techniques. Commonly employed local detection methods, such as the Q, delta, or swirling-strength criterion, rely on the local velocity gradient tensor to locate the vortex cores. Despite their reasonable accuracy, these methods tend to produce false positives and negatives, necessitating user-defined tuning pa- rameters to maintain an acceptable error level. Moreover, this method presupposes prior knowledge of the vortices, limiting its robustness and self-contained nature. To overcome this shortcoming, a hybrid computer vision and machine learning ap- proach is proposed to enhance the detection features of vortex cores and reduce false positives and negatives. Initially, computer vision was employed to identify the areas of vortex structures, followed by machine learning to identify the vortex core within the vortex region. A convolutional neural network (CNN) was trained to analyse streamline plots based on line integral convolution (LIC) for the computer vision process. Through the use of computer vision, false positives and negatives in flow-specific problems are reduced without the need for calibrating user-defined parameters. Furthermore, the trained CNN was successfully applied to three test cases, indicating its universal applicability. As such, computer vision offers a reli- able convolutional neural network approach to detect vortex areas, which requires training once and is suitable for a broad range of flow scenarios. To identify the exact location of vortex cores, machine learning was combined with the computer vision approach. Various sets of input features were tested for both hybrid and pure machine learning approaches, starting with primitive variables such as velocity and pressure and expanding to more derived quantities such as velocity gradients, pres- sure gradients, Q-criterion, vorticity, and magnitude of vector quantities. In addi- tion, a method for automatically labelling the dataset using K-means clustering was proposed to preprocess input images for machine learning. Results demonstrated that the K-means clustering-based labelling approach had a mean square error of only 0.45%, comparable to the manual labelling approach. The hybrid approach significantly reduced training time for all tested cases and led to fewer false posi- tives and negatives when using primitive variables and their derivatives compared to pure machine learning using the Artificial Neural Network approach applied to the entire flow. At the same time, using the variable set with all possible inputs does not provide a more accurate prediction of vortex cores and thus the hybrid approach is demonstrated as an effective way to reduce false positives and negatives entirely using just the primitive variables and their derivatives.