Algorithm to Generate Liutex Core Lines Based on Forward Liutex Magnitude Gradient Lines

Abstract

Vortex definition and identification are extremely important for the study of fluid dynamics research. Liutex is a newly proposed concept that correctly represents vortex. Liutex is a vector whose direction is the local rotation axis and whose magnitude is twice the angular speed. To identify the unique structure of a vortex, a method known as the Liutex Core Line method has been developed, which displays the rotational core axis of a vortex. However, the original method is a manual method, which is not practical for real application, and an automatic algorithm is required for practical usage. Xu et al. proposed an algorithm by selecting the best line from a group of candidate lines, which is an important progress. In this chapter, from another perspective to solve this problem, a new algorithm is introduced based on forward Liutex magnitude gradient lines. Since gradient lines have the feature that they advance to the local maximums, the route will still result in a unique line, which avoids the process to find the best line. This algorithm has achieved some success for the Lambda vortex in early boundary layer transition.