Rotation Invariant Predictor-Corrector for Smoothed Particle Hydrodynamics Data Visualization

In order to extract the vortex features more accurately, a new method of vortex feature extraction on the Smoothed Particle Hydrodynamics data is proposed in the current study by combining rotation invariance and predictor-corrector method. There is a limitation in the original rotation invariance, which can only extract the vortex features that perform equal-speed rotations. The limitation is slightly weakened to a situation that the rotation invariance can be used, given that a specific axis is existed in the fluid to replace the axis needed for it. Therefore, as long as the axis exists, the modified rotation invariant method can be used. Meanwhile, the vortex features are extracted by predictor-corrector method. By calculating the cross product of the parallel vector field, the seed candidates of vortex core lines can be obtained, and the real seed points can be gained from the rotation invariant Jacobian. Finally, the seed point and a series of candidates based on the predictor-corrector method are connected to draw the vortex core lines. Compared with the original method, the rotation invariant predictor-corrector method not only expands the application scope, but also ensures the accuracy of extraction. Our method adds the steps of calculating the rotation invariant Jacobian, the performance is slightly lower, but with the increase of the particle number, the performance gradually tends to the original method.