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Smoothed Particle Hydrodynamics (SPH) is a mesh-free method that has been widely used in several fields such as astrophysics, solids mechanics, and fluid dynamics. This computational fluid dynamics model has been extensively studied and is mature enough to enable detailed quantitative comparisons with laboratory experiments. Therefore, understanding and revealing the underneath behaviors of SPH fluid simulation becomes more meaningful when SPH is used to help us understand similar phenomena in the real world. In the thesis, we use the Finite Time Lyapunov Exponent (FTLE) and a novel rotation metric as well as other analysis methods to analyze the SPH. First of all, we modify traditional FTLE by using Moving Least Squares to calculate the deformation matrix, and extend the usage from mesh-based to mesh-free data sets; we are the first to apply FTLE on free surface SPH fluid simulation. In addition, we are the first to apply rotation sum and gradient of rotation sum on particles based fluid simulation. We present a new way of using Moving Least Squares to calculate the gradient of rotation sum for mesh-free data sets. What's more, we are the first to apply asymmetric tensor field analysis on particle based fluid simulation. Furthermore, we utilize a number of visualization techniques on different analysis results. We present why choosing a proper visualization is crucial to reveal useful information, and we also demonstrate how to utilize transfer functions to decrease perturbations of data sets. Lastly, we compare different analysis results, such as FTLE versus gradient of rotation sum. Our methods are also useful to enhance the rendering of SPH simulation results, which reveals many small-scale detailed flow behaviors that would not be seen using existing rendering approaches. Our results are more realistic in terms of revealing the underneath behaviors of fluid simulation.



Smoothed particle hydrodynamics (SPH), MLS, Finite time lyapunov exponent (FTLE), Rotation Sum, Gradient of Rotation Sum, Visualization