Viscous and gravitational flow instabilities cause a displacement front to break up into finger-like fluids. The detection and evolutionary analysis of these fingering instabilities are critical in multiple scientific disciplines such as fluid mechanics and hydrogeology. However, previous detection methods of the viscous and gravitational fingers are based on density thresholding, which is sensitive to the user-specified threshold value. Also, the geometric structures of fingers and their evolution are little studied. In this work, we explore the topological and geometric detection and evolution of the fingers in detail to elucidate the dynamics of the instability. We first detect finger cores in three-dimensional (3D) scalar fields to capture the central structures of fingers guided by a ridge voxel detection method ; then, we skeletonize finger cores to reveal their overall topological and geometric structures by a Reeb-graph skeletonization method. From the identified finger skeletons, we design a spanning contour tree-based method to capture how fingers branch in 3D space . Then, to display different facets of finger branches, we employ various tree-based visualization methods to plot the finger branches in a plane . Finally, to track the evolution of time-varying fingers and their branches, we nest tree-based geometric glyphs of fingers on a tracking graph. The geometric-glyph augmented tracking graph allows us to study how the fingers  grow, merge, and split over time. Feedbacks from earth scientists demonstrate the usefulness of our approach to analyze the evolution of fingers.
Viscous and gravitational flow instabilities cause a displacement front to break up into finger-like fluids. The detection and evolutionary analysis of these fingering instabilities are critical in multiple scientific disciplines such as fluid mechanics and hydrogeology. However, previous detection methods of the viscous and gravitational fingers are based on density thresholding, which is susceptible to the user-specified threshold value. Also, the geometric structures of fingers and their evolution are little studied. In this work, we explore the geometric detection and evolution of the fingers in detail to elucidate the dynamics of the instability. Guided by a new ridge voxel detection method , we first extract finger cores from three-dimensional (3D) scalar fields. After skeletonizing finger cores into skeletons, we design a spanning tree based approach to capture how fingers branch in 3D space from the finger skeletons . Finally, we devise a novel geometric-glyph augmented tracking graph to study how the fingers and their branches grow, merge, and split over time. Feedback from earth scientists demonstrates the usefulness of our approach to analyzing the evolution of fingers.
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We first detect finger cores in three-dimensional (3D) scalar fields to capture the central structures of fingers guided by a
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; then, we skeletonize finger cores to reveal their overall topological and geometric structures by a Reeb-graph skeletonization method. From the identified finger
, we first extract finger cores from three-dimensional (3D) scalar fields. After skeletonizing finger cores into
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contour tree-based method
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. Then, to display different facets of finger branches, we employ various tree-based visualization methods to plot the finger branches in a plane
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to track the evolution of time-varying fingers and their branches, we nest tree-based geometric glyphs of fingers on a tracking graph. The
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