Multi Scale Color Coding of Derived Curvature and Torsion Fields on a Multi-Block Curvilinear Grid

We present a method to compute and visualize the curvature and torsion scalar fields derived from a vector field defined on a multi-block curvilinear grid. In order to compute the curvature and torsion fields, we define a uniform Cartesian grid of points in the volume occupied by the curvilinear grid and interpolate from the curvilinear grid to the Cartesian grid to get the vector field at the Cartesian grid points. We can then use finite difference formulas to numerically compute the derivatives needed in the curvature and torsion formulas. Once the curvature and torsion have been computed at the Cartesian grid points, we employ a multi scale color coding technique to visualize these scalar fields in orthoslices of the Cartesian grid. This multi scale technique allows one to observe the entire range of values of the scalar field, including small, medium and large values. In contrast, if uniform color coding is used to visualize curvature and torsion fields, it sometimes shows most of the values in a single predominant color, which makes it impossible to distinguish between the small, medium and large values. As an example of this multi-scale technique, we displayed the curvature and torsion fields in a computational fluid dynamics (CFD) simulation of an industrial stirred tank and used these images to identify regions of low, medium and high fluid mixing in the tank.