Streak lines and particle traces are effective visualization techniques for studying unsteady fluid flows. For real time applications, accuracy is often sacrificed to achieve interactive frame rates. Physical space particle tracing algorithms produce the most accurate results although they are usually too expensive for interactive applications. An efficient physical space algorithm is presented which was developed for interactive investigation and visualization of large, unsteady, aeronautical simulations. Performance has been increased by applying tetrahedral decomposition to speed up point location and velocity interpolation in curvilinear grids. Preliminary results from batch computations showed that this approach was up to six times faster than the most common algorithm which uses the Newton-Raphson method and trilinear interpolation. Results presented show that the tetrahedral approach also permits interactive computation and visualization of unsteady particle traces. Statistics are given for frame rates and computation times on single and multiprocessors. The benefits of interactive feature detection in unsteady flows are also demonstrated.

Flow volumes are extended for use in unsteady (time-dependent) flows. The resulting unsteady flow volumes are the 3D analogs of streaklines. There are few examples where methods other than particle tracing have been used to visualize time-varying flows. Since particle paths can become convoluted in time, there are additional considerations to be made when extending any visualization technique to unsteady flows. We present some solutions to the problems which occur in subdivision, rendering and system design. We apply the unsteady flow volumes to a variety of field types, including moving multi-zoned curvilinear grids.

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation, and step size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations, and expensive matrix inversions are eliminated. Integration accuracy is maintained using an adaptive step size control scheme which is regulated by the path line curvature. The problem of point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells, and produces almost identical traces.

Time-dependent (unsteady) flow fields are commonly generated in computational fluid dynamics (CFD) simulations; however, there are very few flow visualization systems that generate particle traces in unsteady flow fields. Most existing systems generate particle traces in time-independent flow fields. A particle tracing system has been developed to generate particle traces in unsteady flow fields. The system was used to visualize several 3D unsteady flow fields from real-world problems, and it has provided useful insights into the time-varying phenomena in the flow fields. The design requirements and the architecture of the system are described. Some examples of particle traces computed by the system are also shown.>

Presently, there are very few visualization systems available for time-dependent flow fields. Although existing visualization systems for instantaneous flow fields may be used to view time-dependent flow fields at discrete points in time, the time variable is usually not considered in the visualization technique. We present a simple and effective approach for visualizing time-dependent flow fields using streaklines. A system was developed to demonstrate this approach. The system can process many time frames of flow fields without requiring that all the data be in memory simultaneously, and it also handles flow fields with moving grids. We have used the system to visualize streaklines from several large 3-D time-dependent flow fields with moving grids. The system was able to provide useful insights to the physical phenomena in the flow fields.>

Effective methods for visualizing several sets of volumetric data simultaneously are presented. The methods involve the composition of multiple volumetric rendering techniques. These techniques include contour curves, color-blended contour regions, projection graphs on surfaces, isovalue surface construction, and hypersurface projection graphs.>

The authors discuss effective techniques for representing scalar and vector valued functions that interpolate to irregularly located data. Special attention is given to the situations where the sampling domain is a two-dimensional plane, 3-D volume, or a closed 3-D surface. The authors first discuss the multiquadric and thin-plate spline methods for interpolating scalar data sampled at arbitrary locations in a plane. Straightforward generalizations are then made to data sampled in 3-D volumetric regions as well as in higher dimensional spaces. The globally defined interpolants can be evaluated on a fine regular grid and they can then be visualized using conventional techniques. Triangular and tetrahedral based visualization techniques are also presented.>

Abstract Ray‐tracing volumetric data may take several minutes to compute a single image from a fixed viewpoint. We present techniques that generate approximate ray‐traced volumetric images in less than one second per image, after a lengthy initialization process is performed. These approximate images are based on methods that interpolate data sampled at locations on a sphere.