Fast and Accurate Integration of Vector Fields in Unstructured Grids (Schnelles exaktes Integrationsverfahren für Vektorfelder auf unstrukturierten Gittern )

Particle tracing is a widely used method to analyze and interpret results of a flow simulation. In addition, it is a preliminary step for more advanced techniques of flow visualization, e.g. line integral convolution.

For interactive exploration of large data sets, a very efficient and reliable particle tracing method is needed. For data on unstructured grids and data sizes, as they appear in the simulation of wind channel experiments (e.g. automative industry) and flight simulation (e.g. aircraft industry), the traditional approach, based on numerical integration methods of ordinary differential equations does not allow sufficiently accurate path calculation at the speed required for interactive use.

Traditional integration techniques require small stepsizes in order to achieve sufficient accuracy. T his results in many cell search operations, which means especially for unstructured grids a bottleneck of the whole procedure.

In [5] Nielson and Jung have proposed a new method, called further on locally exact method, which gives sufficient accuracy and traverses each cell in a single step. In this note we extend the approach of Nielson and Jung in such a way that it can be performed in real time. This will be achieved by a sophisticated preprocessing, which allows a fast execution of the locally exact integration method, interactive particle tracing in large data sets can be done. We describe the procedure, compare it with Nielson´s original approach, as well as with the traditional method based on numerical integration and report on the performance of the different methods.