PDE Methods in Flow Simulation Post Processing

Vector field visualization is an important topic in scientific visualization. The aim is to graphically represent field data in an intuitively understandable and precise way. Two novel methods are described which enable an easy perception of flow data. The texture transport method especially applies to timedependent velocity fields. Lagrangian coordinates are computed solving the corresponding linear transport equations numerically. Choosing an appropriate texture on the reference frame the coordinate mapping can be applied as a suitable texture mapping. Alternatively, the aligned diffusion methods serves as an appropriate scale space method for the visualization of complicated flow patterns. It is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. Here an initial noisy image is smoothed along streamlines, whereas the image is sharpened in the orthogonal direction. The two methods have in common that they are based on a continuous model and discretized only in the final implementational step. Therefore, many important properties are naturally established already in the continuous model.