Transport and anisotropic diffusion in time-dependent flow visualization

The visualization of time-dependent flow is an important and challenging topic in scientific visualization. Its aim is to represent transport phenomena governed by time-dependent vector fields in an intuitively understandable way, using images and animations. Here we pick up the recently presented anisotropic diffusion method, expand and generalize it to allow a multiscale visualization of long-term, complex transport problems. Instead of streamline type patterns generated by the original method now streakline patterns are generated and advected. This process obeys a nonlinear transport diffusion equation with typically dominant transport. Starting from some noisy initial image, the diffusion actually generates and enhances patterns which are then transported in the direction of the flow field. Simultaneously the image is again sharpened in the direction orthogonal to the flow field. A careful adjustment of the models parameters is derived to balance diffusion and transport effects in a reasonable way. Properties of the method can be discussed for the continuous model, which is solved by an efficient upwind finite element discretization. As characteristic for the class of multiscale image processing methods, we can in advance select a suitable scale for representing the flow field.