Analysis and postprocessing of space-time compressed flow computations

非定常流数据的后处理需要大量的数学方法和算法工具。特别是在三维流体动力学中的多尺度、复杂现象的情况下，人们面临着各种困难。所考虑的数据的典型的巨大的量防止在空间和时间上同时处理足够大的数据部分。用于可视化的标准工具无法支持对潜在现象的直观理解。事实上，它们经常导致视觉混乱。自动特征提取方法将是有用的，而不是使用简单的图形工具进行耗时的手动数据探索。我们将研究和实现适当的压缩方法的基础上稳定的时间步进计划和空时自适应错误控制，以减少大量的数据。此外，我们将应用图像处理方法来适当地可视化复杂的时间依赖性流，并提取重要的流动模式。因此，将考虑多尺度方法，其自然地支持数据分辨率的尺度，范围从细到粗的流动可视化或从许多详细特征到仅少数提取的基本特征。此外，特别是对于动力学较弱的问题（非湍流），现代数值方法允许显着大的时间步长。在后处理中，简单的插值证明不是适当的解决方案。我们将考虑图像匹配方法作为一种新的方法来插值的流动模拟的动画目的的时间步长。最后，开发的可视化和分析工具将与数值流求解器一起被纳入一个独特的框架中。

Postprocessing of nonstationary flow data requires significant effort concerning the involved mathematical methods and the algorithmical tools. Especially in case of multi-scale, complex phenomena in 3D fluid dynamics one faces various difficulties. The typically enormous amount of considered data prevents a simultaneously handling of a sufficiently large part of the data in space and time. Standard tools for visualization are unable to support an intuitive understanding of the underlying phenomena. In fact they often lead to visual clutter. Instead of a time consuming manual data exploration with simple graphic tools, automatic feature extraction methods would be helpful. We will study and implement suitable compressing methods based on stable time stepping schemes and space-time adaptive error control to reduce the amount of data considerable. Furthermore, we will apply image processing methodology to appropriately visualize complex time-dependent flows and to extract important flow patterns. Thus, multi-scale methods will be considered, which naturally support a scale of data resolutions, ranging either from fine to coarse flow visualization or from many detailed features to only a few extracted, essential features. Furthermore, especially for problems with weaker dynamics (non turbulent flows), modern numerical methods allow significantly large time steps. In the postprocessing a simple interpolation turns out to be not the appropriate solution. We will consider image matching methods as a new approach to interpolate time steps of the flow simulation for animation purposes. Here a suitable balance between interactive performance and accuracy has to be found. Finally the developed visualization and analysis tools will be incorporated in a unique frame together with the numerical flow solvers.