Analysis and postprocessing of space-time compressed flow computations

非定常流动数据的后处理需要涉及的数学方法和算法工具的大量工作。尤其是在三维流体动力学中存在多尺度、复杂现象的情况下，更是面临着各种困难。通常考虑的数据量巨大，阻碍了在空间和时间上同时处理足够大的数据部分。可视化的标准工具不能支持对潜在现象的直观理解。事实上，它们经常会导致视觉混乱。自动特征提取方法将有所帮助，而不是使用简单的图形工具进行耗时的手动数据探索。我们将研究和实现合适的基于稳定时间步进和空时自适应差错控制的压缩方法，以大幅减少数据量。此外，我们将应用图像处理方法来适当地可视化复杂的依赖于时间的流动并提取重要的流动模式。因此，将考虑多尺度方法，这些方法自然支持数据分辨率的尺度，范围从精细到粗略的流动可视化，或者从许多详细特征到仅提取的几个基本特征。此外，特别是对于动力学较弱的问题(非湍流)，现代数值方法允许大得多的时间步长。在后处理中，简单的插值法不是合适的解决方案。我们将把图像匹配方法作为一种新的方法来对流动模拟的时间步长进行内插以达到动画的目的。在这里，必须在交互性能和准确性之间找到适当的平衡。最后，开发的可视化和分析工具将与数值流动解算器一起整合到一个独特的框架中。

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.