Kinetic lattice group models: structure and applications

该项目涉及微稀薄气体流动和流体动力学过渡区数值流体流动模拟的离散动力学模型的构建、分析研究和计算机实现。在微流领域出现了重要的应用。该项目继续了前一个项目的研究，在前一个项目中，稀薄气体理论和流体动力学之间的联系可以根据修正项建立起来。基于线性化理论，这有助于在广泛的应用中构建模型。这些研究将以分析的方式进行，并使用计算机代数，并扩展到非线性理论。在前面的项目中，开发并实现了一个软件工具箱，用于在CPU和GPU上进行有效的流模拟。为了提高复杂流型的分辨率，需要特别通过补充自适应元素对其进行改进和扩展。

The project concerns the construction, analytic investigation and computer implementation of discrete kinetic models for numerical fluid flow simulations in the transition regime between slightly rarefied gas flows and fluid dynamics. Important applications arise in the field of microflows.The project continues the investigations of the predecessor project in which a link between rarefied gas theory and fluid dynamics could be established in terms of a correction term. Based on linearized theory, this assists in constructing models in a wide range of applications. These studies are to be carried on analytically and with the use of computer algebra and extended to nonlinear theory. In the preceding project, a software toolbox was developed and implemented for efficient flow simulations on CPU's and GPU's. This is to be refined and extended in particular by supplementing adaptive elements in order to improve the resolution of complex flow patterns.