Approximation of Divergence-free Vector Fields on Regular Lattices

正则格子上无散向量场的近似

• 批准号: 435780-2013
• 负责人: Alim, Usman
• 金额: $ 1.46万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=634650
• 关键词: Approximation; Divergence; free; Vector; Fields

As computational power increases and storage becomes cheaper, 'big-data' - a term used to refer to huge quantities of acquired or simulated data - is becoming more and more pervasive. A lot of research effort nowadays is focused towards efficiently managing and analyzing big-data. This research program, on the other hand, aims at cutting down the amount of data by devising more informative acquisition and processing tools. The particular focus is the visualization and simulation of flow data that arises in disciplines such as computer graphics, climatology, automotive design and petroleum engineering, where the fluid flow is usually described by a discrete unsteady three-dimensional velocity field: a finite set of time-varying velocity vectors strategically distributed throughout the simulation domain. A fundamental task in flow visualization is the approximation of a continuous flow field from the finite set of velocity vectors. The usual practice in the community is to interpolate each velocity component independently. This straightforward approach is preferred since it gives the practitioner access to various optimized interpolation routines. However, it has its drawbacks since it does not take into account the fact that many flow fields encountered in practice are incompressible, i.e. the fluid density does not change as the fluid flows through the domain.The long-term aim of this research program is to improve the quality of flow simulations and visualizations by seeking continuous flow representations that are more efficient and at the same time, preserve the incompressible nature of the flow. Owing to their incompressibility, these representations will be more accurate thus allowing domain experts to simulate flows at coarser resolutions without sacrificing quality. Due to their efficiency, they also have the potential of capturing more details in simulations and visualizations without increasing the computational budget. Additionally, by addressing some of the theoretical challenges, we also hope to gain a better fundamental understanding of the complex dynamics of fluids.

随着计算能力的增加并变得更便宜，“大数据”（用于指代大量获取或模拟数据的术语）变得越来越普遍。如今，许多研究工作都集中在有效管理和分析大数据。另一方面，该研究计划的目的是通过设计更多信息丰富的获取和处理工具来减少数据量。特别的重点是在学科中产生的流数据的可视化和模拟，例如计算机图形，气候学，汽车设计和石油工程，其中流体流量通常由离散的三维速度领域的离散的三维速度领域：有限的时间变化速度媒介在整个仿真域中策略性地分布在策略上。流动可视化的基本任务是从有限的速度向量集的连续流场的近似。社区中通常的做法是独立插值每个速度组件。这种直接的方法是首选的，因为它使从业者可以访问各种优化的插值例程。但是，它具有缺点，因为它没有考虑到实践中遇到的许多流场是不可压缩的事实，即流体密度不会随着流体流经域流过域而不会发生变化。该研究计划的长期目的是通过寻求更有效的连续流动性来提高流动模拟和可视化的质量，以使其具有更高的流动性，并且要保持流动率不足。由于它们的不可压缩性，这些表示形式将更加准确，因此允许域专家在不牺牲质量的情况下模拟较粗的分辨率流动。由于它们的效率，他们还可以在不增加计算预算的情况下捕获模拟和可视化的更多细节。此外，通过解决一些理论挑战，我们也希望对流体的复杂动态有更好的基本理解。