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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=596752
• 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.

随着计算能力的提高和存储变得越来越便宜，“大数据”（一个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上。另一方面，该研究计划旨在通过设计更多信息获取和处理工具来减少数据量。特别关注的是计算机图形学、气候学、汽车设计和石油工程等学科中出现的流动数据的可视化和模拟，其中流体流动通常由离散的非稳态三维速度场来描述：策略性地分布在整个模拟域中的一组有限的时变速度向量。流可视化的一项基本任务是从有限的速度矢量集近似连续流场。社区中的通常做法是独立插值每个速度分量。这种简单的方法是首选，因为它使从业者可以访问各种优化的插值例程。然而，它也有其缺点，因为它没有考虑到实际中遇到的许多流场是不可压缩的这一事实，即流体密度不会随着流体流过域而改变。