Multiscale Numerical Strategies for Models with Quadratic Nonlinearity

二次非线性模型的多尺度数值策略

• 批准号: 0713793
• 负责人: Ilya Timofeyev
• 金额: $ 14.37万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0713793&HistoricalAwards=false
• 关键词: Multiscale; Numerical; Strategies; Models; Quadratic

The main goal of the proposed research is to develop a novel mathematical approach to allow faster numerical integration of certain types of Partial Differential Equations. The types of Partial Differential Equations considered in this proposal are very common in many areas of physics and, in particular, play a crucial role in numerical weather and climate studies. The main idea behind the proposed approach is that in many applications the main quantities of interest are large-scale averaged quantities (e.g., mean temperature changes over the next five to ten years, mean wind velocities during the summer, mean sea-surface temperature). Therefore, in such applications it is not necessary to resolve all small-scale physics (e.g., local wind speed at any particular location) accurately. On the other hand, the time-step of numerical integration is often limited (for technical reasons) by these small-scale processes. The proposed research seeks systematic modification of the underlying partial differential equations to reduce the overall influence of small-scale processes and, thus, to allow for a bigger time-step in numerical simulations.

拟议研究的主要目标是开发一种新的数学方法，以允许某些类型的偏微分方程的更快的数值积分。 在这个建议中考虑的偏微分方程的类型是非常常见的物理学的许多领域，特别是在数值天气和气候研究中发挥着至关重要的作用。 所提出的方法背后的主要思想是，在许多应用中，感兴趣的主要量是大尺度平均量（例如，未来五至十年的平均温度变化、夏季的平均风速、平均海面温度）。 因此，在这样的应用中，没有必要解决所有小尺度物理（例如，在任何特定位置处的局部风速）准确。 另一方面，数值积分的时间步长往往受到这些小尺度过程的限制（出于技术原因）。 拟议的研究寻求系统的修改的基本偏微分方程，以减少小规模的过程的整体影响，从而允许在数值模拟中的一个更大的时间步长。