Geometric foundation of invariant and conservative parameterization schemes

不变保守参数化方案的几何基础

• 批准号: RGPIN-2016-06457
• 负责人: Bihlo, Alexander
• 金额: $ 1.68万
• 依托单位: Memorial University of Newfoundland
• 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=635608
• 关键词: Geometric; foundation; invariant; conservative; parameterization

I propose a novel framework for developing physical parameterization schemes. The key paradigm is to use the geometric properties of the original governing equations of hydro-thermodynamics to formulate parameterization schemes that preserve these properties in the approximated equations. This will then form the basis for numerical models. These properties will include both symmetries and conservation laws, which are among the most important features of any physical model. The construction of geometry-preserving parameterization schemes will mainly rely on methods from the group analysis of differential equations.

我提出了一个新的框架，开发物理参数化方案。关键的范例是使用的几何性质的原始控制方程的流体热力学制定参数化方案，保持这些属性的近似方程。这将成为数字模型的基础。这些性质将包括对称性和守恒定律，这是任何物理模型最重要的特征之一。保几何参数化方案的构造主要依赖于微分方程组分析的方法。