Geometric foundation of invariant and conservative parameterization schemes

我提出了一个新的框架来开发物理参数化方案。关键的范例是利用水热动力学原始控制方程的几何性质来制定在近似方程中保留这些性质的参数化方案。这将构成数值模型的基础。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。几何保持的参数化格式的构造将主要依赖于微分方程组的群分析方法。

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.