物理守恒律保真格式构造与数值预报斜压原始方程传统谱模式改进研究

文中构造并证明了一般二次和三次物理守恒律时间差分保真格式两个构造定理,以往一些主要时间离散守恒格式构造方案可作为两个定理特例给出。它们不仅可为解决更加广泛类别的时间离散保真格式构造基本问题提供适用数学基础,而且也为结合已有瞬时空间离散守恒格式,解决更加广泛类别的时-空离散意义下保真格式构造基本问题提供适用的数学基础。此外,文中两个定理还可解决两大类问题的线性和非线性计算不稳定性问题。斜压原始方程传统半隐式全球谱-垂直有限差分模式目前是世界上许多国家的业务预报和大气环流模式。本工作利用文中新构定理,构造并且实现了斜压原始方程全球谱-垂直有限差分模式半隐式高阶全能量守恒方案。以往该项基本问题无论在理论还是实践上长期以来一直都未能得到解决。

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SCHEME OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL WEATHER PREDICTION

In this paper,two form ulation theorems of time-differ encefidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,withear lier major conserving time-discretized schemesgiven as special cases.These two theorems can provi denew mathem atical basis for solving basic formulation problem sofmore types of conservative time-discretef idelity schemes,and even for formulating conserv ative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schenes.Besides,the two theorems canalso solve two large categories of problems about linear and nonlinear computational instability.