在经典中心差分格式的基础上提出对流扩散方程的四阶紧凑差分格式，具体方法是，先就一维情形，将中心差分格式改造为不受网格Reynolds数限制的恒稳二阶格式，再在不增加相关网格点的前提下，通过桔式中对流系数和源项的摄动处理，使稳格式的精度提高至四阶。本文并作一、二、三维流动模型方程及高Rayleigh数自然对流传热问题的数值求解，例示本文格式的优良性态。

本文提出所谓迎风变换，将对流扩散方程分解为对流迎风函数和扩散方程，并构造相应的有限差分格式。对流迎风函数以简明的指数解析形式反映对流扩散现象的迎风效应，原则上消除了源于不对称对流算子的困难，能够便利对流扩散方程的数值求解，有限差分格式具有二阶精度和无条件稳定性，算例表明其准确性、收敛速度及对边界层效应的适应能力均明显优于中心差分格式和迎风差分格式。

The time evolution of a turbulent lock release gravity current, formed by a finite volume of homogeneous fluid released instantaneously into another fluid of slightly lower density, was studied by experimental measurements of the density structure via elaborate digital image processing and by a numerical simulation of the flow and mixing using a two-equation turbulence model. The essential fact that the gravity current passes through an initial slumping phase in which the current head advances steadily and a second self-similar phase in which the front velocity decreases like the negative third power of the time after release is satisfactorily presented by the laboratory observation. An overall entrainment ratio proportional to the distance from the release point is found by the numerical simulation. The renormalization group (RNG) K-E model for Reynolds-stress closure is validated to characterize the gravity current with transitional and localized turbulence.

Prsented in this paper are a systematic study on the global exergy consumption in the earth and a budget and a budget of the exergy consumption with respect to main terrestrial processes. Based on Szargut's definition of exergy for thermal radiation, a global exergy balamce of the thermodynamic system of the earth, driven by cosmic exeryflow originated from the temperature difference between the sun and the cosmic background, is carried out to give the global cosmic exergy consumption as the multiplication of the cosmic background microwave (CBM) radiation temperature and the global entropy generation due to irreversibility in the earth system. Concrete formulae are derived for cosmic exergy, with emphasis on generalization of a simple blackbody relationship between entropy and energy flux densities to the cases of gray body radiation with moderate or large emissivity associated with the earth system. Global entropy generation is evaluated with a result compared very with a widely accepted datum based on satellite observations in earth science. A budget of the global entropy generation is made with respect to the terrestrial radiation processes associated with the atmosphere and the earth's surface and to the molecular transport phenomena in the material earth. A mechanism of multiplication goveming transformation between cosmic exergy and terrestrial exergy is developed. An overall exergy budget of the earth system, based on the entropy budget by means of the Gouy-Stodola law, are presented with essential implication to the problem of global sustainability.