紧致平方守恒格式的构造和检验

为了适应气候和环境数值模拟的需要，本文在原有的显式平方守恒格式和紧致差分格式的基础上，研究构造出高阶紧致的平方守恒格式。文中给出格式的具体构造方法，也给出格式平方守恒性的严格证明。具体算例的计算表明，新构造的格式既提高了计算精度，又有良好的计算稳定性，并且适合推广应用于众多的大气、海洋和环境问题的数值模拟和预测问题。

Construction and Test of Compact Scheme with Square-Conservation

Based on explicit square--conservative scheme and compact difference scheme, a high-order compact square--conservative scheme is proposed to satisfy the requirments of climate and environment numerical simulations. The construction method of this scheme and the proving ofsquare-conservative characteristics are presented in this paper. Numerical examples show that thisscheme not only improves computing accuracy but also has better computational stability, and therefore can be applied to solve many problems in numerical simulations of the atmosphere, ocean and environment.