三维指数型迎风格式以及在环境数值模拟中的初步应用

A 3-D Exponential Up-wind Scheme and Its Preliminary Application in Environment Numerical Simulations

为了适应大气,海洋的环境数值模拟需要,在前人工作基础上提出了三维随流格式和指数型迎风格式。随流格式能使方程对流项中的对流速度误差明显减小。三维指数型迎风格式能有效抑制对流占优问题的数值振荡,并用简单的七点差分格式获得O（h2）精度的三维模式数值结果。因此,所建的模式具有格式简单,计算稳定性良好和计算精度较高的优点。初步计算表明,这个模式能有效应用于强迫-耗散型大气、海洋运动和环境问题的数值模拟。

In order to satisfy (he requirement of environmental numerical simulations in atmosphere, ocean, both a 3-D with-flow scheme and a 3-D exponential up-wind scheme, based on the rescarchs of, are proposed in this paper. Using the with-How scheme it is possible to obviously decrease the velocity's error of the convection term in the equation. Only using simple seven points difference scheme, the 3-D exponential up-wind scheme can give results of precision under the condition it can efficiently re-slrains the numerical oscillation in problem that convection occupies superiority. Therefore, the model in the paper has advantages of the simple scheme, good compulive stability and higher precision. Preliminary computing shown that it can efficiently use in numerical simulation on forcing-and-dissipating atmospheric, oceanic motion and environment problems.