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本文从天气学的事实出发,应用自共轭椭圆型边值问题解的简单格林函数表达式,建立适合解动力气象学中椭圆型方程狄氏边界值问题的数值迭代解法,这个方法有较普遍的意义。目前,气象中常用的近似方法——方法、方法、Fjortoft方法以及外推Liebmann方法都是本文所提方法的特殊情形。在本文所提方法的一般形式基础上,还可以对上述各种近似方法的准确度、收敛情况以及改进途径得到明确的了解。作者将公式Ⅱ_1用在数值解平衡方程的计算中,作为本文所提方法的数值计算的检验,试用结果表明本文所提方法有理论概括意义和实用前途。
In this paper, based on the facts of the weather, a simple Green’s function expression of self-conjugate elliptic boundary value problem is applied to establish a numerical iterative method suitable for solving the boundary value problem of elliptic equations in dynamical meteorology. This method is more general Meaning. At present, the approximate methods commonly used in meteorology - methods, methods, Fjortoft methods and extrapolation Liebmann methods are all special cases of the method proposed in this paper. Based on the general form of the method presented in this paper, we can also get a clear understanding of the accuracy, convergence and improvement of the above approximation methods. The author uses the formula II_1 in the calculation of the numerical equilibrium equation as a test of the numerical calculation of the method proposed in this paper. The experimental results show that the method proposed in this paper has theoretical generalization and practical prospects.