多相流微分积分方程组的精确数值解法
An accurate numerical method for systems of differentio-integral equations associated with multiphase flow
摘要：
本文提出了一种适用于具有一般边界条件的微分积分方程组的简单而精确的数值方法。虽然这种方法的基本思想源于凯勒箱方法，但它解决了以前凯勒箱方法没有考虑的涉及积分算子的微分方程系统的问题。两个主要的准备阶段是必需的：（一）合并程序的微分方程和条件没有积分算子和;（二）减少程序的微分方程和条件积分算子。单位阶跃函数的引入有效地简化了差分过程。采用块箭形矩阵分解技术，用牛顿法求解非线性差分方程。作为应用该方法的一个例子，层流膜状冷凝中重力和强制对流的组合方程组可以求解为预定的物理常数值。
英文摘要：
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integral operators. The differencing processes are effectively simplified by means of the unit-step function. The nonlinear difference equations are solved by Newton method using an efficient block arrow-like matrix factorization technique. As an example of the application of this method, the systems of equations for combined gravity body force and forced convection in laminar film condensation can be solved for prescribed values of physical constants.
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