THE SOLUTIONS OF STEADY－STATE CONVECTION EQUATIONS IN THE SPACES THAT POSSESS RESTORI NGNUCLEUS

In this paper ,in the space that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution .Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].

THE STABILITY AND CONVERGENCE OF THE FINITE ANALYTIC METHOD FOR THE NUMERICAL SOLUTION OF CONVECTIVE DIFFUSION EQUATION

In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.

再生核空间中求解定态对流扩散方程

本文在再生核空间Ｗ中，给出定态对流扩散方程的一种级数形式的解析解，此解析解具有如下特点：１）解是由精确的形式给出；２）解是显式计算，不须解方程组；３）在数值求解中，每增加一个基数项，近似解的误差在空间范数意义下单调下降。最后对［２］中的算例，进行了计算，结果比［２］中给出的渐近解精度高。

三维对流扩散方程的混合有限分析解

本文应用线性徽分方程的算子迭加原理，将二维对流扩散方程的有限分析法交替方向用于三维对流扩散方程，从而得到较三维有限分析法简单实用的混合有限分析法．接着用数学分析法证明了该方法的稳定性和收敛性．并用指定强迫解方法对方程离散格式和程序设制等做了验证．最后计算了三维紊动射流，计算结果与实验资料一致，表明用混合有限分析法计算三维对流扩散问题是可行的．

对流扩散方程的涡区分离解法

对流扩散方程是流体计算中一个基本方程,常用的数值方法导至解一个高阶的代数方程组,要求较大的存贮量和较长的计算时间。本文提出一种涡区分离解法,它利用对流扩散方程的迎风性质,把涡区从对流支配区分离出来,仅在各个涡区建立代数方程组并求解。而在对流支配区,则充分利用其抛物性,只需采用显式格式进行计算。由于在各涡区建立的这些方程组阶数和带宽都较小,因此要求存贮量较小,计算速度较快。对于雷诺数较大,涡区范围较小的问题,该方法特别有效。

解溶质运移问题的特征有限分析法

针对解溶质运移模型会出现数值误差的问题,结合特征线法求解对流问题和有限分析法能求单元解析解的优点,推导得到了求解对流扩散方程的特征有限分析格式。算例表明,该格式有较高的计算精度,是对有限分析格式的拓展。