求解

Expansions in orthogonal functions is used to solve the Orr-Sommerfeld equation in studies of the linear stability of parallel flow. For the plane Poiseuille flow the critical Reynold number is given accurately. Furthermore, the Blasius flow which is considered locally parallel has been studied, and the neutral stability curves, which are very important for the stability study, are given.

对于平行流的托尔明—施里希廷(Tollmien-Schlichting，T-S)波的线性稳定性，采用谱方法求解平面Poiseuille流的Orr-Sommerfeld方程，得到了精确的临界雷诺数；并研究了局部平行假设下的Blasius边界层流动，分别给出对稳定性研究至关重要的中性稳定性曲线。

Then how to work out the frequency response function of various blasting system is particularly introduced.

然后详细介绍了各种震动系统的频响函数的求解方法。

Tridiagonal block matrix elemination and sweep algorithm is successfully applied to solve the large matrix involved; central difference method is supplemented to Houbolt method to form a time integration method with estimation and correction, to solve the time integration of second order implicit non-linear equation; simplification of system equation by decoupling between the physical coordinates x and y further improves the calculation accuracy and speed.

其中：成功地引入块三对角矩阵追赶法求解上述问题构成的大型矩阵；提出中心差分法+Houbolt法的预估计—校正时间积分法，以解决二阶隐式非线性方程的时间积分问题；系统方程在物理坐标x和y上的"解耦"简化，使计算速度和计算精度得以进一步的提高。

It is impossible to describe this complex flow with a single method. Specially to transition flow, there is no suitable theory. The equation that fits it is Boltzmann equation, but the solution of it is almost impossible.

特别是对于过渡领域的流动，目前尚无完善的理论，与之相对应的数学方程是完全的Boltzmann方程，它是一个非常复杂的非线性的积分-微分方程，除了极其简单的情形，它的求解根本是不可能的。

Through a construction of a distribution function,the normal form of KFVS is deduced based on the nocollision Boltzmann equation .

通过构造一个分布函数，利用无碰撞的 Boltzmann方程，推导出求解一般形式的KFVS方法，对一维溃坝进行了模拟，并与精确解进行了比较，说明了这种方法的进步性和可行性

Using spherical harmonic function expansion and finite element method,Boltzmann transport equation is solved numerically,the convergence of the method is approved.

讨论了谱有限元方法在中子测井数值模拟中的应用，用球谐函数谱展开和有限元耦合方法求解Boltzmann中子输运方程，得到了这种耦合方法的收敛性。

As implicit pressure and explicit saturation method is selected to calculate black oil model and the bottom-hole pressure is introduced, the coefficient matrix of pressure equation becomes bordered seven-symmetrical matrix.

用IMPES法求解黑油模型，引入井底压力为未知数时，压力方程的系数矩阵变成了加边的七对角阵。

As implicit pressure and explicit saturation method is selected to calculate black oil model and the bottom-bole pressure is introduced, the coefficient matrix of pressure equation becomes bordered seven-symmetrical matrix.

IMPES法求解黑油模型，引入井底压力为未知数时，压力方程的系数矩阵变成了加边的七对角阵。

While the problem is solved by IPM, KKT (Karush-Kuhn-Tucker) matrix is a block diagonal bordered matrix. To solve this special kind of large-scale nonlinear programming problem, a predictor-corrector decomposed IPM is proposed.

针对这样一类特殊的大规模非线性规划问题，提出了预测——校正解耦内点法，采用分块LU分解技术和分块三角矩阵求解实现预测——校正环节与解耦技术的融合。

Moreover, it makes the coefficient matrix of centralized IPM's linear correction equation a block diagonal bordered matrix, which can be decomposed into the constraints equation on internal variables of independent sub-areas and coupled constraints equation. During each IPM iteration, internal variables and coupled variables are solved distributedly; thus distributed algorithm of multi-area ORPF is implemented.

在此基础上，论文将该线性方程分解为相互独立的子区域内部约束方程和复制节点的耦合约束方程，在每次内点法迭代中分布分块求解内部变量和耦合变量，从而实现多区域无功优化的分布式计算。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。