数值方程

Based on fluid numerical results, a new parameter and its calculating method which are both strictly derived from basic equations of hydromechanics and thermodynamics are used to evaluate the mixing effect of viscous fluid.

从流体力学及热力学的基本方程出发，经严格推导给出了一种新的基于流场数值计算结果的评价粘性流体混合均化效果的参量及其计算方法。

First of all, the report introduced evolution, achievments and problems in the study of anisotropy in the inner of earth. The first-order hyperbolic system of equations is work out, which is used to describe the wave motion in 2D transversely isotropic media. Utilizing the characteristics of free-divergence, We have imposed MacCormack theme that is used to simulate multicomponent records in anisotropic media and have developed a fast high order vectorized finite-difference algorithm adapted for the vector supercomputer.

本文首先阐述了地球内部介质各向异性研究的沿革、成就和问题，接着给出了描述二维横向各向同性介质中波动的一阶双曲型方程，利用其自由发散特性，构制了各向异性介质中多波多分量地震记录数值模拟的MacCormack算式，导出了适用于并行计算的二维横向各向同性介质中波动的有限差分模拟算子，该算子具有可并行化计算、相位差小等优点。

The research on numerical method for hyperbolic conservation laws is one of the important directions in computational mathematics.

中文摘要：双曲型守恒律方程数值方法的研究，是计算数学中的一个重要研究方向。

Numerical computation is to simulate on the atmospheric circulation of the Northern Hemisphere with this model under ideal boundary conditions.

从该模型出发可导出地球流体力学方程，用这一模型对理想边界条件下的北半球大气环流进行了数值计算。

The furnace gas is applied with the ideal gas state equation.

为了改善大型渗碳炉的均匀性，本文应用数值计算方法研究圆筒形井式渗碳炉炉膛内的流动传热过程，假设炉内流场满足定常、不可压缩轴对称条件，炉内气体可以应用理想气体状态方程。

To calculate the aerodynamic forces on the vehicle and grid-fins, we use time-dependent method to solve the Navier-Stokes equation of ideal gas, and flux conservational multizones method to divide the complex vehicle and grid-fins into eight computational zones which are relatively independent, and correlative with each other at once with satisfactory results.

为了计算作用在飞行器和栅格翼上的气动力，采用时间相关法数值求解完全气体的三维Navier－Stokes方程，并运用通量守恒的分区计算方法，将复杂的飞行器和栅格翼系统分解成八个既相对独立，又相互关联的计算区域，得到了满意的结果。

In the two-dimensional simulation, the fully implicit difference scheme is used for the continuity equations to ensure numerical stability; Jacobian iteration is used to solve the difference equations, and only nonzero elements in the coefficient matrixes of these equations are dealt with, which reduce the requirement for memory and shorten the calculation time.

在两维模拟计算中，对连续性方程采用全隐式差分方案以保证数值稳定性；运用雅可比迭代法求解差分方程组，并且在求解过程中，只对差分方程组系数矩阵中的非零元素进行处理，因此减少了对内存的需求量，而且缩短了计算时间。

The boundary singular kernel method and the modified pen alty method are utilized to treat the essential boundary conditions and incompressibility constraint, respectively. The stiffness equation for analysis of metal forming using RKPM is derived and its key algorithms are given.

分别采用边界奇异权法和修正的罚函数法处理本质边界条件和体积不可压缩条件，推导了金属塑性成形过程无网格RKPM法数值模拟的刚度方程，给出了关键算法。

The boundary singular kernel method and modified penalty method are utilized to treat the velocity boundary conditions and incompressibility constraint, respectively. The arc-tangential friction model is employed to treat the contact conditions.

分别采用边界奇异权法和修正的罚函数法处理速度边界条件和体积不可压缩条件，采用反正切摩擦模型处理摩擦边界条件，推导了金属三维塑性成形过程EFGM法数值模拟的刚度方程，给出了关键算法。

Chapter 1 we introduce the risk process with positive and negative risk sums,show the background of the risk process. Chapter 2 we show the integral and differential equation of birth probability,give the Lundberg inequation that the ruin probability satisfies with martingale approach,then discuss then ruin probability of the risk process with two dependent positive and negative risk sums,study how the dependence impacts on the ruin probability. Chapter 3 we compare the concrete examples by numbers,and makes further comparison between the two results coming out of independency and dependency,with the purpose of narrating their respective impacts on the probability of ruin probability.

本文第一章引入含正、负风险和的风险模型，介绍风险过程的实际背景；第二章给出生存概率Φ所满足的积分-微分方程，利用典型鞅方法给出破产概率Ψ满足的Lundberg不等式，并且讨论两个相关正、负风险和模型的破产概率，研究相关性对破产概率的影响；第三章对具体实例给出数值比较，进一步把相关性和独立性两种情形的结果进行比较，说明对破产概率的影响。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新