数值方程

In the aspect of virtual unexpected events, focus on the shortage of existing flame model, paper proposes a random Lagrangian method based on non-grid, which through a group of particles to modeling the fluid. Its statistical properties and the equation based on fluid changes in the same particles, but more stable.

5针对虚拟火灾突发事件，鉴于现有火焰模型的不足，论文提出了通过一组粒子建立流体模型，它们的统计特性和基于流体方程变化的粒子相同，且在数值上比方程的确定性解更加稳定。

It adopts Reynolds time-average N-S equation and k-s turbulence model to calculate the inner 3-D viscid turbulence flow of hydraulic turbine. In the unstructured grid, the governing equations are discredited with Finite Volume Method based on Finite Element Method. And the pressure correction method is proposed in numerical calculations.

然后采用基于雷诺时均N-S方程与标准k-ε湍流模型来计算水轮机三维粘性湍流场，在非结构化网格中，采用基于有限元的有限体积法对方程进行离散，用压力校正法进行数值求解。

Stability of theoretical and numerical solution to stiff integro-differential equa-tionsand to stiff integro-differential equations of integral limit which depends on state function yare discussed in this paper.

中文摘要：本文研究刚性积分微分方程初值问题及积分限依赖于状态函数y的刚性积分微分方程初值问题的理论解及数值解的稳定性和收敛性。

The nonlinear one-dimensional advective equation and the twodimensional inertial wave equations are used to verify the validity of the VCA technique and the new method of calculating the step size.

本论文也同时结合了非线性一维平流方程和二维惯性波方程进行了具体数值试验，从而验证了VCA技术对模式修正的有效性以及推导出的计算优化步长公式的有效性

The fluid flows and heat coupled calculation method is used. The standards two equations turbulence models, velocity and pressure coupled arithmetic are used.According to the results of numerical simulation analysis the local coefficient distribution changes along the pin fins.Study the effection that its height and shape of the pin fins have on the average Nu and the average number of pressure loss coefficient Eu.The circle-shaped and elliptic-shaped pin fins have different circumcolumnar regional,therefore the mixed conditions are effected.

数值计算中采用标准双方程湍流模型，速度压力耦合算法；根据数值模拟的结果分析沿扰流元的局部换热系数分布变化，研究其扰流柱高度及形状对扰流柱通道平均努赛尔特数Nu和平均压力损失系数Eu的影响，圆形和椭圆形扰流柱的绕流尾涡影响的区域的不同对扰流柱群内流体混合状况的影响。

Based on the dynamic equation, the transport and acceleration of out-flowing ionospheric ions in the magnetosphere are studied by means of finding the ion distribution function. They include two parts: the study of static ion distribution with analysis and numerical compute; the study of ion acceleration by induced electric feild in the period of dipolarization of taillike geomagnetic lines in the substorm expansion phase with the numerical simulation of the ion distribution function.

本文在磁层中上行离子的加速与传输理论研究领域中，采用动力论方程，用求解离子分布函数的方法来研究问题：(1)用解析求解和数值计算的方法，对上行离子在不同Kp指数条件下磁场位形中的定态分布进行了研究；(2)用数值模拟计算分布函数的方法，对上行离子在亚暴膨胀相磁场向偶极形驰豫过程中受磁尾的感应电场加速进行了研究。

According the experiential formulas of headbox to design the stepped diffuser headbox's geometry parameters. Supposing Paper suspension flow as potential flow and basing on hydrokinetic and computational fluid dynamics theories, we can solve the elliptoid partial differential equations which are followed by the flow functions and the potential functions by finite element method and simulate the flow's speed distribution with pde toolbox of matlab software. The simulate results and the flow analysis have good precision.

按照流浆箱的经验设计公式，设计阶梯扩散式流浆箱的各组件几何参数，以流体动力学、计算流体力学等理论为基础，假定浆流的流动为势流，采用有限元法求解浆流流动时其流函数和速度势函数所符合的椭圆型偏微分方程，应用matlab软件的偏微分方程工具包pde toolbox，模拟出所设计的流浆箱各组件内的浆流的流场流速分布，模拟结果与数值计算流动分析结果吻合。

The nonlinear hyperbolic conservation laws of the transient flow of the media in gas pipeline are hard to he solved, so, the control conservation laws are constituted of mass, momentum arid energy conservation laws, TVD/Godunov hydrid algorithm is used to simulate the transient flow in gas pipeline, and the traditional splitting approach processing nonlinear convection in momentum equation is dismissed ,the convection tern; is directly processed, in the way, the stablization of the algorithm and emulating accuracy of the transient flow are greatly improved.

针对管道中介质瞬变流动的非线性偏微分方程组难以解析求解的问题，由质量、动量、能量三个偏微分方程构成的控制方程组，应用TVD/Godunov混合算法数值模拟天然气管道中气体的瞬变流动，摒弃了传统的差分方法时动量方程非线性时流项的线性化处理，而直接处理非线性对流项，从而大大提高了算法的稳定性和管道瞬变流动的仿真精度。

To discuss the hygrothermal stress influence on strength of the building material caused by the change of temperature and moisture content,on the basis of the coupling equations of thermal conduction and moisture diffusion,its transient temperature and humidity field are derived.

为探讨温湿度变化引起的热湿应力对建筑材料强度的影响，从热传导、湿扩散的耦合方程出发，求得瞬态温度场和湿度场，并推导出包含热湿效应的各向同性材料的本构方程，从而由数值法得出材料应力大小及分布。

Based on the real observation data, forecast equitation or forecast model, the dynamics method such as divergence and vorticity calculation, real data correction, ascending and subsidence calculation was used to simulate the 4D field of divergence, vorticity and vertical velocity at different time, different range and different levels. The field was connected to 3D fields of insect trajectories, yielding the flying speed, direction, ascending area and subsidence. Thus the peak of immigratory insect could be timely monitored. A system of the peak of immigratory insect forecast was set up.

根据实际观测资料、数值预报方程或数值预报模式等输出的风场网格化处理结果，利用运动学方法、散度推算法、涡度推算法、实际资料订正法、升降法等对不同时间、不同范围、不同层次的四维散度、涡度和垂直运动速度场进行计算或模拟，将计算或模拟得到的散度场、涡度场、垂直运动速度场与昆虫迁飞的三维气流场联系起来，得到该类昆虫所具有的迁飞速度、方向、上升区和下降区，从而对昆虫的迁入峰进行实时预警。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。