数值微分

In this paper , we consider the Expanded Mixed Finite Element Method and mixed covolume method for the quasilinear parabolic integro-differential equation and quasilinear parabolic problem.

本文中我们采用扩展混合有限元方法和混合体积元方法数值模拟了二阶拟线性抛物型积分微分方程和二阶拟线性抛物问题。

The bifurcation and chaos behavior of impact and rubbing fault rotor system caused by the parameters of nonlinear rigidity, rotor rotating speed, eccentric mass is analyzed, in the numerical value analysis method. The bifurcation diagrams, maximum Lyapunov exponent diagrams, Poincaré maps, phase plane portraits, trajectories of journal center, time-history curve, amplitude spectra diagrams of the rotor motion are used. The convert and evolution course of periodical response, quasi-periodical response, double-periodical bifurcation, chaos of the system response is analyzed.(3). It is deduced that the general differential equation of bending-torsional-pendular coupling vibration about rotor with the gyroscopic moment. On the basis of this equation, the general differential equations of coupled bending, torsional and pendular nonlinear vibration about rotor with unbalance character and rubbing character are deduced.

2建立了具有非线性刚度的转子系统在非稳态非线性油膜力作用下的径向碰摩动力学微分方程，并应用含高阶余项的非线性动力方程的线性化数值法研究了此类系统响应的复杂动力学行为，利用转子响应的分岔图、最大Lyapunov指数曲线、Poincaré截面映射、时域波形、相轨线、轴心轨迹、幅值谱等图形分析了系统响应的周期运动、拟周期运动、倍周期分岔、混沌等运动形式的转化与演变过程，重点研究了非线性刚度、转子转速、偏心质量等系统参数对碰摩故障转子系统的分岔和混沌行为的影响。

CFD-fluent simulation software and measurement are applied to establish the math models of exhaust gas concentration distribution and boundary conditions. Finite volume methods and PISO are used to solve the differential equations of exhaust gas distribution in a kitchen. After the adjustment and comparison with those from the practical measure, the simulation results of CO2 and CO concentration distributions accord with experimental ones.

运用CFD-fluent模拟软件和实测相结合的方法，建立废气的浓度和扩散分布的数学模型与边界条件，利用数值分析法中的有限体积法和PISO算法对厨房内废气分布的微分方程进行离散和求解，对模拟结果进行校正并与实际测试结果进行比较。

A set of quadruply coupled equations (fluid flow, convection-diffusion, energy conservation and mechanical equilibrium) with a number of cross-couplings and coupled constitutive relations is formulated to quantify the multi-physics of oil displacement by CO2 injection, implemented into and solved by using FEMLAB. FEMLAB is the first engineering tool that performs equation-based multi-physics modeling in an interactive environment. With FEMLAB, the coupled multi-physics model can be solved simultaneously. The applicability of this model has been demonstrated through an example of simulations for a two-dimensional reservoir of size 1000 m×1000 m with one injection and one production wells. Model results illustrate the significant importance of the cross-couplings between individual (thermal, hydrological, chemical and mechanical) physics.

首先，建立一套流、固、热、多相流等多场全耦合控制方程组及其相应的耦合本构关系；然后，采用FEMLAB为工具来模拟三次采油阶段CO2驱油过程中的流、固、热、物质守恒等多场之间的全耦合作用，是第一个人机交互式的基于偏微分方程组的多物理场耦合分析的工程工具，利用FEMLAB，该4个耦合方程组成的方程组可以一次同时被求解出来：最后，应用该模型来求解一个二维油田的驱油情况，数值计算结果表明，原位应力、注入温度、注入压力等因素对CO2的地下贮存效率、驱油速度等有重要影响。

Aslak Tveito and Ragnar Winther,Introduction to Partial differential Equations: A Computational Approach,Springer ...

这门课程将将微分方程的理论、数值逼近和相关的应用结合在一起讲述。

A continuum model integrated with heat, mass, momentum transport behavior is applied to simulation of solidification process of continuous casting billets, and the effects of undercool degree on simulation are considered in particularly.

将连铸坯凝固过程三个区（固相区、固液两相区、液相区）的三个场的定量描述统一在同一组微分方程中，实现了连铸坯凝固过程温度场、流场和溶质场的数值模拟。

The principle of interaction between rail and bridge has been reasoned, the mechanism of the formation of longitudinal additional forces including braking force, bending force and temperature ...

文中深入探讨了线桥相互作用原理，论述各种纵向力的产生机理及其求解方法，对传统的微分方程解法及现代的数值解法进行了分析与对比。

Analyzing on the fault of local rubbing caused by compatible misalignment of rotors, a dynamic model for the rotor system with misalignment and rub-impact was established. Then the dynamic behaviors of this system, which varied with the values of parallel misalignment and declination, were investigated by using numerical integral method.

以水轮发电机组转子系统为研究对象，针对刚性联轴器综合不对中引起转子局部碰摩的问题，建立了机组转子不对中–碰摩耦合故障的动力学模型和微分方程，并利用数值积分方法研究该系统随不对中平行量和偏角参数变化的动力学行为。

The applications of modified Jameson's scheme to the complex flow around the missiles with canards and tails, result in good agreement between computations and experiment data of the standard missile model of U.S.A..

将改进的Jameson格式应用到多翼导弹的三维流场计算中，并使用分区技术和三维椭圆微分方程数值网格生成技术以精确模拟此复杂构形的复杂流态，计算结果与美国导弹标模的实验吻合很好。

This current is extra high and exceeds the permitted value of 10 % error curve of protection current transformer.It will affect the performance of relevant protection equipment.

文中以n次曲线模拟TA铁心饱和时的非线性磁化曲线，由此导出TA回路的非线性微分方程，并采用数值方法计算出在典型暂态短路电流作用下的TA二次电流波形。

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。