数值方程

The fundamental and higher-order harmonic ultrasound fields of a zeroth-order Bessel ultrasound field and focused Gaussian field in absorbing medium are computed and simulated by solving the KZK equation using a frequency domain finite difference method.

通过频域有限差分方法求解KZK方程，对吸收媒质中的零阶Bessel超声场、Gauss聚焦超声场进行计算，得到基波和高次谐波声场的数值解和仿真图，计算仿真结果验证了上述的理论结论。

The physical character of the super-critical hydrogen in the regenerative cooling channel is studied : started with the physical character of the super-critical hydrogen , using the method of least square , figuring out the state equation which is applicable to the state from liquid to the super-critical in the super-critical pressure , the constrained convection and the heat transfer in the super-critical channel are simulated using the equation , the results of the simulation are identical with the experiment in the same condition .

对再生冷却通道内的超临界氢的物性进行了研究：从超临界氢物性的实验结果入手，用最小二乘法拟合出适用于超临界压力下氢由液态过渡到超临界态的状态方程，并利用该方程对超临界氢管内强迫对流换热进行了数值仿真，仿真结果与相同条件下实验结果相一致。

For some typical ship manoeuvring motions in restricted waters, numerical study on simulation of the viscous flow and calculation of the hydrodynamic forces is carried out by solving the RANS equations:(1) Numerical study on the viscous flow and the hydrodynamic forces on a ship in oblique motion in shallow water.

本文针对如下几种典型的限制水域中的船舶操纵运动，通过求解RANS方程，对其粘性流场和水动力进行了数值研究：(1)浅水域船舶斜航运动的粘性绕流场及水动力数值计算研究。

Using this fundamental solution, a general method for solving the above mentioned problem is given. Finally, the stress intens...

文中还使用奇异积分方程的数值理论，对二条非共线的等长径向裂纹的应力强度因子和抗扭刚度作了数值计算。

Many methods have been developed in evaluating the QNMs, such as evolving the time dependent wave equation method, integration of the time independent wave equation method, semi-classical method and fraction function method.

许多方法被用来研究黑洞的似正规模：波动方程的时间数值演化方法；波动方程的时间积分方法；半经典近似方法；连分数方法。

In the paper, a way of amending λ was introduced to solve the point-reactor neutron kinetics equations so that the numerical solution of single-group delayed neutron model is closed to that of six groups delayed neutron model when a positive step changed reactivity was introduced.

通过修正单组缓发中子先驱核衰变常量λ值，使点堆中子动力学方程单组缓发中子模型在正反应性阶跃输入时的数值计算结果趋近于六组缓发中子模型数值计算结果。

During the lateral parabolic profile was computed,numerical methods of calculating angle of inclination on initial point of the lateral paracurve and calculating angle of inclination based on interval length were analyzed.It is pointed out that the key of the lateral parabolic profile design is a circular function equation which can be applied to solving the angle of inclination on initial point of the lateral paracurve.

对侧位抛物线剖面设计求解过程中的求侧位抛物线初始点井斜角的数值方法和从段长求井斜角的数值方法进行了分析，指出其关键是求解侧位抛物线初始点井斜角所满足的一个三角函数方程。

In chapter 2, we present the numerical schemes for resolving Shallow Water Equations on structured and unstructured meshes, such as Godunov and composite schemes.

第二章介绍了结构网格上和非结构网格上解浅水波方程的数值方法，详细介绍了具有代表性的求解浅水波方程的Godunov型有限体积格式和复合有限体积格式。

To compute the solution to the nonlinear equation of pressure in the Riemann problem for the pressure grdient equations, the Godunov scheme gives a reasonable approximate value for the exact solution. By using the Newton-Ruphson iteration method and some necessary computation, we get the inter-cell numerical flux directly.

为求压差方程黎曼问题中关于压力的非线性方程的解，Godunov格式给出一个合理的初始近似值，利用Newton迭代法和一些必要的计算得到格式中的数值流。

In the description, the fluid lump and the precursor film are calculated as a whole using order parameter coupled Navier-Stokes equations, CHW (Cahn, Hilliard and van der Waales) equation and GNBC (Generalized Navier boundary condition).

流体团和先驱膜作为一个整体用与组分序参数耦合的Navier-Stokes方程， CHW(Cahn， Hilliard， van der Waales)方程和GNBC(广义Navier边界条件)进行数值模拟和分析。

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