提出一种基于匹配渐进展开法对Navier-Stokes 方程进行渐进展开求得渐进合成解的方法.在边界层根据边界条件并利用坐标变换放大坐标的方法解出两个同轴旋转圆柱间流体流动Navier-Stokes方程的内解,并在Navier-Stokes方程的外解已经解出的基础上根据内、外解的匹配原则对内、外解进行匹配,从而解出具有二阶有效、简洁的渐进合成解.通过举例证明,该合成解准确性好并且与基本流接近程度很好.

@@@@Based on the matching asymptotic expansion method , the authors develop a new method to solute the composite solution for the Navier -Stokes equation.The interior solution of Navier -Stokes equation is solved by using the boundary conditions and the way of coordinate transformation at boundary region .In accordance to the matching of outer solution and interior solution , the second, effective and concise gradual composite solution is solved and this method is on the basis of the finished outer solution .For example, the accuracy and the degree of closeness to the basic flow is very well ..

数值求解非定常不可压缩Navier-Stokes方程的难点之一在于强烈的非线性容易引发非物理震荡，本文结合可以有效减弱此种震荡的特征线离散方法，基于局部Gauss积分之差的稳定化格式，采用最低等阶非协调混合有限元对NCP1-P1，构造出求解非定常不可压缩Navier-Stokes方程的特征稳定化非协调混合有限元方法。证明了该方法的全离散格式是无条件稳定的，并给出逼近解的相应误差估计。

One of the difficulties for numerical simulation of the unsteady Navier-Stokes equa-tions is the nonlinearity, when characteristic discretization can effectively weaken the non-physical concussion caused by nonlinear form. Based on the local Gauss quadrature, this paper proposes a characteristic stabilized nonconforming finite ele-ment method to solve the unsteady incompressible Navier-Stokes equations, where the characteristic method and lowest equal-order nonconforming pair NCP1-P1 are employed. We obtain the unconditional stability of its full discrete format and the corresponding error analysis of the approximate solutions.

本文研究了L′evy过程驱动的随机二维Navier-Stokes方程弱解的指数性态.给出了不同条件下解的长时间形态,获得了一些特殊情形下解的样本轨道的指数稳定性.

In this paper, some results on the pathwise exponential stability are established for the weak solutions of stochastic 2D Navier-Stokes equation driven by L′evy noise. Also, some results and comments concerning the stabilizability and stabilization of these equations are stated.

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβwith β≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ)=ρβwith β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.

为了研究边界滑移对上游泵送机械密封性能的影响，建立液膜三维几何模型和计算模型，基于 Navier 线性滑移模型对液膜壁面边界条件进行修正，采用商用软件 Fluent 的 SIMPLEC 算法及层流模型求解三维 Navier －Stokes 方程，并分析相对滑移量对液膜静压分布、开启力、摩擦扭矩、泄漏量的影响规律。结果表明：相对于边界滑移发生的位置，滑移速度的大小对密封性能的影响更大；当相对滑移量较小时，存在边界滑移与无滑移的模拟结果无明显区别，能很好地解释宏观无滑移边界假设的应用，当相对滑移量较大时液膜动压效应随滑移的增加而减弱，开启力、摩擦扭矩、泄漏量都随边界滑移的增加而减小；相对于开启力的降低，边界滑移的减阻和降低泄漏的效果更为明显；当开启力较小，应避免边界滑移发生；当开启力足够大时，加工成超疏水表面形成边界滑移，可极大地减少摩擦扭矩，降低能耗。

To study effects of boundary slip on performance of upstream pumping mechanical seal,the geometric and computational models of fluid film are built.The Navier -Stokes equations of the fluid film flow are solved in Fluent by employing SIMPLEC algorithm and finite volume method.The boun-dary conditions are modified with the Navier linear slip model and the effects of boundary slip on the film pressure distribution,opening force,friction torque and fluid leakage are analyzed.The results show that the slip velocity has a greater influence than the location of slip occurrence.When the slip velocity is tinier,the results of simulation are almost the same as the data without slip,indicating the non-slip assumption for macro flow of a fluid is reasonable.However,when the slip is larger,the dy-namic effect of fluid film is weakened and the opening force,friction torque and fluid leakage are de-creased with the increasing slip velocity.Additionally,the reduction in both friction torque