不可压粘流N－S方程的边界积分解法

对原变量的Ｎ－Ｓ方程进行一阶时间离散，采用共轭梯度法解除压强－速度的耦合．对所得的一系列Ｌａｐｌａｃｅ方程、Ｐｏｓｓｉｏｎ方程和Ｈｅｌｍｈｏｔｚ方程均进行边界积分法求解，首次得到了粘性Ｎ－Ｓ方程的边界积分表示式．圆柱的定常、非定常尾迹计算结果表明了本文方法的有效性．     

关于Orr—Sommerfeld方程的Chebyshev谱方法的讨论

本文讨论了Ｏｒｒ－Ｓｏｍｍｅｒｅｌｄ方程的各种Ｃｈｅｂｙｓｈｅｖ谱离散方法，数值证明了Ｃｈｅｂｙｓｈｅｖ配置法离散Ｏｒｒ－Ｓｏｍｍｅｒｆｅｌｄ方程没有伪谱，并以此构造了适于任意平面平行速度剖面情形，对时间和时空稳定性模式一致有效的无伪谱的离离散方法，其中，对时空稳定性问题本文给出了一种新的迭代法可以快速有效地求出复频率的鞍点，对平面Ｐｏｉｓｅｕｉｌｌｅ流，Ｂｌａｓｉｕｓ边界层流和Ｇａｕｓｓ模型尾迹     

返回舱三维高超声速绕流及近尾迹流场数值模拟

为使返回舱安全、稳定、可靠地飞行，准确地计算其周围的复杂绕流流场，对飞船的初步设计是十分必要的。用Ｈａｒｔｅｎ－Ｙｅｅ的二阶迎风ＴＶＤ有限差分格式求解薄层Ｎ－Ｓ方程，模拟了返回舱三维高超声速流场，Ｍ＿∞＝７．３５，Ｒｅ＿∞＝７．５×１０￣５，α＝１０°、２０°。给出了详细的绕流结构，不同攻角、不同子午面上的物面压力分布与Ｍｏｓｅｌｅｙ和ｗｅｌｌｓ的实验数据进行了比较，符合较好。通过分析表明，在一定的攻角下，倒锥体上低压区压力的计算精度，对力矩系数及压心位置仍有明显的影响。     

液体调谐减振器的分析

本文利用Ｌａｍｂ变换，考虑液体的粘性，略去二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程中的非线性预后，建立了频域内Ｎａｖｉｅｒ－Ｓｔｏｋｒｅｓ方程的边界积分表达式，完整地处理了边界条件（包括自由面边界条件和固壁边界条件）并且给出了液体随结构振动时的附加质量与阻尼的计算表达式。     

高超声速三维化学非平衡流动N－S方程数值解

详细地叙述了模拟三维高超声速电离空气化学非平衡粘性流全流场（前体和底部近尾迹）的数值方法，化学反应粘性流求解是基于带有化学源项的Ｎ－Ｓ方程的守恒形式，总的连续方程由组元守恒方程组所代替．对于高温电离空气流动，存在如下７个主要组元，它们依次为Ｎ＿２，Ｏ＿２，ＮＯ，ＮＯ￣＋，Ｎ，Ｏ和ｅ￣－．研究发展了求解完全耦合的，与时间相关的偏微分方程组的数值方法．利用一类新的迎风ＴＶＤ激波捕捉有限差分格式求解守恒形式的控制方程组，对高超声速层流有攻角钝锥体绕流流场，在非催化壁条件下、对包括底部近尾迹在内的全流场各参数，如组元浓度，电子密度和温度，以及物面压力分布和热流率分布得出了计算结果．对化学反应气体和完全气体模型的计算结果进行了比较，计算的流场电子密度与飞行实验结果符合很好．     

Reissner裂板表面裂纹应力强度因子的线弹簧—不连续位移…

本文由Ｒｅｉｓｓｎｅｒ型板的不连续位移基本解，根据Ｂｅｔｔｉ互换定理，导出了Ｒｅｉｓｓｎｅｒ型板的不连续位移边界积分方程，结合平面问题的不连续位移边界积分方程－－边界元方法和线弹簧模型，给出了Ｒｅｉｓｓｎｅｒ型板表面裂纹应力强度因子的线弹簧－不连续位移边界积分方程解法。     

A uniformly valid asymptotic solution of the Navier-Stokes equations

ＡＵＮＩＦＯＲＭＬＹＶＡＬＩＤＡＳＹＭＰＴＯＴＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＱｉｎＳｈｅｎｇ－ｌｉ（秦圣立）ＺｈａｎｇＡｉ－ｓｈｕ（张爱淑）（Ｄｅｐｔ．ＯｆＰｈｙｓｉｃｓ,ＱｕｆｕＴｅａｃｈｅｒｓＵｎｉｖｅ...     

A THREE-FLUID MODEL OF THE SAND-DRIVEN FLOW

ＡＴＨＲＥＥ－ＦＬＵＩＤＭＯＤＥＬＯＦＴＨＥＳＡＮＤ－ＤＲＩＶＥＮＦＬＯＷ￥(刘大有，董飞)ＬｉｕＤａｙｏｕ；ＤｏｎｇＦｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓ...     

环氧树脂－SiO_2空心微球复合材料的Mie－GrUneisen方程

本文描述了三种不同密度（０．６，０．７６和０．９ｇ／ｃｍ￣３）的环氧树脂－ＳｉＯ＿２空心微球复合材料的Ｈｕｇｏｎｉｏｔ关系。讨论了上述材料以其相应的Ｈｕｇｏｎｉｏｔ关系作为参考方程的Ｍｉｅ－Ｇｒｕｎｅｉｓｅｎ方程，并与Ｐ－α模型进行了比较，结果相当一致。由此得出结论，在本文研究的压力范围内，Ｍｉｅ－Ｇｒｕｎｅｉｓｅｎ方程可应用于上述孔隙材料。     

A STABILITY STUDY OF NAVIER-STOKES EQUATIONS (Ⅲ)

ＡＳＴＡＢＩＬＩＴＹＳＴＵＤＹＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳ（Ⅲ）ＳｈｉＷｅｉ－ｈｕｉ（施惟慧）（ｓｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ．Ｓｈａｎｇｈａｉ）（ＲｅｃｅｉｖｅｄＪａｎ．２０．１９９４；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅ...     

Lagrangian finite element analysis applied to viscous free surface fluid flow

A new Lagrangian finite element formulation is presented for time-dependent incompressible free surface fluid flow problems described by the Navier-Stokes equations. The partial differential equations describing the continuum motion of the fluid are discretized using a Galerkin procedure in conjunction with the finite element approximation. Triangular finite elements are used to represent the dependent variables of the problem. An effective time integration procedure is introduced and provides a viable computational method for solving problems with equality of representation of the pressure and velocity fields. Its success has been attributed to the strict enforcement of the continuity constraint at every stage of the iterative process. The capabilities of the analysis procedure and the computer programs are demonstrated through the solution of several problems in viscous free surface fluid flow. Comparisons of results are presented with previous theoretical, numerical and experimental results.     

二维定常不可压缩粘性流动N-S方程的数值流形方法

将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法.     

A high-order nodal discontinuous Galerkin method to solve preconditioned multiphase Euler/Navier-Stokes equations for inviscid/viscous cavitating flows

In this study, a high-order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier-Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual-time stepping method is used for the time integration. An artificial viscosity approach is implemented and assessed for capturing the steep discontinuities in the interface between the two phases. The accuracy and robustness of the proposed method in solving the preconditioned multiphase Euler/Navier-Stokes equations are examined by the simulation of different two-dimensional and axisymmetric cavitating flows. A sensitivity study is also performed to examine the effects of different numerical parameters on the accuracy and performance of the solution of the NDGM. Indications are that the solution methodology proposed and applied here is based on the NDGM with the implicit dual-time stepping method and the artificial viscosity approach is accurate and robust for the simulation of the inviscid and viscous cavitating flows.     

非稳态流动的隐式最小二乘等几何方法

对非稳态粘性不可压流动问题提出了一种隐式最小二乘等几何计算方法。该方法先用隐式的向后多步差分格式对Navier-Stokes方程进行时间离散,再用Newton法线性化对流项,最后在每个时间步上用最小二乘等几何方法进行求解。根据该算法编制了计算程序,通过构造解析解的方法验证了程序的正确性,用该程序求解了雷诺数为5000时的非稳态二维顶盖驱动流问题,计算结果捕捉到了流动过程中涡的演化过程,表明本文方法可用于非稳态流动的求解。     

Fractional step method for solution of incompressible Navier-Stokes equations on unstructured triangular meshes

In this paper an implicit fractional step method for the solution of the two-dimensional, time-dependent, incompressible Navier-Stokes equations is presented. The current method was developed for use on an unstructured grid made up of triangles. The basic principles of this method are that the evaluation of the time evolution is split into intermediate steps and that for the spatial discretization of the flow equations a finite volume discretization on an unstructured triangular mesh is used. The present approach has been used to simulate viscous, laminar flows for various Reynolds numbers in test cases such as a backward-facing step, a square cavity and a channel with wavy boundaries.     

Computation of free surface waves around an arbitrary body by a Navier-Stokes solver using the psuedocompressibility technique

A Navier-Stokes equation solver is developed for computing free surface wave and viscous flow around an arbitrary body, in which a free surface model is introduced into the pseudocompressibility solution. The governing equations are classified in a vectorial form, with primitive variables, and a block diagonal system is generated by the discretization of an implicit factorization method. A moving grid system fitted to both the free surface and body surface is generated by an effective cubic spline fitting technique. Two zero-equation turbulence models, namely the Cebeci-Smith model and the Baldwin-Lomax model, are used for turbulent calculations. Numerical simulations are carried out for the free surface viscous flows generated by a submerged hydrofoil and a ship model. Computed results are in reasonable agreement with measurements.     

Finite Element Analysis for 3-D High Reynolds Number Flows

A Petrov-Galerkin finite element method using exponential weighting functions for the computation of three-dimensional incompressible viscous flow problems is presented. The unsteady incompressible Navier-Stokes equations are discretized by means of a semi-explicit scheme with respect to the time variable. As the time-marching scheme, the fractional step method is used effectively. Numerical results demonstrate that the present method is capable of solving the cubic cavity flow accurately and in a stable manner for Reynold numers up to 10⁴     

A new implicit factored scheme for the compressible Navier-Stokes equations

A new scheme for solving the compressible Navier-Stokes equations is developed. For the inviscid portion of the equations the single step scheme used by the authors is factored according to the sign of the eigenvalues of Jacobian matrix. For the viscous portion of the equations a scheme corrected with operator addition is factored too. The scheme obtained has second order accuracy in time and in space and is used to solve two-dimensional problem. The numerical results of 2-D shock wave-boundary layer interaction are compared with experimental data.     

AN APPROXIMATE MODEL OF UNSTEADY AERODYNAMICS FOR HYPERSONIC PROBLEMS AT HIGH ALTITUDE

针对高空高马赫数飞行环境和强黏性干扰的物理特性, 在当地流活塞理论的基础上引入有效外形修正, 发展了黏性修正当地流活塞理论, 结合定常N-S方程解给出了高空高马赫数下针对该方法的有效外形的判据, 并通过数值算例对该判据进行了验证.通过对典型尖头薄翼和典型钝头翼的一系列二维非定常算例, 将该方法与一阶活塞理论、基于欧拉(Euler)方程的当地流活塞理论和非定常N-S方程数值解进行了对比. 结果显示在高度为40~70 km、马赫数为10~20范围内, 通过该方法计算得到的非定常气动力与非定常N-S方程数值解吻合较好, 明显优于活塞理论和基于Euler方程的当地流活塞理论.该方法克服了传统的活塞理论和当地流活塞理论不能用于高空高马赫数这类强黏性效应情况的弊端, 在较宽的马赫数、攻角、飞行高度范围内都有良好的适用性, 同时其计算效率远高于非定常N-S方程.