一种用边界元方法求解二维不可压缩粘性流动的方法

本文用边界元方法求解了二维不可压缩粘性流动的涡量——速度方程,利用求解区域边界上的速度法向导数和速度值直接得到了涡量的边界条件,克服了利用涡量方程求解二维不可压缩粘性流动时涡量边界条件(主要是壁面边界条件)难以给定的困难,算例表明:这种方法比较简单且计算结果基本上是令人满意的。     

高阶紧致格式求解二维粘性不可压缩复杂流场

提出了一种求解二维不可压缩复杂流场的高精度算法．控制方程为原始变量、压力Ｐｏｉｓｓｏｎ方程提法．在任意曲线坐标下，采用四阶紧致格式求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，时间推进采用交替方向隐式（ＡＤＩ）格式，在非交错网格上用松弛法求解压力Ｐｏｉｓｓｏｎ方程．对于复杂的流场，采用了区域分解方法，并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场．利用该算法计算了二维受驱空腔流动，弯管流动和垂直平板的突然起动问题．计算结果与实验结果和其他研究者的计算结果相比较吻合良好．对于平板起动流动，成功地模拟了流场中旋涡的生成以及Ｋａｒｍａｎ涡街的形成     

数值求解不可压缩流动的投影方法研究进展

在过去的20多年中, 投影方法通过速度和压力的解耦计算, 获得了比全耦合方法更高的计算效率, 这个显著优点使之得以广泛应用. 目前, 在计算非定常不可压缩流动的原始变量形式的数值方法中, 投影方法得到了越来越广泛的应用. 本文根据投影方法的构造思路,将众多的投影方法分成了3类, 即: Helmholtz-Hodge分解类投影方法、算子分裂类投影方法和局部连续投影方法, 并详细的介绍了3类投影方法的发展历程和求解步骤. 从投影方法的求解过程不难发现, 通过速度和压力的解耦计算, 提高了投影方法的计算效率, 但同时也给投影方法的时间精度分析带来了困难, 并长期成为大家争论的焦点. 普遍认为, 速度的时间精度比较容易达到高阶, 但是压力一般来说只有一阶精度. 但通过对3类投影的对比分析后, 我们认为, 局部连续投影方法将有助于澄清目前投影方法存在的相关争议, 并使得发展高阶精度的投影方法在理论上和技术上成为可能.      

数值流形方法的粘性边界问题初探

在实际工程数值流形方法分析中,采用固定约束边界的方法处理无限域或者半无限域的情况,边界处应力波的反射造成模拟结果与实际情况不符.本文基于Lysmer等人提出的粘性边界理论,在边界上设置阻尼器,推导相应粘性边界条件下流形单元刚度矩阵的数值计算格式,经岩石长条中弹性波传播算例,并与有限元结果对比,验证了该粘性边界的有效性,有利于数值流形方法的工程中推广应用.     

二维振荡叶栅非定常粘性流动数值模拟

采用显式四步Runge-Kutta格式，结合Baldwon-Lomax紊流模型求解Navier-Stokes方程，借助运动网格技术，完成了对二维振荡叶栅非定常粘性流动的数值模拟。为了加速求解过程，引入了变系数隐式残差光顺方法，取得了较好效果。数值结果与已公布的数据有很好的一致性。     

可压缩气体定常非Darcy渗流的流动分析及其应用

气体通过多孔介质的非Darcy流动具有广泛的工程应用背景，因此对多孔介质中的气体非Darcy流动进行流动分析有着非常重要的意义。然而，在通常的研究中，一般都将气体考虑为不可压缩流体，很少考虑气体的压缩性。对于高压气体以较高的速度通过多孔介质的情况，在进行流动分析时，不仅要考虑非Darcy效应，还必须考虑气体的压缩性。在本文中，对可压缩气体通过多孔介质的定常非Darcy流动进行了一维流动分析，得出了多孔介质中气体的压力分布和速度分布。还进一步给出了在高压差和高流速情况下，测定多孔介质材料渗透率和惯性系数的方法，以及多孔介质材料前后压力差与材料厚度的比Δp/L和材料有气流速度u1的解析关系。     

基于局部DQ-RBF不可压缩N-S方程的数值求解

以RBF作为DQ方法的基函数,将迎风机制引入DQ-RBF中,建立了二维不可压缩黏性N-S方程数值求解模型,采用Levenberg-Marquardt算法求解非线性方程组.求解时分析了形状参数对求解精度的影响,改进了边界速度的处理方法.对平板Couette流及有限宽台阶绕流流动问题进行了数值求解.比较了本文方法和FLUE...     

以压力为基本求解变量数值模拟粘性超、跨音速流动

应用以压力为基本求解变量的SIMPLE方法 ,对一双喉喷管中的层流超音速流动和一扩压器中的紊流跨音速流动进行了数值计算。计算结果显示 ,本文的计算结果与文献数据及实验结果相符很好。表明本文方法对可压缩流动有很高的模拟精度。进而表明经过可压缩推广的SIMPLE方法适用于任何马赫数的流动计算     

Numerical study of Navier-Stokes equations

The problem of a viscous incompressible fluid flow around a body of revolution at incidence, which is described by Navier-Stokes equations, is considered. For low Reynolds numbers, the solutions of these equations are smooth functions. A numerical algorithm without saturation is constructed, which responds to solution smoothness. The calculations are performed on grids consisting of 900 (10 × 10 × 9) and 700 (10 × 10 × 7) nodes. On the grid consisting of 900 nodes, a system of 3600 nonlinear equations is solved by a standard code. The pressures on the shaded side of the body of revolution are compared. It is found that a numerical study (on this grid) is feasible for problems with Re ≈ 1. For high Reynolds numbers, the number of grid nodes has to be increased. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 43–52, September–October, 2007.     

Direct spectral domain decomposition method for 2D incompressible Navier-Stokes equations

An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and incompressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangular sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method (CSM) is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neumann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet boundary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison between the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.     

UNSTEADY／STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.     

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.     

Accurate 3D viscous incompressible flow calculations with the FEM

A second-order-accurate (in both time and space) formulation is developed and implemented for solution of the three-dimensional incompressible Navier–Stokes equations involving high-Reynolds-number flows past complex configurations. For stabilization, only a fourth-order-accurate artificial dissipation term in the momentum equations is used. The finite element method (FEM) with an explicit time-marching scheme based on two-fractional-step integration is used for solution of the momentum equations. The element-by-element (EBE) technique is employed for solution of the auxiliary potential function equation in order to ease the memory requirements for matrix. The cubic cavity problem, the laminar flow past a sphere at various Reynolds numbers and the flow around the fuselage of a helicopter are successfully solved. Comparison of the results with the low-order solutions indicates that the flow details are depicted clearly even with coarse grids. © 1997 John Wiley & Sons, Ltd.     

A high-order compact scheme for solving the 2D steady incompressible Navier-Stokes equations in general curvilinear coordinates

In this paper, a high-order compact finite difference algorithm is established for the stream function-velocity formulation of the two-dimensional steady incompressible Navier-Stokes equations in general curvilinear coordinates. Different from the previous work, not only the stream function and its first-order partial derivatives but also the second-order mixed partial derivative is treated as unknown variable in this work. Numerical examples, including a test problem with an analytical solution, three types of lid-driven cavity flow problems with unusual shapes and steady flow past a circular cylinder as well as an elliptic cylinder with angle of attack, are solved numerically by the newly proposed scheme. For two types of the lid-driven trapezoidal cavity flow, we provide the detailed data using the fine grid sizes, which can be considered the benchmark solutions. The results obtained prove that the present numerical method has the ability to solve the incompressible flow for complex geometry in engineering applications, especially by using a nonorthogonal coordinate transformation, with high accuracy.     

Three-dimensional motion of a viscous incompressible fluid in a narrow tube

An approximate solution of the problem of unsteady motion of a viscous incompressible fluid in a long narrow deformable tube at low Reynolds numbers is obtained. Pressure oscillations and tube deformation are shown to be related by an integrodifferential equation. The solution obtained extends the Poiseuille solution in elliptic tubes to the case of comparatively arbitrary small deformations in terms of the tube length and angle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 28–32, July–August, 2009.     

A new method for obtaining the exact solutions of the Navier-Stokes (NS) equations and its applications

In this paper we propose a new method for obtaining the exact solutions of the Mavier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations developed by the first author^[1,2], Using the present method we can find some new exact solutions as well as the well-known exact solutions of the NS equations. In illustration of its applications, we give a variety of exact solutions of incompressible viscous fluid flows for which NS equations of fluid motion are written in Cartesian coordinates, or in cylindrical polar coordinates, or in spherical coordinates. The project supported by National Natural Science Foundation of China.     

黏性不可压缩流体流动前沿的数值模拟

提出了模拟注射成型中黏性、不可压缩流体流动前沿的新方法. 将Hele-Shaw流动应用于非 等温条件下的黏性、不可压缩流体，建立了流动分析模型，用充填因子的输运方程描述流动 前沿. 应用高阶Taylor展开式计算每一时间步长的充填因子，用Galerkin方法导出了计算 充填因子各阶导数的递推公式. 给出了时间增量的选取方法，证明了它的稳定性. 针对Han 设计的试验模具，用相同的材料及工艺条件模拟充填过程，比较了传统方法和该方法的模 拟结果与实验结果的差异. 算例分析表明，该方法可以有效地提高注射成型中流动前沿的 模拟精度和计算效率.     

A high-order discontinuous Galerkin method for the incompressible Navier-Stokes equations on arbitrary grids

A high-order discontinuous Galerkin (DG) method is proposed in this work for solving the two-dimensional steady and unsteady incompressible Navier-Stokes (INS) equations written in conservative form on arbitrary grids. In order to construct the interface inviscid fluxes both in the continuity and in the momentum equations, an artificial compressibility term has been added to the continuity equation for relaxing the incompressibility constraint. Then, as the hyperbolic nature of the INS equations has been recovered, the local Lax-Friedrichs (LLF) flux, which was previously developed in the context of hyperbolic conservation laws, is applied to discretize the inviscid term. Unlike the traditional artificial compressibility method, in this work, the artificial compressibility is introduced only for the construction of the inviscid numerical fluxes; therefore, a consistent discretization of the INS equations is obtained, irrespective of the amount of artificial compressibility used. What is more, as the LLF flux can be obtained directly and straightforward, no numerical iteration for solving an exact Riemann problem is entailed in our method. The viscous term is discretized by the direct DG method, which was developed based on the weak formulation of the scalar diffusion problems on structured grids. The performance and the accuracy of the method are demonstrated by computing a number of benchmark test cases, including both steady and unsteady incompressible flow problems. Due to its simplicity in implementation, our method provides an attractive alternative for solving the INS equations on arbitrary grids.