通过求解输运方程计算壁面距离

壁面距离在当代湍流模化中仍然扮演着关键角色,然而苦于遍历计算壁面距离的高昂代价,该文考虑了求解偏微分方程的途径．基于Eikonal方程构造出类Euler形式的输运方程,这样,可以直接利用求解Euler和Navier-Stokes方程的CFD程序使用的高效数值格式和部分代码．基于北航的MI-CFD(CFD for missles)数值平台,详尽地介绍了该输运方程在直角坐标下的求解过程．使用隐式LUSGS时间推进和迎风空间离散,发现该方程具有鲁棒快速的收敛特性．为了保证精度,网格度量系数必须也迎风插值计算．讨论了初始条件和边界条件的特殊处理．成功应用该壁面距离求解方法计算了几个含1-1对应网格和重叠网格的复杂外形．     

固液两相流中的K－ε双方程湍流模式

建立了固液两相流中更一般的Ｋ－ε双方程湍流模式．模化了固相和液相的连续方程、动量方程及Ｋ方程和ε方程．该湍流模型考虑了固液两相间速度的滑移，颗粒间的作用及相间作用．使用本文所建立的湍流模型，数值预测了一管湍流中的沙水混合流动，其预测结果与实验结果比较一致．     

可压缩均匀各向同性湍流的直接数值模拟

采用8阶精度的中心差分格式及7阶精度的迎风偏斜格式对Re_l = 72~153, M_t= 0.2~0.7的均匀各向同性湍流进行了直接数值模拟, 建立了湍流数据库. 与他人的计算结果吻合十分理想, 说明方法的有效性. 数值结果表明, 采用适当的迎风型差分格式可以克服起动问题(start-up problem)对湍流Mach数的限制, 提高可计算的湍流Mach数, 是可压湍流直接数值模拟的有效方法. 分析了压缩性效应对湍流统计量的影响, 发现压缩性使得湍动能的衰减加快. 探讨了可压湍流中微激波产生的机理, 对流场进行了标度律分析. 发现在本文的Reynolds数和湍流Mach数条件下, 流场中扩展自相似性仍然成立, 同时发现压缩性对标度指数影响不大.     

同位非结构和结构网格摄动有限体积法（PFV）求解二维Navier-Stokes方程组

根据NS方程组的一阶迎风和二阶中心有限体积（UFV和CFV）格式,导出NS方程组迎风和中心摄动有限体积(UPFV和CPFV)格式．该格式通过把控制体界面质量通量摄动展开成网格间距的幂级数,并由守恒方程本身求得幂级数系数而获得．迎风和中心摄动有限体积格式使用了与一阶迎风和二阶中心格式相同的基点数和相同的表达形式,宜于计算机编程．顶盖驱动方腔流和驻点流标量输运的数值实验证明,迎风PFV格式比一阶UFV、二阶CFV格式有更高的精度,更高的分辨率．尤其是良好的鲁棒特性．对顶盖驱动方腔流,在Re数从102到104范围内,亚松弛系数可在0.3～0.8任取,收敛性能良好．     

油藏数值模拟中动边值问题的迎风差分格式

考虑了三维油藏数值模拟中的动边值问题,对压力方程,给出中心差分格式;对饱和度方程给出隐式迎风差分格式及修正的迎风差分格式,并证明了格式的收敛性。数值算例与理论结果是一致的。     

运动壁面槽道流动的直接数值模拟

采用谱方法,在曲线坐标系下对不可压缩Newton流体的N-S方程进行求解,采用定义在物理空间中的流动物理量以避免使用协变、逆变形式的控制方程．在计算空间采用Fourier-Chebyshev谱方法进行空间离散,时间推进采用高精度时间分裂法．为了减小时间分裂带来的误差,采用了高精度的压力边界条件．与其他求解协变、逆变形式控制方程的谱方法相比,该方法在保持谱精度的同时减小了计算量．首先通过静止波形壁面和行波壁面槽道湍流的直接数值模拟,对该数值方法进行了验证;其次,作为初步应用,利用该方法研究了槽道湍流中周期振动凹坑所产生的流动结构．     

基于有限分析法的平面铅垂壁羽流的相似解

应用计及浮力对湍动能及其耗散率的影响的k-epsilon湍流模式,结合有限分析法对密度差引起的平面铅垂紊动壁羽流进行了数值分析．在均匀环境条件下控制该类流动的连续性方程、流动方向的动量方程、浓度扩散方程、湍动能及其耗散率方程存在相似解．考虑到浮力通量守恒条件,应用有限分析法给出了铅直壁羽流的速度、相对密度差、湍动能及耗散率的分布,进而给出了各物理量最大值沿主流方向变化的关系式．湍流Schmidt数为1.0时的计算结果与实验资料吻合较好,表明应用有限分析法分析铅垂平面羽流是有效的,即在分析壁羽流时浮力对湍动能及其耗散率的影响应该予以考虑．     

固液两相流中的K-ε双方程湍流模式*

建立了固液两相流中更一般的K-ε双方程湍流模式。模化了固相和液相的连续方程、动量方程及K方程和ε方程。该湍流模型考虑了固液两相间速度的滑移,颗粒间的作用及相间作用。使用本文所建立的湍流模型,数值预测了一管湍流中的沙水混合流动,其预测结果与实验结果比较一致。     

三维两相渗流驱动问题迎风区域分裂显隐差分法

对三维两相渗流驱动问题提出了两种迎风区域分裂显隐差分格式．压力方程采用了七点差分格式,为了能达到实际并行计算的要求,对饱和度方程采用了迎风区域分裂差分法,内边界处和各子区域分别对应显隐格式．得到了离散l2模收敛性分析,最后给出数值试验,支撑了理论分析结果．     

三维可压缩Boltzmann模型及其在低Mach数湍流中的应用

改进了有限差分格子Boltzmann方法(FDLBM),以直接数值模拟气动噪声.基于LB求解器特性,采用动力学方程中的恒定对流速度以实施高阶迎风差分,提高了声波和湍流的分辨率.通过建立一个新的三维粒子模型,计算得到了任意比热容的三维可压缩Navier-Stokes系统.此外,利用Bhatnagar-Gross-Krook (BGK)碰撞算子,通过引入热流量修正,实现了Prandtl数的可变性.在激波管内弱声波以及伴随有温度梯度的Taylor-Couette层流的验证计算中,提出的新方法结果良好.此外也对NACA0012翼型绕流进行了三维模拟.其中,Reynolds数、Mach数和攻角分别取2× 105,8.75×10-2以及9°.计算发现,在机翼前缘附近的分离气流位置,以及表面压力波动强度的Maeh数依赖性方面,数值计算结果与实验结果相吻合.     

Turbulent flow around single concentric long capsule in a pipe

A numerical solution was developed for the equations governing the turbulent flow around single concentric long capsule in a pipe. First, a turbulence model was established for the concentric annulus between the capsule and the pipe to simulate the flow as axi-symmetric, two dimensional, steady flow without edge effect. Second, the same case was considered taking into account the edge effect. Finally, turbulence modelling was established to simulate the case as a three dimensional steady flow, with a view of investigating the validity of axi-symmetric flow assumption. Three different turbulence models were used: an algebraic model (Baldwin–Lomax model) and two types of two-equation models (k–ε and k–ω). Obtained results of pressure gradient along the capsule were compared with available experimental data to verify the used models. In addition, experimental data of the velocity profiles of other investigators were also used in this concern. The results predicted by the three different turbulence models were shown to agree well with the experimental data, though precision differed from one to another.     

Turbulent compressible fluid flow computation in a male rotor-housinggap of screw compressors

This contribution is devoted to a turbulent compressible fluid flow computation through a 2-D model of the male rotor-housing gap in screw compressors. For the numerical solution of the nonlinear conservative system of the Favre-averaged Navier-Stokes equations the cell-centred finite volume formulation of the explicit two-step TVD MacCormack scheme proposed by Causon on a structured quadrilateral grid is used. The turbulent viscosity is calculated by using the algebraic Baldwin-Lomax turbulence model which is implemented into the own developed numerical code. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients

We present a symbolic computation procedure for deriving various high order compact difference approximation schemes for certain three dimensional linear elliptic partial differential equations with variable coefficients. Based on the Maple software package, we approximate the leading terms in the truncation error of the Taylor series expansion of the governing equation and obtain a 19 point fourth order compact difference scheme for a general linear elliptic partial differential equation. A test problem is solved numerically to validate the derived fourth order compact difference scheme. This symbolic derivation method is simple and can be easily used to derive high order difference approximation schemes for other similar linear elliptic partial differential equations.     

动脉血管流动计算的伽辽金有限元法研究

得到大动脉三维模型的过二重分叉的二维截定常流的NS方程有限元解,采用了物理坐标系统换到曲线边界贴休坐标系的数学技巧,以支流至主动脉流率为参数,计算了雷诺数为1000的壁面切应力,所得结果与前人的工作（包括实验数据）进行了比较,发现与他们的结果非常接近,改进了Sharma和Kapoor(1995)的工作,相比之下,所用的数值方法上更经济,适用的雷诺数更大。     

Laguerre polynomial approach for solving linear delay difference equations

This paper presents a numerical method for the approximate solution of mth-order linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre series expansion approach. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple.     

Numerical scheme for solving system of fractional partial differential equations with Volterra‐type integral term through two‐dimensional block‐pulse functions

In the current study, an approximate scheme is established for solving the fractional partial differential equations (FPDEs) with Volterra integral terms via two‐dimensional block‐pulse functions (2D‐BPFs). According to the definitions and properties of 2D‐BPFs, the original problem is transformed into a system of linear algebra equations. By dispersing the unknown variables for these algebraic equations, the numerical solutions can be obtained. Besides, the proof of the convergence of this system is given. Finally, several numerical experiments are presented to test the feasibility and effectiveness of the proposed method.     

A high order finite difference method with Richardsonextrapolation for 3D convection diffusion equation

In this paper, we extend the Sun and Zhang’s [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on the fine and the coarse grids. Then, we use the Richardson extrapolation technique by combining the two approximate solutions to get a sixth order accurate solution on coarse grid. Finally, we apply an operator interpolation scheme to achieve the sixth order accurate solution on the fine grid. During this process, we use alternating direction implicit (ADI) method to solve the resulting linear systems. Numerical experiments are conducted to verify the accuracy and effectiveness of the present method.     

Singly diagonally implicit runge‐kutta method for time‐dependent reaction‐diffusion equation

In this article, an efficient fourth‐order accurate numerical method based on Padé approximation in space and singly diagonally implicit Runge‐Kutta method in time is proposed to solve the time‐dependent one‐dimensional reaction‐diffusion equation. In this scheme, we first approximate the spatial derivative using the second‐order central finite difference then improve it to fourth‐order by applying Padé approximation. A three stage fourth‐order singly diagonally implicit Runge‐Kutta method is then used to solve the resulting system of ordinary differential equations. It is also shown that the scheme is unconditionally stable, and is suitable for stiff problems. Several numerical examples are solved by the scheme and the efficiency and accuracy of the new scheme are compared with two widely used high‐order compact finite difference methods. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1423–1441, 2011     

Numerical simulation of axisymmetric afterbody flows with jet exhaust

A fifth-order accurate compact difference scheme was used to compute the flow over an axisymmetric afterbody with jet exhaust. The solution was based on the mass-averaged Navier-Stokes equations combined with a two-parameter differential model of turbulence. The computations were performed on a specially generated mesh such that the flow in the exterior and interior of the nozzle could be described simultaneously. Numerical results are presented for various external flow conditions and various chamber pressures.