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.

IMPLICIT TVD SCHEMES APPLIED TO GAS-DROPLET DETONATION CALCULATION

In order to investigate parameters of FAE (fuel air explosive) explosion, the two-phase gas-droplet conservation equations with two-dimensional axial symmetry in the Euler coordinate were used. High-resolution implicit TVD ( total variation diminishing) schemes were applied to gas phase equations and MacCormack schemes to liquid equations. The formation and propagation of gas-droplet detonation wave were simulated numerically. The simulation results and the others are compared with a good agreement.

A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS

In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.

NUMERICAL SIMULATION OF THREE DIMENSIONAL INTERACTING TURBULENCE FLOW FIELD OVER PROJECTILE WITH LATERAL JETS

In order to study complicated interacting flow field over projectile with lateral jets. External interacting turbulence flow over projectile with lateral jets was numerically simulated firstly in supersonic speed and zero attack angle. The three dimensional Reynolds averaged Navier Stokes equations and implicit finite volume TVD scheme were applied. In order to avoid zonal method, ’O’ type grid of single zone including projectile base was produced by algebraic arithmetic. Body fitted grid was generated for the lateral nozzle exit successfully so that the nozzle exit can be simulated more accurately. The high Reynolds number two equation κ ε turbulence models were used. The main features of the complex flow are captured. The two kinds of flow field over projectile with and without lateral jets are compared from shock structure, pressure of body and base, etc . It shows that lateral jets not only can provide push force, but also change aerodynamics characteristic of projectile significantly. The results are very important for the study of projectile with lateral rocket boosters.

Upwind Compact Method and Direct Numerical Simulation of Driven Flow in a Square Cavity*

A high-order accurate finite-difference scheme, the upwind compact method, is proposed. The 2-D unsteady incompressible Navier-Stokes equations are sOlved in primitive variables. The nonlinear convection terms in the governing equations are approximated by using upwind biased compact difference, and other spatial derivative terms are discretized by using the fourth-order compact difference. The upwind compact method is used to solve the driven flow in a square cavity. Solutions are obtained for Reynolds numbers as high as 10000. When Re≤5000, the results agree well with those in literature. When Re=7500 and Re=10000, there is no convergence to a steady laminar solution, and the flow becomes unsteady and periodic.

Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.

One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

In this paper, a new numerical scheme for solving first-order hyperbolic partial differential equations is proposed and is implemented in the simulation study of macroscopic traffic flow model with constant velocity and linear velocity-density relationship. Macroscopic traffic flow model is first developed by Lighthill Whitham and Richards (LWR) and used to study traffic flow by collective variables such as flow rate, velocity and density. The LWR model is treated as an initial value problem and its numerical simulations are presented using numerical schemes. A variety of numerical schemes are available in literature to solve first order hyperbolic equations. Of these the well-known ones include one-dimensional explicit: Upwind, Downwind, FTCS, and Lax-Friedrichs schemes. Having been studied carefully the space and time mesh sizes, and the patterns of all these schemes, a new scheme has been developed and named as one-dimensional explicit Tolesa numerical scheme. Tolesa numerical scheme is one of the conditionally stable and highest rates of convergence schemes. All the said numerical schemes are applied to solve advection equation pertaining traffic flows. Also the one-dimensional explicit Tolesa numerical scheme is another alternative numerical scheme to solve advection equation and apply to traffic flows model like other well-known one-dimensional explicit schemes. The effect of density of cars on the overall interactions of the vehicles along a given length of the highway and time are investigated. Graphical representations of density profile, velocity profile, flux profile, and in general the fundamental diagrams of vehicles on the highway with different time levels are illustrated. These concepts and results have been arranged systematically in this paper.

NUMERICAL SOLUTION OF VISCOUS FLOW PAST A SOLID SPHERE WITH THE CONTROL VOLUME FORMULATION

The control volume formulation with the QUICK finite difference scheme is used to solveincompressible liquid flow past a solid sphere in terms of stream function and vorticity.Several tech-nical points are addressed on improving the accuracy and efficiency of numerical simulation of similarproblems of fluid flow.In particular,the importance of suitable specification of the distortion func-tion to enforcing the far field boundarv conditions is emphasized.

Application of Factor Difference Scheme to Solving Discrete Flow Equations Based on Unstructured Grid

A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gradient method and applied to discretizing the Navier-Stokes equation in an unstructured grid.The transform of nonorthogonal diffusion items generated by the scheme in discrete equations is provided.The Delaunay triangulation method is improved to generate the unstructured grid.The computing program based on the SIMPLE algorithm in an unstructured grid is compiled and used to solve the discrete equations of two types of incompressible viscous flow.The numerical simulation results of the laminar flow driven by lid in cavity and flow behind a cylinder are compared with the theoretical solution and experimental data respectively.In the former case,a good agreement is achieved in the main velocity and drag coefficient curve.In the latter case,the numerical structure and development of vortex under several Reynolds numbers match well with that of the experiment.It is indicated that the factor difference scheme is of higher accuracy,and feasible to be applied to Navier-Stokes equation.

具有TVD性质的三阶精度GODUNOV格式在粘性流场计算中的应用

本文发展了一种具有TVD性质的三阶精度的Godunov格式。隐式部分采用迎风对角线形隐式近似因式分解法。并引入了粘性通量的简化算法。显式部分采用三阶精度TVD格式。为进一步增强格式的稳定性及对间断的捕捉能力，在单元边界上构造Riemann问题。应用上述方法对某型涡轮高压级及压气机进行了数值模拟。

一类TVD型组合差分方法及其在磁流体数值计算中的应用

根据太阳风数值模拟的特点,考虑到算法的质量（收敛速度、稳定性、精度等）,结合磁流体数值计算的特性,对三维球坐标下磁流体动力学（MHD）方程组中的流体部分采用一种修正Lax-Friedrichs差分法而对磁场部分采用MacCormack格式,发展了一类快捷的具有TVD特性的组合数值新方法.作为格式的检验,在一维情况下,将其与PPM格式进行了比较,对一维快慢磁流体激波问题得到了与PPM格式精度相同的结果,然后将其应用到定态太阳风的数值模拟上,在不同等离子体β情形下,可得到理想的太阳风定态结构,为今后将此数值模式应用到具有复杂磁场位型或三维真实太阳风暴的数值模拟研究奠定了基础.

迎风TVD格式在粘性流计算中的应用研究与改进

首先以高超声速钝楔绕流热流计算和Ｍ∞＝２０、激波角θ＝３２５８°的平板激波附面层干扰分离流动计算，研究了迎风ＴＶＤ格式的粘性特性，发现即使在很小的物面网格下，原有格式计算驻点热流仍较实验和文献结果低，激波附面层干扰的分离区小于实验值，原因主要在于熵修正公式。针对这些不足提出了新的熵修正公式，用改进后的格式重新计算，得到了与实验符合较好的结果。最后用改进的格式对分离流动的壁面温度控制效应进行了研究。

曲线坐标网格下二维涌波数值模拟的TVD型格式

针对水动力学中的涌波现象导出二维曲线坐标系下的守恒型方程 ,然后利用算子分裂法和TVD差分格式思想构造出计算格式 ,在此基础上建立起由实际流场区域至方形计算区域的全局同胚映射 ,对急流过缩窄河道产生的涌波结构进行数值模拟 ,结果表明 ,本文的数值方法能够很好地模拟附体涌波、交叉涌波等复杂结构现象 ,所得波系结构和有关物理量与理论分析结果非常吻合 。

隐式TVD格式在气液两相爆轰数值模拟中的应用

为研究FAE(燃料_空气炸药 )爆炸参数规律 ,运用二维轴对称气液两相方程组模型 ,针对其中的气相方程组采用高分辨率的隐式TVD格式 ,液相方程组采用MacCormack格式 ,较好地对FAE气液两相爆轰产生的爆轰波的发展和传播过程进行了数值模拟 ,计算结果与国内外的研究结果符合良好·

TVD自相容流体力学拉氏格式研究

流体力学数值模拟格式总体上可分为Eulerian(欧氏)、Lagrangian(拉氏)和ALE(Arbitrary LagrangianEulerian),TVD广泛应用于Eulerian格式。本文利用具有TVD保持性质的Runge-Kutta型时间离散方法,构造了流体力学Lagrangian(拉氏)自相容格式,应用von Neumann小扰动技术分析了该格式的稳定性,并进行了相应的数值模拟,较好地抑制了激波波后非物理振荡。

一种改进型内嵌特征压缩机制的智能间断指示器

高精度高分辨率数值格式是模拟高速含激波复杂流动最有效的计算方法之一,而其中对于激波等间断结构的捕捉和辨识,是设计鲁棒的高精度高分辨率数值格式的关键问题之一。借助先验的数理知识及人工神经网络(artificial neural network,ANN)方法,构造了一种改进型内嵌“特征压缩”机制的智能间断指示器,以提高高精度格式框架下间断捕捉的精准度。该间断指示器模型是通过借助先验的数学物理知识进行预建模,然后借助数据驱动方法学习模型中的待定参数而得到。这使得间断指示器模型形式简洁,在训练过程中具有小样本依赖的优势,还使训练后的模型具备计算复杂度低、数理可解释等优秀性质,且其一维形式可以自然地推广到高维非结构网格下的方程组中。已证明该间断指示器模型包含两种间断捕捉机制,即基于特征压缩的激波捕捉机制和基于大梯度跳跃的膨胀波起点、接触间断捕捉机制。一系列数值实验结果验证了所构造的间断指示器对于流场不同间断类型的捕捉精准性。

应用TVD格式数值分析低阻远程弹丸绕流场

从全Navier Stokes方程出发 ,结合高雷诺数两方程κ ε湍流模型 ,应用三维隐式有限体积TVD格式 ,数值仿真了低阻远程弹丸在来流马赫数Ma∞ =0 .96 ,Ma∞ =1.1和Ma∞ =2 5 ,攻角α =4°时的绕流流场。为避免分区计算而用代数方法生成了弹丸绕流场O型网格 ,计算结果得到了清晰的流场波系结构 ,弹体的迎风面和背风面流场呈现明显的非对称性 。

水击波数值模拟中高分辨率TVD格式优选

TVD方法特别适合数值模拟双曲型偏微分方程间断波问题,选用4种典型的TVD格式应用于水击方程的数值模拟。通过水击实例计算,将数值结果与理论解比较,揭示4种不同构造形式的TVD格式在捕捉水击波方面耗散性和压制性数值性能的差异,且TVD格式均优于常规的差分方法;改变计算库朗数条件下的计算结果表明:Harten修正通量TVD格式、TVD-MC格式以及全离散TVD格式在大范围库朗数条件下计算稳定性较差,优选Sweby反扩散TVD格式模拟水击,其计算稳定性良好,精度较高。

TVD格式在数值求解两相渗流问题中的应用

本文把ＴＶＤ格式引入油藏模拟，给出了数值求解两相渗流方程组的ＴＶＤ差分格式，并讨论了相应的ＴＶＤ条件。在此基础上对目前流行的商业软件ＶＩＰ黑油模拟器中的流度上游权格式进行了二阶校正。数值算例表明，使用ＴＶＤ格式求解两相渗流问题比使用传统的流度上游权格式有较高的精度，且少用可观的计算机内存和ＣＰＵ时间。

TVD格式数值模拟四通管阀门关闭特性研究

水击问题是管道输水中重要的安全问题,管网水击直接制约着管道输水技术的发展。正确进行四通管水击及其影响分析并采取适当控制措施对管网安全运行有重要意义。将TVD格式运用到四通管阀门关闭特性对水击过程影响的研究中,对其阀门关闭规律及组合关闭方式进行模拟,以期遴选出使得水击压力不影响管网安全运行的关阀模式。由模拟结果可以看出:两阶段直线关阀方式优于加速曲线和直线关闭方式,可操作性强,两阀门同时直线关闭方式优于一个或两个阀门瞬时关闭方式,产生水击压强最小且衰减最快,可分别作为保证四通管在瞬变工况下安全运行的阀门关闭模式和组合关阀方式,进而为四通管乃至管网在瞬变工况下的安全运行和管理提供理论依据和参考。