Higher-Order Flux-Limiting Schemes for the Finite Volume Computation of Incompressible Flow

Numerical modelling of convection suitable for cell-centred finite volume methods for incompressible flow is considered. Higher-order accurate and oscillation-free solutions are obtained through flux limiting, Two improvements are discussed: the enhancement of accuracy at smooth extrema of the TVD solution, and the construction of flux limiters, which is based on polynomial interpolants in the normalized variable space. Some implementation issues are outlined. Numerical examples are provided to illustrate these advancements.     

适用于间断Galerkin方法的限制器研究

开发了一种适用于高精度间断Galerkin方法的斜率（多项式系数）限制器。与现有的斜率限制器不同,该限制器实施过程不考虑网格单元类型（三角形或四边形）,通过全微分方法构造新的多项式系数,因此,该限制器能够适用于各种类型网格——结构化网格、具有单一单元的非结构化网格和具有混合单元的非结构化网格。由于该限制器能够方便地应用于具有混合单元的非结构化网格,因此,本文使用的程序能够方便地求解具有复杂几何结构的流动问题。本文利用一些典型算例对其性能进行了验证,表明该限制器适用于不同类型的网格单元,能够在光滑解区保证高的精度,并能够在阊断区抑帛3非物理振荡。     

Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media

The one‐dimensional flow field generated by the passage of a shock wave in a rigid, thermoelastic porous foam has been simulated using a two‐phase mathematical model. The work presented here makes use of the weighted average flux method to solve the system of six equations that govern the problem. Spurious oscillations are eliminated through the application of total variation diminishing limiting methods. Four different limiters were tested: van Leer, SuperA, MinA and van Albada. Numerical tests were carried out to verify the performance of each flux limiter in terms of accuracy. The results were compared to analytical and previously obtained data to assess the performance of the mathematical model. Excellent agreement was obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

Krylov subspace projection method and its application on oil reservoir simulation

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NND schemes and numerical simulation of axial symmetric free jet flows

Through a study on one-dimensional Navier-Stokes equations, it was found that the spurious oscillations occuring near shock waves with finite difference equations are related to the dispersion term in the corresponding modified differential equations. If the sign of dispersion coefficient is properly adjusted so that the sign changes across shock waves, the undesirable oscillations can be totally suppressed. Based on this finding, the non-oscillatory, containing no free parameters and dissipative shheme (NND scheme) is developed. This scheme is one of “TVD”. The axisymmetric free jet flows are simulated numerically using this scheme. The results obtained by the present scheme are compared with the experimental picture. It is shown that the agreement is very good, and that this scheme has advantages of high resolution for capturing shocks and contact discontinuities. Project supported by National Science Foundation of China     

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.     

Numerical simulation of axisymmetric turbulent jets

The flow in axisymmetric turbulent jets is numerically simulated with the use of a semi-empirical second-order turbulence model including differential transport equations for the normal Reynolds stresses. Calculated results are demonstrated to agree with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 55–60, September–October, 2008.     

Spectral analysis of flux vector splitting finite volume methods

New results are presented here for finite volume (FV) methods that use flux vector splitting (FVS) along with higher‐order reconstruction schemes. Apart from spectral accuracy of the resultant methods, the numerical stability is investigated which restricts the allowable time step or the Courant–Friedrich–Lewy (CFL) number. Also the dispersion relation preservation (DRP) property of various spatial and temporal discretization schemes is investigated. The DRP property simultaneously fixes space and time steps. This aspect of numerical schemes is important for simulation of high‐Reynolds number flows, compressible flows with shock(s) and computational aero‐acoustics. It is shown here that for direct numerical simulation applications, the DRP property is more restrictive than stability criteria. Copyright © 2001 John Wiley & Sons, Ltd.     

Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging

I compare application of the method of multiple scales with reconstitution and the generalized method of averaging for determining higher-order approximations of three single-degree-of-freedom systems and a two-degree-of-freedom system. Three implementations of the method of multiple scales are considered, namely, application of the method to the system equations expressed as second-order equations, as first-order equations, and in complex-variable form. I show that all of these methods produce the same modulation equations.I address the problem of determining higher-order approximate solutions of the Duffing equation in the case of primary resonance. I show that the conclusions of Rahman and Burton that the method of multiple scales, the generalized method of averaging, and Lie series and transforms might lead to incorrect results, in that spurious solutions occur and the obtained frequency–response curves bear little resemblance to the actual response, is the result of their using parameter values for which the neglected terms are the same order as the retained terms. I show also that spurious solutions cannot be avoided, in general, in any consistent expansion and their presence does not constitute a limitation of the methods. In particular, I show that, for the Duffing equation, the second-order frequency–response equation does not possess spurious solutions for the case of hardening nonlinearity, but possesses spurious solutions for the case of softening nonlinearity. For sufficiently small nonlinearity, the spurious solutions are far removed from the actual response. But as the strength of the nonlinearity increases, these solutions move closer to the backbone and eventually distort it. This is not a drawback of the perturbation methods but an indication of an application of the analysis for parameter values outside the range of validity of the expansion.Also, I address the problem of obtaining non-Hamiltonian modulation equations in the application of the method of multiple scales to multi-degree-of-freedom Hamiltonian systems written as second-order equations in time and how this problem can be overcome by attacking the state-space form of the governing equations. Moreover, I show that application of a variation of the method of Rahman and Burton to multi-degree-of-freedom systems leads to results that do not agree with those obtained with the generalized method of averaging.Contributed by Prof. R.A. Ibrahim.     

Spectral methods for the simulation of incompressible flows in spherical shells

A spatial discretization of the incompressible Navier–Stokes equation is presented in which the velocity is decomposed using poloidal and toroidal scalars whose spatial dependence is given in terms of spherical harmonics and Chebychev polynomials. The radial resolution needs to be large enough at any given angular resolution in order to avoid instability in the simulation of rotating flows. Several semi‐implicit time steps are discussed. The most accurate scheme is an integrating factor technique. Copyright © 1999 John Wiley & Sons, Ltd.     

简化CH4/O2/N2基元反应模型在爆轰模拟中的应用

基于改进的全耦合TVD格式和简化的基元化学反应模型,建立了二维可燃预混合气爆轰波传播过程的模型并编制了相应的CFD程序,对CH4／O2／N2预混气爆轰波的形成和传播进行了数值模拟。使用不同的计算初始条件来考察模型的计算模拟能力,计算结果表明,该模型能够精确捕捉爆轰波及其波后的反射过程,同时,也能够预测不同计算初始条件下爆轰波的传播轨迹。计算结果与相同条件下CJ爆轰理论模型的计算结果进行了比较,两者符合较好,这表明简化的CH4／O2／N2机理能够较好地应用于可燃气爆轰过程的数值计算中。     

随机复合材料结构非线性热-力耦合模拟的统计高阶多尺度方法

对于具有复杂随机细观构造的复合材料结构的非线性热-力耦合问题的随机多尺度建模和计算仍是一个具有挑战性的问题。本文发展了一个新的统计高阶多尺度方法,克服了随机多尺度问题直接模拟时巨大的计算量,实现了具有随机复合材料结构非线性热-力耦合问题的数值模拟。借助统计多尺度渐近分析和泰勒级数方法,本文严格推导了可以精确分析随机复合材料结构宏-细观尺度非线性热-力耦合响应的统计高阶多尺度计算模型。然后,通过局部误差分析证明了统计高阶多尺度计算模型中高阶校正项在保持计算模型局部能量和动量守恒的重要意义。进一步,建立了可以高效模拟随机复合材料结构非线性热-力耦合行为的具有离线和在线两阶段的时空多尺度算法。最后,通过数值实验验证了统计高阶多尺度方法的计算高效率和高精度。     

航天器火工冲击模拟试验及响应预示方法研究综述

航天器火工冲击力学环境是由星箭分离、部组件展开等工作过程中的火工品起爆引起的作用于结构上的高频、高加速度量级的瞬态冲击响应,能对航天器上含有晶振、脆性材料等的精密电子设备造成致命损伤,是航天器需要经历的最苛刻的力学环境之一。本文中,对国内外航天器火工冲击地面试验方法和环境预示方法做了全面、详细的介绍,总结了这两个方面的研究进展,分析了我国在这两个方面与航天强国的差距。最后,从我国航天工程实际需求出发,提出了今后航天器火工冲击领域应重点开展的研究方向。     

Numerical simulation of drop migration in channell flow under zero-gravity

The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finitedifference method coupled with the front-tracking technique. The objectives of this study are to examine the effectiveness of the present approach for predicting the migration of drops in a shear flow and to investigate the behavior of the drop migration in the channel flow under zero-gravity. To validate the present calculation, some typical results are compared with available computational and theoretical data, which confirms that the present approach is reliable in predicting the drop migration. With respect to the drop migration in the channel flow at finite Reynolds numbers, the drops either move to an equilibrium lateral position or undergo an oscillatory motion under different conditions. The effects of some typical parameters, e.g., the Reynolds number, the Weber number, the viscosity ratio and the density ratio of the drop fluid to the suspending medium, and the drop size, on the migration of drops are discussed and analyzed. The project supported by the National Natural Science Foundation of China (10125210) and the Hundred-Talent Programme of the Chinese Academy of Sciences     

非常规结构武器两相流内弹道的高精度数值模拟

针对侧装药武器的结构特点,在提出等效物理模型的基础上建立了双一维两相流模型,并对主膛的气、固相方程组分别采用二阶精度TVD算法进行了模拟,结果与12.7 mm口径的发射实验进行了对比分析,模型和算法是可行的。     

断裂过程的有限元模拟

讨论了材料断裂过程的有限元模拟技术。基于自适应有限元的一般原理，并针对多相材料的裂纹扩展的特点，提出了一种简化的高精度和高效率有限元网格的动态重新划分策略。裂纹被假设沿着单元之间的路径连续扩展，利用节点力释放技术生成新的裂纹自由表面，发展了一种可随裂尖连续移动的网格动态加密和释放方法。这种方法已在各种裂纹问题中得以实现与应用。     

弹塑性变形油藏中多相渗流的数值模拟

基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。     

Full-wave numerical simulation of nonlinear dissipative acoustic standing waves in wind instruments

A finite volume full-wave method is used to simulate nonlinear dissipative acoustic propagation in ducts with a circular cross-section. Thermoviscous dissipative effects, due to bulk viscosity and shear viscosity in the boundary layer adjacent to the duct walls, are also considered. The propagation is assumed to be axisymmetric, and two different geometries are considered: a straight cylindrical tube, and a cylindrical tube joined smoothly to a slowly-flaring bell. Of special interest is the study of the onset of standing waves in the nonlinear regime. The full-wave numerical scheme is particularly well-adapted for this purpose, as it is not necessary to impose boundary conditions at the open end of the duct. A simplified model of excitation is adopted, where the lips are replaced by a spring–mass system which behaves like a pressure valve with a single degree of freedom. The full system behaves as expected, with a feedback cycle established between the pressure valve and the air column. The simulation is validated successfully in the linear regime using a theoretical solution. It is shown that increasing the stiffness of the lips leads to discrete jumps in playing frequency, which is behaviour typical of brass instruments. In the nonlinear regime, shock formation is observed for sufficiently high amplitudes of oscillation, and the radiation of these shock waves by the open end of the ducts can be visualised in the time-domain, along with edge-diffraction effects. The formation and evolution of standing waves in the nonlinear regime, where the effect of these shocks is very noticeable, is also examined.     

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, cross-stream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.     

Averaging methods for numerical simulations of flows through heterogeneous porous media

Many natural rock systems contain small patches of different permeability which affect the flow of fluids through them. As these heterogeneities become smaller and more numerous, they become harder to model numerically. We consider how to reduce the computational effort required in simulations by incorporating their effects in the boundary conditions at the edges of each grid block. This is in contrast with current methods which involve often arbitrary changes in the fluid properties. The method is restricted to the case of widely-spaced patches, which simplifies interaction effects. The system then reduces to an array of dipoles, and two averaging methods are proposed for finite grid blocks. Several infinite systems, including vertical and horizontal bands, are also considered as further approximations. There is a great wealth of existing results from different fields which lead to identical mathematical problems and which can be used in these cases. Finally, we consider how to use these techniques when the precise configuration of the grid block is not known, but only its statistical properties. This can lead to results which are very different from the deterministic case.