Lagrangian cell-centered conservative scheme

This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time sub-cell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.     

舰船惯性导航系统海上无阻尼状态的校准

为满足装备高机动舰船的惯性导航系统海上重调的需求,设计了一种无阻尼状态下的校准方案,以保证惯性导航系统的续航导航精度。设计中采用卡尔曼滤波器估计系统误差和陀螺漂移,并利用残差检验方法进行故障检测与隔离。仿真分析和系统试验结果表明：无论载体在静态还是动态机动情况下,采用该方案进行校正后的系统精度都明显提高。该方案具有：滤波估计过程在无阻尼状态下进行,不受舰船运动状态的限制;分别估计陀螺常值漂移和随机漂移,隔离随机漂移对常值漂移量测的影响,精确补偿系统误差和陀螺常值漂移;以及在外参考信息源有误差干扰情况下仍能获得理想的校正效果等特点,具有重要的应用价值。     

连续分层海洋中内波传播的一种数值模式

基于Euler方程,使用有限体积法建立了一种密度为连续分层情况下、适应水深变化的水域中内波传播的数值模式.为了使计算格式能够达到二阶精度,对流项的处理使用了TVD (total variation diminishing)格式.将SIMPLE算法引入连续分层海洋中内波的数值计算,为了简化计算并方便地适应多种TVD格式,在计算预估速度场时采用了显式格式,而没有采用传统的隐式格式;鉴于在原始的SIMPLE算法中没有涉及到由于密度扰动而引起的静水压力场的改变问题,给出了该问题的计算方法.因此改进了SIMPLE算法.出流边界的处理采用阻尼消波和Sommerfeld辐射条件相结合的方式,以使内波得到有效的衰减和释放.将等水深水域的数值解和理论解进行了比较,两者吻合较好;并对存在潜堤时数值计算的不同时刻密度变化的空间分布进行了详细的定性分析.计算结果表明,所建立的数值模式能有效地模拟内波的传播和变形.      

Static and dynamic analysis of the DCB problem in fracture mechanics

A finite difference scheme for treating the static and dynamic stress fields under plane-strain conditions in the DCB, is proposed. The adequacy of the scheme is established via the static solution by comparing the results obtained numerically with those obtained experimentally. Both the numerical and experimental results are also compared with data available in the literature. Discrepancies found are explained and discussed. For the numerical scheme adjusted to handle the propagating crack problem, the results represent a situation which is close to that observed experimentally; namely, an essentially constant steady state crack propagation speed from the start, with crack length at arrest and velocity values depending on the initial conditions. In addition, the velocities predicted by the analysis are shown to be in good agreement with those reported in the literature.     

Efficient high‐resolution relaxation schemes for hyperbolic systems of conservation laws

In this work, we present a total variation diminishing (TVD) scheme in the zero relaxation limit for nonlinear hyperbolic conservation law using flux limiters within the framework of a relaxation system that converts a nonlinear conservation law into a system of linear convection equations with nonlinear source terms. We construct a numerical flux for space discretization of the obtained relaxation system and modify the definition of the smoothness parameter depending on the direction of the flow so that the scheme obeys the physical property of hyperbolicity. The advantages of the proposed scheme are that it can give second‐order accuracy everywhere without introducing oscillations for 1‐D problems (at least with) smooth initial condition. Also, the proposed scheme is more efficient as it works for any non‐zero constant value of the flux limiter ? ? [0, 1], where other TVD schemes fail. The resulting scheme is shown to be TVD in the zero relaxation limit for 1‐D scalar equations. Bound for the limiter function is obtained. Numerical results support the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.     

利用弹上器件测风方法

导弹子母弹携带的子弹药战斗部在开舱之后受到风况的影响很大,需要对子弹药的落点进行修正控制以提其的作战效能。针对这一需求,研究了适用于导弹稳定平飞阶段的常值风测量方法。根据导弹弹体姿态＂随风飘＂的特性,提出了一种只利用弹上器件的测风方案,并以水平面内的常值风为例,以概率统计的方法进行了测量误差分析。计算分析结果表明,若在导弹开舱之前稳态平飞阶段内,根据弹上组合导航系统和空速表的多次测量值进行简单的计算处理,测风误差将大大减小。该方案简单可行,易于实现,具有一定的工程应用价值。     

Incompressible flows with combustion simulated by a preconditioning method using multigrid acceleration and MUSCL reconstruction

A numerical algorithm for the steady state solution of three‐dimensional incompressible flows is presented. A preconditioned time marching scheme is applied to the conservative form of the governing equations. The preconditioning matrix multiplies the time derivatives of the system and circumvents the eigenvalue‐caused stiffness at low speed. The formulation is suitable for constant density flows and for flows where the density depends on non‐passive scalars, such as in low‐speed combustion applications. The k–ε model accounts for turbulent transport effects. A cell‐centred finite volume formulation with a Runge–Kutta time stepping scheme for the primitive variables is used. Second‐order spatial accuracy is achieved by developing for the preconditioned system an approximate Riemann solver with MUSCL reconstruction. A multi‐grid technique coupled with local time stepping and implicit residual smoothing is used to accelerate the convergence to the steady state solution. The convergence behaviour and the validation of the predicted solutions are examined for laminar and turbulent constant density flows and for a turbulent non‐premixed flame simulated by a presumed probability density function (PDF) model. Copyright © 2001 John Wiley & Sons, Ltd.     

A new volume of fluid advection algorithm: the defined donating region scheme

This paper presents a new volume of fluid (VOF) advection algorithm, termed the defined donating region (DDR) scheme. The algorithm uses a linear piecewise method of free surface reconstruction, coupled to a fully multi‐dimensional method of cell boundary flux integration. The performance of the new scheme has been compared with the performance of a number of alternative schemes using translation, rotation and shear advection tests. The DDR scheme is shown to be generally more accurate than linear constant and flux limited schemes, and comparable with an alternative linear piecewise scheme. The DDR scheme conserves fluid volume rigorously without local redistribution algorithms, and generates no fluid ‘flotsam’ or other debris, making it ideal in applications where stability of the free surface interface is paramount. Copyright © 2001 John Wiley & Sons, Ltd.     

Multigrid flow solutions in complex two-dimensional geometries

A finite difference solution algorithm is described for use on two-dimensional curvilinear meshes generated by the solution of the transformed Laplace equation. The efficiency of the algorithm is improved through the use of a full approximation scheme (FAS) multigrid algorithm using an extended pressure correction scheme as smoother. The multigrid algorithm is implemented as a fixed V-cycle through the grid levels with a constant number of sweeps being performed at each grid level. The accuracy and efficiency of the numerical code are validated using comparisons of the flow over two backward step configurations. Results show close agreement with previous numerical predictions and experimental data. Using a standard Cartesian co-ordinate flow solver, the multigrid efficiency obtainable in a rectangular system is shown to be reproducible in two-dimensional body-fitted curvilinear co-ordinates. Comparisons with a standard one-grid method show the multigrid method, on curvilinear meshes, to give reductions in CPU time of up to 93%.     

Shock-induced inorganic reactions and condensed phase detonations

Existing hugoniot calculations of inorganic chemical reactions in powder mixtures are found to contain errors and ambiguities. Most of the problems were caused by improper identification of the thermodynamic reference state. The derivations have been revised using two different integration paths: i) constant volume, and ii) constant pressure. Sample calculations with a Ni-Al system show that the two schemes yield close results. The constant pressure scheme presents the possibility of self-sustained chemical reactions (detonations) occurring in condensed phase. An example of such a detonation in the Ni-Al system is numerically demonstrated with hydrocode calculations.     

A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity

This article describes new a priori stability for the full nonlinear systems of coupled thermoplasticity at finite strains and presents a fractional step method leading to a new class of unconditionally stable staggered algorithms. These results are shown to hold for general models of multiplicative plasticity that include, as a particular case, the single-crystal model. The proposed product formula algorithm is designed via an entropy based operator split that yields one of the first known staggered algorithms that retains the property of nonlinear unconditional stability. The scheme employs an isentropic step, in which the total entropy is held constant, followed by a heat conduction step (with nonlinear source) at fixed configuration. The nonlinear stability analysis shows that the proposed staggered scheme inherits the a priori energy estimate for the continuum problem, regardless of the size of the time-step. In sharp contrast with these results, it is shown that widely used staggered methods employing an isothermal step followed by a heat conduction problem can be at most only conditionally stable. The excellent performance of the methodology is illustrated in representative numerical simulations.     

On axisymmetrical problem of layer with temperature dependent properties

The paper deals with the axisymmetrical problem of thermoelastic layer with mechanical properties dependent on temperature. The boundary planes of the body are kept at constant but different temperatures. Moreover, the layer is assumed to be ideal fixed to a rigid foundation. The upper boundary plane is loaded by normal forces dependent on the radius. The considered stationary problem is solved according with the following scheme: (1⁰) firstly the distribution of temperature is found, (2⁰) secondly, assuming that the Young modulus is a power function of temperature and Poisson ratio is constant, the displacements and stress are calculated from adequate boundary value problem. The obtained results in the form of Hankel integrals are analysed numerically for the case of linear dependence of Young modulus on the temperature.     

Numerical solution of three-dimensional static problems of elasticity for a body with a noncanonical inclusion

A boundary-element scheme is proposed for the numerical determination of the stress-strain state of a three-dimensional composite body, which is an elastic inclusion of arbitrary shape perfectly bonded to an infinite elastic matrix. The scheme involves the reduction of the original problem to six boundary integral equations for the components of interfacial displacements and forces and the boundary-element parametrization and discretization of these equations using generalized Gaussian integrals and topological maps with regularizing Jacobians. Numerical results are obtained for a cylindrical inclusion with rounded ends in a matrix subject at infinity to constant forces acting along this fiber. The influence of the length-to-radius ratio of the fiber and the ratio of the elastic moduli of the matrix and fiber on the stresses is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 27–35, April 2007.     

Vibration and stability of an axially moving viscoelastic beam with hybrid supports

Vibration and stability are investigated for an axially moving beam constrained by simple supports with torsion springs. A scheme is proposed to derive natural frequencies and modal functions from given boundary conditions of an elastic beam moving at a constant speed. For a beam constituted by the Kelvin model, effects of viscoelasticity on the free vibration are analyzed via the method of multiple scales and demonstrated via numerical simulations. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams in parametric resonance. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity.     

Algebraic-Complex Scheme for Dirichlet–Neumann Data for Parabolic System

In this paper, we use the Laplace–Laplace transformation and complex analysis to give a systematical scheme to determine the proper boundary conditions for initial-boundary value problems in the half space and to construct exponentially sharp pointwise structures of the boundary data. Here, we have used the boundary value problems with the Robin boundary conditions for the convection heat equations and the linearized compressible Navier–Stokes equation with a constant convection velocity to demonstrate this scheme.     

Flow of an oldroyd-type fluid through a sinusoidally corrugated tube

We report some experimental data on the flow of an Oldroyd-type fluid through a sinusoidally corrugated tube and describe a numerical method which is based on a Boundary Element method to solve the problem. The numerical method relies on an iterative scheme which allows us to obtain resolved numerical solutions up to Deborah number of the order 20, the results show a decrease in the frictional factor at first, and then the frictional factor increases with the Deborah number over a small range of Deborah number after which it remains constant until a numerical instability sets in. The predictions compare quite reasonably with our experimental data.     

Inlet flow disturbance effects on direct numerical simulation of incompressible round jet at Reynolds number 2500

This letter reports inlet flow disturbance effects on direct numerical simulation of incompressible round jet at Reynolds number 2500.The simulation employs an accurate projection method in which a sixth order biased upwind difference scheme is used for spatial discretization of nonlinear convective terms,with a fourth order central difference scheme used in the discretization of the divergence of intermediate velocity.Carefully identifying reveals that the inlet flow disturbance has some influences on the distribution pattern of mean factor of swirling strength intermittency.With the increase of inlet disturbance magnitude jet core cone slightly shortens,observable differences occur in the centerline velocity and its fluctuations,despite the negligible impacts on the least square fitted centerline velocity decay constant(B_u)and distribution parameter(K_u)for velocity profile in self-similar region.     

杆的差分离散系统一个新的模态反问题

本文研究杆的差分离散系统一个新的模态反问题,所考虑的杆件是同一种均匀材料构成的,但横截面积不恒定.首先,我们给出了变截面杆的纵向自由振动方程,采用分离变量法,得到了模态方程.然后,在最一般的边界条件,即两端弹性支承的边界条件下,采用二阶中心差分公式,导出了杆的差分离散模型.结果表明,所得到的系统属于标准雅可比系统.只对...     

A combined finite volumes - finite elements method for a low-Mach model

In this paper, we develop a finite volumes - finite elements method based on a time splitting to simulate some low-Mach flows. The mass conservation equation is solved by a vertex-based finite volume scheme using a τ-limiter. The momentum equation associated with the compressibility constraint is solved by a finite element projection scheme. The originality of the approach is twofold. First, the state equation linking the temperature, the density, and the thermodynamic pressure is imposed implicitly. Second, the proposed combined scheme preserves the constant states, in the same way as a similar one previously developed for the variable density Navier-Stokes system. Some numerical tests are performed to exhibit the efficiency of the scheme. On the one hand, academic tests illustrate the ability of the scheme in term of convergence rates in time and space. On the other hand, our results are compared to some of the literature by simulating a transient injection flow as well as a natural convection flow in a cavity.