不同当量强爆炸早期火球现象的数值模拟

采用一维球对称辐射流体力学方程组,研究了不同当量强爆炸早期火球阵面、冲击波的形成发展过程,对计算结果进行了相似律分析。结果表明,随爆炸当量增加,火球阵面、冲击波扩张速度加快,火球扩张过渡阶段开始结束位置及持续范围增加,火球中心温度下降变慢;在火球阵面以冲击波扩张传播以后,火球阵面参量满足立方根相似律。     

激波与火焰的相互作用过程

基于带化学反应的Navier Stokes方程和有关的热力学和反应动力学数据,利用改进的VLS格式,对甲烷 空气混合物中激波与火焰的相互作用进行了数值模拟。根据计算结果,讨论了激波掠过火焰时的变形、分叉和发展,以及激波作用下火焰的失稳、变形、破碎和相应的带旋涡的流场。     

Evolution of the fronts of quasi-compressional and quasi-shear discontinuous waves in inhomogeneous transversely isotropic elastic media

The propagation and evolution of the fronts of discontinuous waves in inhomogeneous transversely isotropic elastic media are studied. A method to draw evolving rays and fronts is proposed. Geometrical singularities on the fronts are studied for different parameters of anisotropy and inhomogeneity     

The Structure of Precipitation Fronts for Finite Relaxation Time

When convection is parameterized in an atmospheric circulation model, what types of waves are supported by the parameterization? Several studies have addressed this question by finding the linear waves of simplified tropical climate models with convective parameterizations. In this paper’s simplified tropical climate model, convection is parameterized by a nonlinear precipitation term, and the nonlinearity gives rise to precipitation front solutions. Precipitation fronts are solutions where the spatial domain is divided into two regions, and the precipitation (and other model variables) changes abruptly at the boundary of the two regions. In one region the water vapor is below saturation and there is no precipitation, and in the other region the water vapor is above saturation level and precipitation is nonzero. The boundary between the two regions is a free boundary that moves at a constant speed. It is shown that only certain front speeds are allowed. The three types of fronts that exist for this model are drying fronts, slow moistening fronts, and fast moistening fronts. Both types of moistening fronts violate Lax’s stability criterion, but they are robustly realizable in numerical experiments that use finite relaxation times. Remarkably, here it is shown that all three types of fronts are robustly realizable analytically for finite relaxation time. All three types of fronts may be physically unreasonable if the front spans an unrealistically large physical distance; this depends on various model parameters, which are investigated below. From the viewpoint of applied mathematics, these model equations exhibit novel phenomena as well as features in common with the established applied mathematical theories of relaxation limits for conservation laws and waves in reacting gas flows.     

Evaporation and Condensation Fronts in Porous Media

Flow of a fluid through a porous medium is considered with allowance for heat conduction. Both fronts at which the liquid is transformed into steam or a liquid-steam mixture and fronts with inverse transformations are studied. The evolutionarity conditions of these fronts are considered and a model of their structure is proposed.     

Regularity of Transition Fronts in Nonlocal Dispersal Evolution Equations

It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, we establish some general criteria concerning space regularity of transition fronts in nonlocal dispersal evolution equations with a large class of nonlinearities, which allows the applicability of various techniques for reaction–diffusion equations to nonlocal equations, and hence serves as an initial and fundamental step for further studying various important qualitative properties of transition fronts such as stability, uniqueness and asymptotic speeds. We also prove the existence of continuously differentiable and increasing interface location functions, which give a better characterization of the propagation of transition fronts and are of great technical importance.     

Geometrical disorder of the fronts of a tunnel-crack propagating in shear in some heterogeneous medium

A statistical analysis of the deformation of the fronts of a tensile tunnel-crack propagating in fatigue in some medium with spatially varying Paris constant was recently performed, with special emphasis on the evolution of the power spectra and correlation functions of the fluctuations of the fronts around reference straight lines. This study is extended here to coplanar propagation (along a weak plane) of a tunnel-crack loaded in mode 2+3. The results are rather similar to those previously obtained for mode 1. In particular, just like for tensile loadings, there is an effect of gradual selection in time of Fourier components of the fluctuations of the fronts of large wavelength. One novelty, however, is that for shear loadings, the fronts no longer tend to become symmetrical in time, so that correlations between crack front fluctuations at two points are higher for points located on the same front than for points located on distinct ones.     

In-plane perturbation of a system of two coplanar slit-cracks – I: Case of arbitrarily spaced crack fronts

In order to lay the grounds for a future study of the deformation of the fronts of coplanar cracks during their final coalescence, we consider the model problem of a system of two coplanar, parallel, identical slit-cracks loaded in mode I in some infinite body. The first, necessary task is to determine the distribution of the stress intensity factors along the crack fronts resulting from some small but otherwise arbitrary in-plane perturbation of these fronts. This is done here in the case where the distances between the various crack fronts are arbitrary and fixed.The first order expression of the local variation of the stress intensity factor is provided by a general formula of Rice (1989) in terms of some “fundamental kernel” tied to the mode I crack face weight function. In the specific case considered, this fundamental kernel reduces to six unknown functions; the problem is to determine them. This is done by using another formula of Rice (1989) which provides the variation of the fundamental kernel in a similar way. This second formula is applied to special perturbations of the crack fronts preserving the shape and relative dimensions of the cracks while modifying their absolute size and orientation. The output of this procedure consists of nonlinear integro-differential equations on the functions looked for, which are transformed into nonlinear ordinary differential equations through Fourier transform in the direction of the crack fronts, and then solved numerically.     

Spinodal Decomposition and Coarsening Fronts in the Cahn–Hilliard Equation

We study spinodal decomposition and coarsening when initiated by localized disturbances in the Cahn–Hilliard equation. Spatio-temporal dynamics are governed by multi-stage invasion fronts. The first front invades a spinodal unstable equilibrium and creates a spatially periodic unstable pattern. Secondary fronts invade this unstable pattern and create a coarser pattern in the wake. We give linear predictions for speeds and wavenumbers in this process and show existence of corresponding nonlinear fronts. The existence proof is based on Conley index theory, a priori estimates, and Galerkin approximations. We also compare our results and predictions with direct numerical simulations and report on some interesting bifurcations.     

轴对称坐标系下含曲率的水平集方程在非结构网格上的数值方法

为了在三角形和四边形网格上采用水平集方法模拟轴对称爆轰波阵面与曲率相关的运动,假设爆 轰波阵面的法向速度是曲率的线性函数,通过坐标变换得到了轴对称坐标系下的水平集方程。水平集方程的 曲率无关项采用正格式离散,曲率项采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式。算例表 明,在轴对称三角形网格和四边形网格上,含曲率的水平集方程的离散格式为强一阶精度。给出了三角形和 四边形混合网格上不光滑界面以曲率收缩的运动过程,收缩过程未出现不稳定现象。多个爆轰波阵面相互作 用的算例说明本文的格式可有效地模拟曲率相关的爆轰波的相互作用问题     

层结流体中湍流锋面特征的实验研究

在线性分层的水体中；由拖动坚条形栅格产生湍流锋面，通过阴影可视化技术考察了锋面的流态和运动行为，将锋面迹线经过图像处理，获得了锋面运动特征的有关信息：运动速度随时间的增长关系；锋面坍塌的平均无因次特征时间为NTC＝2．9；它随湍流Froude数Fri的增大而减小；锋面的特征尺度Hf与栅格运动的参数有关；当湍流演化成内波时，对锋面与内波运动间的关系进行了初步探讨和分析．     

A multipoint method for detecting coherent features in a turbulent shear flow

A technique is presented for the computer detection of temperature fronts in a turbulent shear flow. The detection variable is the product, averaged over a given duration, of temperature fluctuations at a given number of spatial locations. Efficient algorithms are developed for computing the product and for determining accurately the instants of detection, aided by simulations, using model temperature fronts. Ensemble averages of temperature and velocity are obtained for the self-preserving region of a turbulent plane jet.     

Mach reflection of weak shock waves from a rigid wall

On the basis of experimental observations and theoretical analysis of flow structure in the neighborhood of the triple point, it is shown that one should reject the condition for equality of the angle of deflection of flows passing through the Mach front and the two other fronts and replace it with some supplementary condition. The system of consistency equations in the indicated region is closed by an equation which is obtained under the assumption of the extremality of the deflection angle of a flow passing through the incident and reflected fronts. Calculations of the pressure drops behind the shock fronts agree with experimental data in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 26–33, September–October, 1973.The authors thank S. A. Khristianovich for consideration of the work and advice.     

On third order density contrast expansion of the evolution equation for wrinkled unsteady premixed flames

The dynamics of flat-on-average wrinkled flame front propagating through gaseous premixtures is considered. Leading the asymptotic expansions in powers of the burnt to unburned fractional density contrast (0<γ<1) to third order, an evolution equation (called S3) is obtained for the instantaneous front shapes. It reduces to Sivashinsky's original equation (called S1) as γ?0. It also modifies a previous attempt by Sivashinsky and Clavin (called S2) to improve it. Numerical integrations of the S3 equation reveals that the new quadratic and cubic non-linearities featured at 3rd order happen to mutually compensate partially one another for realistic γ's, and are negligible at γ?1. As a result, the flame shape and speed solutions to S3 nearly coincide with those of a S1/S2 type of equation, even for a 10-fold density variation (γ=0.9) and for unsteady situations, provided a singleO(1) coefficient a(γ) be adjusted therein, once for all for each γ. The O(γ²) (and small) correction to it mainly originates from a quartic non-linearity of geometrical origin. The agreement carries over to comparisons with some DNS of 2D steady wrinkled fronts. A phenomenological (yet asymptotically correct at γ?1 and exact in the linear limit) interpolating model equation is finally proposed to try and account for inertia effects associated with fast transients (e.g. acoustics related) while reproducing the above results on steady patterns.     

On the Relation between Fronts and High-Shear Layers in Wall Turbulence

Direct numerical simulation results of turbulent channel flow are analyzed in order to examine the relation between two kinds of near-wall flow structures, namely the instantaneous shear layers and the fronts which are derived from two-point statistics of the streamwise velocity component. The near-wall shear layers are analyzed by flow visualizations and conditional sampling, while the fronts are examined by means of space-time correlations and spatial two-point correlation functions. The present study focuses on the analysis of the propagation speed and the spatial shape of the structures. Concerning the propagation speed it is shown that the results obtained from flow visualizations are in close agreement with the propagation velocities derived from space-time correlation functions. The comparison of VISA results for the instantaneous shear with spatial structures obtained from two-point correlations of the streamwise velocity and the shear gives evidence that the fronts are intimately related to the pronounced near-wall shear layers.     

Coarsening Fronts

We characterize the spatial spreading of the coarsening process in the Allen–Cahn equation in terms of the propagation of a nonlinear modulated front. Unstable periodic patterns of the Allen–Cahn equation are invaded by a front, propagating in an oscillatory fashion, and leaving behind the homogeneous, stable equilibrium. During one cycle of the oscillatory propagation, two layers of the periodic pattern are annihilated. Galerkin approximations and the Conley index for ill-posed spatial dynamics are used to show existence of modulated fronts for all parameter values. In the limit of small amplitude patterns or large wave speeds, we establish uniqueness and asymptotic stability of the modulated fronts. We show that the minimal speed of propagation can be characterized by a dichotomy which depends on the existence of pulled fronts. The main tools here are an Evans function type construction for the infinite-dimensional ill-posed dynamics and an analysis of the complex dispersion relation based on Sturm–Liouville theory.     

Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability

We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translations of the front. In the case of stationary ergodic reactions, the fronts are proved to propagate with a deterministic positive speed. Our results extend to reaction-advection-diffusion equations with periodic advection and diffusion.     

Growth of discontinuities in fluids with internal relaxation

The growth equation for weak discontinuities headed by wave fronts of arbitrary shape in a relaxing gas flow is derived along the orthogonal trajectories of the wave fronts. An explicit criteria for the growth and decay of weak discontinuities along their orthogonal trajectories is given. It is concluded that the internal relaxation processes in the flow as well as the wave front curvature both have a stabilizing effect on the tendency of the wave surface to grow into a shock in the sense that they cause the shock formation time to increase.     

Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy

A special plasticity-based constitutive model with an up–down–up flow rule used within a finite element framework has previously been shown to simulate the inhomogeneous nature and the thermo-mechanical coupling of stress-induced transformation seen in a NiTi shape memory alloy. This paper continues this numerical study by investigating the trends of localized nucleation and propagation phenomena for a wider range of loading rates and ambient thermal conditions. Local self-heating (due to latent heat of transformation), the inherent Clausius–Clapeyron relation (sensitivity of the material's transformation stress with temperature), the size of the specimen's nucleation barriers, the loading rate, and the nature of the ambient environment all interact to create a variety of mechanical responses and transformation kinetics. The number of transformation fronts is shown to increase dramatically from a few fronts under nearly isothermal conditions to numerous fronts under nearly adiabatic conditions. A non-dimensional film coefficient and non-dimensional conductivity are identified to be the major players in the range of responses observed. It is shown that the non-dimensional film coefficient generally determines the overall temperature response, and therefore force–displacement response, of a transforming specimen; whereas, the non-dimensional conductivity is the more important player in determining the number of nucleations, and therefore the number of transformation fronts, that may occur.     

应用阵面追踪法对散心爆轰波传播的数值模拟

考虑到爆轰波阵面曲率及化学反应区宽度的作用 ,由修正Hugoniot关系式解析求解了波后状态 ,应用阵面追踪法 (FTM)数值模拟了曲面散心爆轰波的传播。计算给出的散心爆轰波走时及波阵面上物理量都达到了波阵面曲率的一阶精度。