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.     

基于映射函数的三阶WENO改进格式及其应用

低耗散、高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义.在传统三阶WENO格式（WENO-JS3）和三阶WENO Z格式（WENO-Z3）基础上,基于映射函数,给出WENO-M3、WENO MZ3格式.选用Sod激波管、激波与熵波相互作用、双爆轰波碰撞及双Mach(马赫)反射等经典算例,考察上述格式的计算性能.数值结果表明,WENO-MZ3格式相较其他格式具有耗散低、对流场结构分辨率高的特性.为了进一步扩展WENO-MZ3格式的应用范围,采用该格式数值研究封闭方形舱室内柱形高压、高密度气体爆炸波传播过程,波系演化规律以及壁面典型测点压力载荷.数值计算结果表明WENO-MZ3格式能够较好地模拟包含高压比、高密度比的爆炸波且给出数值耗散较小的壁面压力载荷.     

装药驱动飞片引爆炸药性能影响参数分析

扩爆装药结构对爆轰波传播、飞片驱动过程以及对主炸药引爆性能有直接的影响。为分析装药结构对飞片威力参数的影响,针对装药直径、飞片厚度、飞片拱起高度等主要结构参数,利用正交实验原理设计了数值实验方案,并采用动力学有限差分程序建立了相应的数值模拟模型。通过对数值实验结果的对比和统计分析,获得了影响飞片速度、动量、比动能等引爆炸药威力指标的主要装药结构参数及其影响规律。其结果可为相关扩爆装药设计提供理论依据。     

基于广义高阶非线性薛定谔方程深海内波传播的数值模拟

基于与实际海洋背景参数相关的广义高阶非线性薛定谔方程,首先讨论了不同的海洋环境参数对方程的非线性项和频散项的影响;然后通过有限差分算子给出了方程的二阶三层数值差分格式,并且分析了该差分格式的稳定性与精度阶;最后又通过得到的差分格式数值模拟了不同的海洋环境参数下深海内波的传播情况,结果显示:内波由深海向浅海的传播过程中,随着总水深的变化,发生了分裂现象,并且密度差之比越大,波的分裂速度越快.     

激波管中动态相变的数值研究

用松弛模型研究了范德瓦流体中的激波管问题．当松弛参数趋于0时模型存在一个确定的黎曼解．在数值方面推导了松弛格式（relaxing）和完全松弛格式（relaxed）．在一维问题中,对于不同的剖面,数值模拟显示结果趋向于黎曼解,在理论上和数值上研究了参数的影响．对于特定的初始激波剖面,观察到了非经典的反射波．在二维问题中,研究了曲面波前的数值演化,得到一些有趣的波斑图．     

炸药爆轰物质点法三维数值模拟

炸药爆轰以及多点起爆所产生的爆轰波汇聚问题很难应用有限元法进行模拟分析,尤其当网格发生畸变时,导致有限元法计算效率和数值精度严重下降,甚至无法得到正确结果.为此,该文应用显式积分算法的物质点法对炸药两点起爆和按时间序列的多点起爆的爆轰过程进行数值模拟,与炸药爆轰的理论计算结果相吻合.物质点法不但可以有效地避免网格畸变问题,而且为炸药爆轰的数值模拟提供了新的思路.     

气体中火焰传播的数学

<正> 人类生活离不开火,在大约一百万年前,我们的祖先已经能够使用天然火,至少在一万多年前,我们的祖先已经懂得人工取火.但是,对火焰传播现象进行系统的科学研究工作的历史并不长,运用现代的数学工具对火焰作定性和定量的分析,可以说还刚刚开始.在气体中火焰的传播实际上是一种波动现象,人们通过长期的观察发现有两种基本的波型:爆燃波和爆轰波.前者反映了一种在气体中较为缓慢的燃烧过程.例如,在汽车和飞机发动机燃烧室内产生的就是这种波.而后者是一种猛烈且高速的燃烧过程,这种过程的结果往往是破坏性的.例如,当煤矿坑道中飞扬的煤粉达到一定浓度以后,就会产生爆轰波,引起爆炸事故.又如面粉厂中面粉的粉尘浓度过大时,也会造成工厂的爆炸事故.这样的事故在国外和我国都曾发生过.大型的运油船如果漏油,就会在周围形成大片可爆炸气云,爆轰波可能在这种气云中形成,这是必须防止的一个潜在危险.利用爆轰波原理,人们制造了气浪弹,这是一种装有环氧乙烷的装置,使用时首先将装置炸开,使     

基于传递矩阵法的周期性圆柱壳体振动特性分析

基于声子晶体理论和Love壳体理论,建立了圆柱壳体的轴对称波动微分方程,数值分析了周期性圆柱壳的能带特性.利用传递矩阵法建立了相邻胞元间的传递矩阵,推导了周期性圆柱壳各胞元环径向轴对称波动动态刚度矩阵.结合数值算例分析了弹性模量变化和几何尺寸变化对圆柱壳体波的传播特性的影响,数值结果表明:振动波在传播过程中存在禁带域和通带域,长度比的变化对周期性圆柱壳体禁带的幅值、宽度和个数影响显著,因此可以通过调整结构尺寸参数改变结构中波的传播特性,该文的研究可以为结构的抗震设计、减振控制提供一种新思路.     

一维非线性周期结构中弹性波传播的辛数学方法

利用辛数学方法分析了质量-弹簧非线性周期结构链中弹性波的传播问题．首先利用能量方法得到频域动力方程,随后通过小量变换将非线性动力方程线性化,得到辛矩阵,进而通过求解辛矩阵的本征值问题来研究波的传播性能．质量-弹簧模型中的弹簧刚度非线性对结构链的传播特性影响很大,研究发现非线性明显改变了周期结构的传播性能,而且不同于线性结构,非线性结构的传播特性与入射波强度有关．数值算例表明随着非线性强度及入射波强度的增大,传播通带宽度逐渐减小,禁带宽度逐渐增大．当入射波强度增大到一定值时,弹性波无法在结构中进行传播．与一般递归方法的比较分析,验证了辛数学方法在非线性周期结构波传播问题中的有效性与优越性．     

弹性固体和充满两种互不相溶粘性流体的多孔固体之间界面的反射和折射及其衰减波

在充满两种互不相溶粘性流体的多孔固体中,研究弹性波的传播.用3个数性的势函数描述3个纵波的传播,用1个矢性的势函数单独描述横波的传播.根据这些势函数,在不同的组合相中,定义出质点的位移.可以看出,可能存在3个纵波和1个横波.在一个弹性固体半空间与一个充满两种互不相溶粘性流体的多孔固体半空间之间,研究其界面上入射纵波和横波所引起的反射和折射现象.由于孔隙流体中有粘性,折射到多孔介质中的波,朝垂直界面方向偏离.将入射波引起的反射波和折射波的波幅比,作为非奇异的线性代数方程组计算.进一步通过这些波幅比,计算出各个被离散波在入射波能量中所占的份额.通过一个特殊的数值模型,计算出波幅比和能量比系数随入射角的变化.超过SV波的临界入射角,反射波P将不再出现.越过界面的能量守恒原理得到了验证.绘出了图形并对不同孔隙饱和度以及频率的变化,讨论它们对能量分配的影响.     

Numerical simulation of spinning detonation in circular section channels

Numerical simulation of three-dimensional structures of gas detonation in circular section channels that emerge due to the instability when the one-dimensional flow is initiated by energy supply at the closed end of the channel is performed. It is found that in channels with a large diameter, an irregular three-dimensional cellular detonation structure is formed. Furthermore, it is found that in channels with a small diameter circular section, the initially plane detonation wave is spontaneously transformed into a spinning detonation wave, while passing through four phases. A critical value of the channel diameter that divides the regimes with the three-dimensional cellular detonation and spinning detonation is determined. The stability of the spinning detonation wave under perturbations occurring when the wave passes into a channel with a greater (a smaller) diameter is investigated. It is found that the spin is preserved if the diameter of the next channel (into which the wave passes) is smaller (respectively, greater) than a certain critical value. The computations were performed on the Lomonosov supercomputer using from 0.1 to 10 billions of computational cells. All the computations of the cellular and spinning detonation were performed in the whole long three-dimensional channel (up to 1 m long) rather than only in its part containing the detonation wave; this made it possible to adequately simulate and investigate the features of the transformation of the detonation structure in the process of its propagation.     

A CELL-CENTERED ALE METHOD WITH HLLC-2D RIEMANN SOLVER IN 2D CYLINDRICAL GEOMETRY

This paper presents a second-order direct arbitrary Lagrangian Eulerian (ALE) method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control vol-ume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone up-wind scheme of conservation law (MUSCL) on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.     

High resolution multi-moment finite volume method for supersonic combustion on unstructured grids

In this study, we present a novel numerical model for simulating detonation waves on unstructured grids. In contrast to the conventional finite volume method (FVM), two types of moment comprising the volume-integrated average (VIA) and the point value (PV) at the cell vertex are treated as the evolution variables for the reacting Euler equations. The VIA is computed based on a finite volume formulation of the flux form where the conventional Riemann problem is solved by the HLLC Riemann solver. The PV is updated in a point-wise manner by using the differential formulation where the Roe solver is used to compute the differential Riemann problems. In order to increase the accuracy around discontinuities, numerical oscillations and dissipations are reduced using the boundary variation diminishing algorithm. Convergence tests demonstrated that the proposed model could achieve third-order accuracy with unstructured grids for reacting Euler equations. The high resolution property of the proposed method was verified based on simulations of several detonation wave propagation problems in two and three dimensions. In particular, the current model could resolve the cellular structures with fewer degrees of freedom for the unstable oblique detonation wave problem. These fine structures may be smoothed out by the conventional FVM due to the excessive amount of numerical dissipation errors. Importantly, a simulation of stiff detonation waves showed that the proposed method could capture the correct position of the reaction front whereas the conventional FVMs produced spurious phenomena. Thus, the proposed model can obtain highly accurate solutions for detonation problems on unstructured grids, which is highly advantageous for real applications involving complex geometrical configurations.     

Dispersion of elastic waves in the contact-impact problem of a long cylinder

Numerical dispersion of two-dimensional finite elements was studied. The outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars. In accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones.     

Existence of Entropy Solutions to Two-Dimensional Steady Exothermically Reacting Euler Equations

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function ?(T) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.     

Features of the linear stage of the development of 3D disturbances in the plane Poiseuille-Couette flow

Within the framework of the triple-deck theory, the linear stage of the development of three-dimensional disturbances in the Poiseuille-Couette flow was investigated. Numerical computations revealed “ripples” developing in the side direction in the initial phase of the linear stage. As in the case of two-dimensional disturbances, an increase in the relative velocity of the walls leads to the splitting of disturbances into two wave packets, of which the first grows faster and moves at a higher velocity. The disturbances propagate within a certain angle range.     

On a Control Problem for a Linear System with Measurements of a Part of Phase Coordinates

We consider a three-dimensional unsteady flow with a rotating detonation wave arising in an annular gap of an axially symmetric engine between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of 45°, the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multiparameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.     

The new alternating direction implicit difference methods for the wave equations

A new second-order alternating direction implicit (ADI) scheme, based on the idea of the operator splitting, is presented for solving two-dimensional wave equations. The scheme is also extended to a high-order compact difference scheme. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical examples are presented and the results are very satisfactory.     

Parallel spectral-element direction splitting method for incompressible Navier–Stokes equations

An efficient parallel algorithm for the time dependent incompressible Navier–Stokes equations is developed in this paper. The time discretization is based on a direction splitting method which only requires solving a sequence of one-dimensional Poisson type equations at each time step. Then, a spectral-element method is used to approximate these one-dimensional problems. A Schur-complement approach is used to decouple the computation of interface nodes from that of interior nodes, allowing an efficient parallel implementation. The unconditional stability of the full discretized scheme is rigorously proved for the two-dimensional case. Numerical results are presented to show that this algorithm retains the same order of accuracy as a usual spectral-element projection type schemes but it is much more efficient, particularly on massively parallel computers.