Euler多物质流体动力学数值方法中的界面处理算法

结合Euler型多物质流体动力学数值方法,将Youngs界面重构技术进行改进,改进后的算法中,混合网格周围网格物质的体积份额不但被用来计算物质界面的位置,还被用来确定混合网格中各物质的输运次序.将改进后的算法加入到自行开发的MMIC-2D通用多物质二维爆炸与冲击问题数值仿真程序中,对二维直角坐标系下圆环在平移流场中的运动过程进行模拟,以此对提出的改进界面处理算法进行数值考核.在此基础上,对聚能装药射流的形成过程进行数值模拟,模拟结果图像显示,其物质分界面清晰,并与实验结果吻合较好,从而验证了该方法的精度及有效性.     

基于界面捕捉的三维多介质辐射流体力学方程MMALE计算方法

针对界面重构产生的混合介质网格,建立基于能量守恒的子网格封闭模型,给出基于混合介质网格上的三维扩散方程求解方法.在此基础上,结合界面重构和流体力学方程MMALE （multi-material arbitrary Lagrangian-Eulerian）算法,给出一种针对三维辐射流体力学的MMALE计算方法.采用解析解算例,验证算法的正确性和精度.通过对典型辐射驱动问题的模拟,展示方法的健壮性.     

二维欧拉多介质流体力学数值模拟-TVD＋VOF方法

用TVD格式结合VOF界面处理方法编制了二维多介质高分辨欧拉程序，以解决冲击波和多介质界面处理。程序包括单介质网格高精度流体力学计算、多介质网格内界面重构、各种介质输运和压力驰豫平衡过程。其中单介质网格的计算采用Harten二阶TVD格式结合MacCormark方法计算含有源项的非齐次守恒定律方程组，通过4节点限制函数保证格式单调。多介质网格采用Youngs方法构造界面，采用x，y方向分裂格式计算体积份额输运，再根据体积份额输运计算质量、动量和能量的输运，最后利用等熵条件计算各种介质的压力驰豫平衡过程。     

三维多介质欧拉有限体积格式的混合算法

对于多介质欧拉方法，混合网格物理量的计算是其难点和关键点之一。这里提出的方法是运用Yonugs界面重构技术确定出混合网格内物质的界面，界面确定后，混合网格内每一部分可能是非规则的四面体、五面体、六面体或七面体，采用对非规则区域适应性很强的有限体积法对每一部分分别进行计算。这种方法虽然比较复杂，但是它兼有拉氏方法的优点，因此计算出的混合网格内每一部分物质的物理量比较精确。     

基于MOF的欧拉方法界面重构技术

欧拉方法和拉格朗日方法是多流体数值模拟中最主要的两种方法。对拉格朗日方法而言,如果存在大变形,就会产生网格扭曲,导致计算无法进行下去;而用欧拉方法进行数值模拟的难点在于混合网格中界面的确定及物理量的处理。因此,界面处理技术是欧拉数值方法的主要研究内容之一。     

随机扰动下三维流体界面不稳定性的并行计算

对三维流体界面不稳定性的数值模拟引进了新的数值计算方法,并在MPI并行计算环境下进行了数值模拟.利用LevelSet方法确定界面位置,零水平集对应界面位置.对应离散LevelSet方程和界面两侧的两套Euler方程,借助于Ghost网格方法来完成离散.对最后网格点上的两套状态量的辨认依赖于该点的LevelSet值的符号.并进行了数值计算.     

非结构网格RKDG有限元方法求解多介质界面问题

在流体力学方程数值模拟中，多介质界面的计算是一个非常重要的问题。已有的数值模拟多采用Lagrange方法。但是，当计算长时间问题时，Lagrange方法会产生网格扭曲，进而使计算无法进行下去。另外一种是采用Euler方法，Euler方法应用于多介质流体力学，首要问题是界面捕捉，即将不同区域介质界面描述清楚，这样才能使得多介质流体计算时，不会发生流体的非物理振荡。     

Ghost Fluid方法与双介质可压缩流动计算

应用带有Isobaric修正的GhostFluid方法配合LevelSet方法计算可压缩双介质无粘流动.该方法可以消除计算流体界面时所产生的数值跳动和耗散,且编程上比界面跟踪法简单.应用WENO格式数值求解欧拉方程和LevelSet方程,对由刚性气体状态方程所支配的一二维双介质流动进行数值计算,得到了分辨率较高的计算结果.     

欧拉计算程序实现非均质炸药冲击起爆的数值模拟

爆轰的数值模拟研究多采用Lagrangian方法，这是因为Lagrangian网格随质点运动，介质之间的界面用滑移面来描述，故能精确地计算介质的界面。但在遇到网格扭曲和网格变形时，计算往往无法继续进行，这时就要用到网格重分等技术，这无疑增加了人为干预和计算误差。Eulerian方法能计算大变形问题，但不能精确地描述物质的界面，对于模拟平面撞击实验，爆轰波在单种介质中传播，对物质界面几乎没有要求。所以，Eulerian方法在模拟此类问题较Lagrangian方法具有明显的优势。     

二维MLSPH无网格方法

给出MLSPH无网格方法的控制方程、移动最小二乘近似、MLSPH守恒格式等,重点研究MLSPH守恒格式中MLS面积向量的数值求解方法,以提高求解的精度.对激波管问题和平面Noh问题进行模拟,得到较好的结果,确定用三次样条积分公式计算面积向量.     

Volume-of-fluid algorithm with different modified dynamic material ordering methods and their comparisons

Volume-of-fluid (VOF) interface reconstruction methods are used to define material interfaces to separate different materials in a mixed cell. These material interfaces are then used to evaluate transport flux at each cell edges in multi-material hydrodynamic calculations. Most of the VOF interface reconstruction methods and volume transport schemes rely on an accurate material order unique to each computational cell. Similarly, to achieve overshoot-free volume fractions, a non-intersecting interface reconstruction procedure has to be performed with the help of a ‘material-order list’ determined prior to interface reconstruction. It is, however, the least explored area of VOF technique especially for ‘onion-skin’ or ‘layered’ model. Also, important technical details how to prevent intersection among different material interfaces are missing in many literature. Here, we present an efficient VOF interface tracking algorithm along with modified ‘material order’ methods and different interface reconstruction methods. The relative accuracy of different methods are evaluated for sample problems. Finally, a convergence study with respect to mesh-size is performed.     

A conservative level-set based method for compressible solid/fluid problems on fixed grids

A three-dimensional Eulerian method is presented for simulating dynamic systems comprising multiple compressible solid and fluid components where internal boundaries are tracked using level-set functions. Aside from the interface interaction calculation within mixed cells, each material is treated independently and the governing constitutive laws solved using a conservative finite volume discretisation based upon the solution of Riemann problems to determine the numerical fluxes. The required reconstruction of mixed cell volume fractions and cut cell geometries is presented in detail using the level-set fields. High-order accuracy is achieved by incorporating the weighted-essentially non-oscillatory (WENO) method and Runge–Kutta time integration. A model for elastoplastic solid dynamics is employed formulated using the tensor of elastic deformation gradients permitting the equations to be written in divergence form. The scheme is demonstrated using selected one-dimensional initial value problems for which exact solutions are derived, a two-dimensional void collapse, and a three-dimensional simulation of a confined explosion.     

A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids

We present a new three-dimensional hybrid level set (LS) and volume of fluid (VOF) method for free surface flow simulations on tetrahedral grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a second-order characteristic based finite volume method. The volume fraction advection is performed using a bounded compressive normalized variable diagram (NVD) based scheme. The interface is reconstructed based on both the level set and the volume fraction information. The novelty of the method lies in that we use an analytic method for finding the intercepts on tetrahedral grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. Furthermore, the advection of volume fraction makes use of the NVD concept and switches between different high resolution differencing schemes to yield a bounded scalar field, and to preserve both smoothness and sharp definition of the interface. The method is coupled to a well validated finite volume based Navier–Stokes incompressible flow solver. The code validation shows that our method can be employed to resolve complex interface changes efficiently and accurately. In addition, the centroid and intercept data available as a by-product of the proposed interface reconstruction scheme can be used directly in near-interface sub-grid models in large eddy simulation.     

Van der Waals状态方程可压缩多流体流动的PPM方法

基于流体体积分数的混合型多流体数值模型，将Piecewise Parabolic Method（PPM）方法应用于可压缩多流体流动的数值模拟，采用双波近似求解多流体van der Waals状态方程的Riemann问题．模拟高密度比且含有激波的可压缩多流体流动，典型的纯界面平移问题模拟结果表明，在接触间断的界面附近，压力和速度没有任何的振荡且界面数值耗散都被控制在2—3个网格之内；一维和二维算例表明，该数值方法可以有效地处理接触间断、激波和多维滑移线等物理问题，并能够比其它多流体数值方法更精细地模拟多流体交界面．     

A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations

A new, second-order accurate, volume conservative, material-order-independent interface reconstruction method for multi-material flow simulations is presented. First, materials are located in multi-material computational cells using a piecewise linear reconstruction of the volume fraction function. These material locator points are then used as generators to reconstruct the interface with a weighted Voronoi diagram that matches the volume fractions. The interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells. Convergence tests are shown demonstrating second-order accuracy. Static and dynamic examples are shown illustrating the superior performance of the method over existing material-order-dependent methods.     

考虑壁面接触效应的微流动数值模拟

使用level set和volume of fluid(VOF)方法对考虑壁面接触效应的不可压缩两相微流动进行数值模拟.对于level set方法,计算基于MAC网格,使用二阶投影算法求解二维Navier-Stokes(N-S)方程和level set函数方程;对于VOF方法,通过引入计算网格内的体积分数,将流场的参数转化为体积平均值,界面的形状由体积分数连续方程的解决定.给出一些计算实例,并和现有的实验结果进行比较.     

Anti-diffusion method for interface steepening in two-phase incompressible flow

In this paper, we present a method for obtaining sharp interfaces in two-phase incompressible flows by an anti-diffusion correction, that is applicable in a straight-forward fashion for the improvement of two-phase flow solution schemes typically employed in practical applications. The underlying discretization is based on the volume-of-fluid (VOF) interface-capturing method on unstructured meshes. The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction. As the solution of the anti-diffusion equation requires regularization, a limiter based on the directional derivative is developed for calculating the gradient of the volume fraction. This limiter ensures the boundedness of the volume fraction. In order to control the amount of anti-diffusion introduced by the correction algorithm we propose a suitable stopping criterion for interface steepening. The formulation of the limiter and the algorithm for solving the anti-diffusion equation are applicable to 3-dimensional unstructured meshes. Validation computations are performed for passive advection of an interface, for 2-dimensional and 3-dimensional rising-bubbles, and for a rising drop in a periodically constricted channel. The results demonstrate that sharp interfaces can be recovered reliably. They show that the accuracy is similar to or even better than that of level-set methods using comparable discretizations for the flow and the level-set evolution. Also, we observe a good agreement with experimental results for the rising drop where proper interface evolution requires accurate mass conservation.     

Electro-hydrodynamic behavior and interface instability of double emulsion droplets under high electric field

Dynamics of multiphase flow under high voltage has attracted extensive research interests due to its wide industrial applications. In this paper, numerical solution of electro-hydrodynamic behavior and interface instability of double emulsion droplet is presented. Level set method and leaky dielectric model coupled with Navier-Stokes equation are used to solve the electro-hydrodynamic problem. The method is validated against the theoretical analysis and the simulation results of the other researchers. Double emulsion droplet with inner droplet (core) and outer droplet (shell) phases immersed in continuous phase is subjected to high electric field. Shell/continuous and core/shell interfaces of the droplet undergo prolate-oblate or oblate-prolate deformation depending on the extent of the penetration of electric potential and sense of charge distribution at the interfaces. The deformation of the shell deviates from theory at larger volume fraction of core for oblate-prolate case whereas it follows theory for prolate-oblate case. The interfaces showing oblate-prolate deformation split at the poles whereas, for prolate-oblate, they split away along the equator. The re-union of the interfaces under high electric field results with production of daughter droplet at the core. The large decrease in critical electric field for oblate-prolate case shows their less interface stability at larger volume fraction of core. When the core is eccentric, the electric field drives it towards the shell center or to the shell/continuous interface depending on electrical parameters. The study is beneficial in understanding the electro-hydrodynamic behavior of emulsion droplets and efficient design of related industrial processes.     

A transient method for measuring the gas volume fraction in a mixed gas-liquid flow using acoustic resonance spectroscopy

In this paper, the feasibility of measuring the gas volume fraction in a mixed gas-liquid flow by using an acoustic resonant spectroscopy (ARS) method in a transient way is studied theoretically and experimentally. Firstly, the effects of sizes and locations of a single air bubble in a cylindrical cavity with two open ends on resonant frequencies are investigated numerically. Then, a transient measurement system for ARS is established, and the trends of the resonant frequencies (RFs) and resonant amplitudes (RAs) in the cylindrical cavity with gas flux inside are investigated experimentally. The measurement results by the proposed transient method are compared with those by steady-state ones and numerical ones. The numerical results show that the RFs of the cavity are highly sensitive to the volume of the single air bubble. A tiny bubble volume perturbation may cause a prominent RF shift even though the volume of the air bubble is smaller than 0.1% of that of the cavity. When the small air bubble moves, the RF shift will change and reach its maximum value as it is located at the middle of the cavity. As the gas volume fraction of the two-phase flow is low, both the RFs and RAs from the measurement results decrease dramatically with the increasing gas volume, and this decreasing trend gradually becomes even as the gas volume fraction increases further. These experimental results agree with the theoretical ones qualitatively. In addition, the transient method for ARS is more suitable for measuring the gas volume fraction with randomness and instantaneity than the steady-state one, because the latter could not reflect the random and instant characteristics of the mixed fluid due to the time consumption for frequency sweeping. This study will play a very important role in the quantitative measurement of the gas volume fraction of multiphase flows.     

Effects of particle/matrix interface and strengthening mechanisms on the mechanical properties of metal matrix composites

A randomly distributed multi-particle model considering the effects of particle/matrix interface and strengthening mechanisms introduced by the particles has been constructed. Particle shape, distribution, volume fraction and the particles/matrix interface due to the factors including element diffusion were considered in the model. The effects of strengthening mechanisms, caused by the introduction of particles on the mechanical properties of the composites, including grain refinement strengthening, dislocation strengthening and Orowan strengthening, are incorporated. In the model, the particles are assumed to have spheroidal shape, with uniform distribution of the centre, long axis length and inclination angle. The axis ratio follows a right half-normal distribution. Using Monte Carlo method, the location and shape parameters of the spheroids are randomly selected. The particle volume fraction is calculated using the area ratio of the spheroids. Then, the effects of particle/matrix interface and strengthening mechanism on the distribution of Mises stress and equivalent strain and the flow behaviour for the composites are discussed.