MGFM在强激波与物质界面作用中的应用

原始的虚拟流方法(GFM)在计算强激波和物质界面作用时无法得到正确的计算结果,而改进虚拟流方法(MGFM)处理这类问题的能力大大提高.本文用Level set捕获物质界面,用MGFM方法定义虚拟流节点参数,Euler方程采用HLLC格式离散求解,完成了强激波和物质界面作用的一维和二维数值实验.结果表明改进虚拟流方法在强激波与物质界面作用中的应用是成功的.     

Level Set方法在地面效应数值模拟中的应用

利用Level Set方法隐式捕捉界面并能处理复杂的物质界面及其拓扑结构变化（如合并、交叉、破碎等）情况的优势,基于可压缩N-S方程的预处理技术,采用基于界面两侧介质黎曼关系的修正虚拟流体方法对介质边界进行处理;将只能应用于可压缩流动界面模拟的修正虚拟流体方法推广应用于不可压缩流动问题的模拟,数值模拟了气-水运动界面与近水面飞行器的相互影响规律。通过与将水面视为对称面的简化模型对比发现：利用自由运动界面模型计算的NACA6409翼型升力较小,能更准确地反映飞行器流场对水面形状的影响,其结果更为符合实际;文中还对比了翼型距水面不同高度时的结果,得到了翼型受水面影响的强弱与翼型距水面的高度成反比的结论。     

用Level Set方法求解具有自由面的流动问题

为采用Ｌｅｖｅｌ Ｓｅｔ方法来计算有自由的流动问题提出了一种方案,把自由水面视为水和空气的交界面,两种介质用统一的Ｎ－Ｓ方法求解,在自由面两侧分别采用各自的密度和粘性,并在自由面上给以适当的光滑;采用边界元法求解双调和方程来确定距离函数;Ｎ－Ｓ方程用投影法求解,文中给出了二维水池水面振荡和瞬时溃坝问题的算例,可以看出用ＬｅｖｅｌＳｅｔ方法求解有自由面流动问题是有效的。     

用Level Set方法追踪运动界面

首先介绍了近年来发展起来的界面追踪技术Level Set方法,然后采用五阶WENO格式和积分平均型TVD格式计算Level Set方程,用修正的Godunov方法求解重新初始化的Level Set方程,数值求解了同心圆在常数流场,圆和矩形界面在剪切流场,缺口圆在旋转流场中的界面变形和还原效果,比较了时间导数离散精度和Level Set函数有无重新初始化对界面追踪效果的影响．最后,通过和其它界面处理方法的比较可以看出,Level Set方法不仅能够比较准确地追踪运动界面,而且无须进行复杂繁琐的界面重构技术,容易编程,具有较大的通用性．     

基于Level Set方法对油水和气水两相界面的数值模拟

为研究两相界面迁移特性,基于LevelSet方法,建立了求解非定常不可压缩两相界面流动的数值方法。计算中使用结构化网格采用LevelSet函数捕捉两相界面。通过对经典算例的模拟,验证了数值方法对界面捕捉的有效性和精确性。模拟了油滴在水中上升、变形,与油层融合的过程,研究了气泡在产生、发展、脱离阶段的变形机理,和表面张力系数对气泡形状的影响。计算结果发现,表面张力系数越大,气泡在发展阶段持续的时间就越长,膨胀的程度也越大,并在脱离时刻,气泡的体积也越大,为进一步研究两相界面迁移特性提供了新的途径。     

Level Set追踪等温非牛顿熔全前沿界面

应用Level Set方法追踪薄壁型腔内Hele-Shaw熔体流动前沿界面,采用5阶加权本质无振荡格式耦合中心差分格式实现了充填阶段的动态模拟.准确追踪到了不同时刻熔体前沿界面,并得到了对应的压力等值线分布,数值结果表明Level Set方法是准确追踪注塑成型熔体前沿界面的一种行之有效的方法.     

基于Level Set方法的气-液-固三相流动模型与模拟

采用基于Level Set方法与离散颗粒模型相结合的方法,建立了一个用于描述气液固三相流动的新模型.模型耦合了颗粒与气泡、颗粒与液相以及气泡与液相之间的相互作用.应用该模型对液固悬浮液中的典型现象--气泡的单孔及多孔形成过程以及颗粒夹带现象进行了三维模拟,检验了其可行性.并进一步研究了颗粒的存在对气泡的形成与上升过程的影响以及气泡诱导的液相流动对颗粒行为的影响.研究结果表明,所提出的模型能够真实地预测三相流中气泡与颗粒分散相的特征,为研究多尺度的三相流动提供了一种新途径.     

三维非牛顿熔体前沿界面的Level Set/Ghost/SIMPLEC模拟

建立了三维粘性不可压非牛顿流体流动的控制方程,采用Level Set/Ghost/SIMPLEC方法模拟了注塑成型充模阶段的三维流动过程;追踪到了不同时刻的熔体前沿界面,预测并分析了流动过程中不同时刻的压力、速度等重要的流动特征参数,并与牛顿流体相应的流动特征参数做了对比.研究结果表明:Lovol Set/Ghost/SIMPLEC方法可以准确追踪非牛顿熔体前沿界面:幂律熔体在流动过程中的压差明显大于牛顿熔体的压差,沿横截面的速度分布也有明显的差别.     

多介质可压缩流体动力学界面捕捉方法

研究多介质流界面捕捉方法的主要目的是消除多介质流体在界面处压力、速度可能出现的非物理振荡现象 ,并通过流体动力学方程和界面捕捉方程的耦合 ,将多介质流体动力学计算形式上转化为单介质流体计算 ,从而可以采用对计算单介质有效的高精度计算方法来处理多介质流动问题。推广了Shyue界面捕捉和其等效方程的推导方法 ,给出的结果可以适用于具有状态方程 p =( ,e,a1 , ,an) +( ,e,b1 , ,bn)e的介质 ,并通过了数值试验验证。     

真实虚拟流方法在多介质可压缩流动模拟中的应用

为了克服原始虚拟流方法(ghost fluid method,GFM)在处理激波与大密度比流体-流体（气-水）界面相互作用时遇到的困难,采用真实虚拟流法(real ghost fluid method,RGFM)处理流体界面附近的虚拟点,结合HLLC(Harten-Lax-Van Leer with contact discontinuities)格式求解Euler方程,采用五阶WENO(weighted essentially nonoscillatory)格式求解level set输运方程。通过一维和二维算例的物质界面捕捉研究,证明RGFM在处理小密度比界面问题时优于GFM,同时RGFM还可用于求解激波与大密度比物质界面相互作用问题。计算表明,将RGFM引入到本文算法中,可精确捕捉到激波与界面（气-气、气-水界面）相互作用的变化细节,包括大密度比界面的剧烈变形和破碎,并具有较高的计算分辨率。     

Kinetic meshless method for compressible flows

We present a grid‐free or meshless approximation called the kinetic meshless method (KMM), for the numerical solution of hyperbolic conservation laws that can be obtained by taking moments of a Boltzmann‐type transport equation. The meshless formulation requires the domain discretization to have very little topological information; a distribution of points in the domain together with local connectivity information is sufficient. For each node, the connectivity consists of a set of nearby nodes which are used to evaluate the spatial derivatives appearing in the conservation law. The derivatives are obtained using a modified form of the least‐squares approximation. The method is applied to the Euler equations for inviscid flow and results are presented for some 2‐D problems. The ability of the new scheme to accurately compute inviscid flows is clearly demonstrated, including good shock capturing ability. Comparisons with other grid‐free methods are made showing some advantages of the current approach. Copyright © 2007 John Wiley & Sons, Ltd.     

A LEVEL SET METHOD FOR MICROSTRUCTURE DESIGN OF COMPOSITE MATERIALS

I. INTRODUCTION Material design refers to the generation of composite materials with prescribed or improved propertiesthat cannot be found in the usual materials. This can be achieved by modifying the microstructureof the composite material. Now a syste…     

Numerical simulations of compressible flows using multi-fluid models

Numerical simulations of two-fluid flow models based on the full Navier–Stokes equations are presented. The models include six and seven partial differential equations, namely, six- and seven-equation models. The seven-equation model consists of a non-conservative equation for volume fraction evolution of one of the fluids and two sets of balance equations. Each set describes the motion of the corresponding fluid, which has its own pressure, velocity, and temperature. The closure is achieved by two stiffened gas equations of state. Instantaneous relaxation towards equilibrium is achieved by velocity and pressure relaxation terms. The six-equation model is deduced from the seven-equation model by assuming an infinite rate of velocity relaxation. In this model, a single velocity is used for both fluids. The numerical solutions are obtained by applying the Strang splitting technique. The numerical solutions are examined in a set of one, two, and three dimensions for both the six- and seven-equation models. The results indicate very good agreement with the experimental results. There is an insignificant difference between the results of the two models, but the six-equation model is much more economical compared to the seven-equation model.     

Numbering techniques for preconditioners in iterative solvers for compressible flows

We consider Newton–Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point‐block Gauss–Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering methods known from multigrid for convection‐dominated elliptic problems is introduced. This reordering algorithm is essentially black‐box and significantly improves the robustness and efficiency of the point‐block Gauss–Seidel preconditioner. Results of numerical experiments using the QUADFLOW solver and the PETSc library are given. Copyright © 2007 John Wiley & Sons, Ltd.     

An efficient shock-capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.     

An efficient algorithm for compressible flows with real gases

An efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.     

Third‐order Cartesian overset mesh adaptation method for solving steady compressible flows

A third‐order mesh generation and adaptation method is presented for solving the steady compressible Euler equations. For interior points, a third‐order scheme is used on Cartesian and curvilinear meshes. Concerning the mesh adaptation, the method of Meakin is also extended to third order. The accuracy of the new overset mesh adaptation method is demonstrated by a grid convergence study for 2‐D inviscid model problems and results are compared with a second‐order method. Finally, the method is applied to the computation of an inviscid 3‐D flow around a hovering blade of the ONERA 7A helicopter rotor exhibiting an improvement in the wake capture. With a 7 million point mesh, the tip vortex can be followed for more than three rotor revolutions with the third‐order method. The CPU time needed for this calculation is only 3% higher than with a conventional second‐order method. Copyright © 2007 John Wiley & Sons, Ltd.     

A high-order Runge-Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two-dimensional compressible inviscid flows

A robust, adaptive unstructured mesh refinement strategy for high-order Runge-Kutta discontinuous Galerkin method is proposed. The present work mainly focuses on accurate capturing of sharp gradient flow features like strong shocks in the simulations of two-dimensional inviscid compressible flows. A posteriori finite volume subcell limiter is employed in the shock-affected cells to control numerical spurious oscillations. An efficient cell-by-cell adaptive mesh refinement is implemented to increase the resolution of our simulations. This strategy enables to capture strong shocks without much numerical dissipation. A wide range of challenging test cases is considered to demonstrate the efficiency of the present adaptive numerical strategy for solving inviscid compressible flow problems having strong shocks.