rGFM和level-set方法在水柱群和喷管流场计算中的应用

计算平面运动激波和水柱群相互作用以及喷管流场.在Descartes网格中利用level-set方法分别追踪气/水和气/固界面,采用rGFM方法处理气/水和气/固界面边界条件.将喷管内壁简化为气/固界面并施加固壁边界条件,内壁型线数据拟合采用三次样条插值.采用5阶WENO格式分别求解Euler方程、level-set方程和界面重新初始化方程.给出激波和水柱群相互作用流场密度纹影图和指定点p-t曲线以及喷管流场压力、密度云图和速度场.改进界面法线确定方法可提高Riemann问题构造精度.可分辨运动激波和水柱群作用产生的复杂激波波系,表明激波在各水柱界面的透射和反射、在列和行水柱界面的多次反射和透射.水柱群下游区域的激波波后压力下降,表明激波加热水柱群附近气流和反向运动的反射激波造成了激波衰减.喷管流场数值解和理论解相符.     

界面追踪方法中的激波限制器研究

针对多介质流体界面追踪(Front Tracking)方法,通过在界面处构造Riemann问题,研究激波限制器应用过程中的若干基本问题.针对气-气和气-水界面问题,通过比较平均守恒误差、L₁误差和激波强度随参数的变化情况,给出激波限制器参数可以在0.3附近选取.同时,通过理论分析和数值算例发现,当有激波接近界面时,选择激波波后状态作为界面处Riemann问题的初始状态,数值模拟结果较满意.     

三角形网格上多介质流动问题界面处理方法

多介质流动问题的求解一般是在结构网格上实现,而三角形网格对于复杂计算区域具有更好的适应性,本文结合rGFM方法,给出三角形网格上多介质流动问题界面处理方法.利用level-set方法跟踪界面,在界面处构造Riemann问题,得到界面处流体准确的流动状态.通过定义界面边界条件,将多介质流动问题转化为单介质流动问题,利用高精度RKDG方法求解.采用多个算例验证该方法的稳健性和有效性,结果表明该方法能准确捕捉界面和激波的位置,保持界面清晰.     

高密度比多介质可压缩流动的PPM方法

介绍一种基于流体体积分数模型的界面捕捉方法,数值模拟高密度比及含强激波的多介质可压缩流动.将PPM方法应用到多介质体积分数形式的Euler方程组,用双波近似求解一般刚性气体状态方程Riemann问题,可方便处理界面强剪切的滑移线问题,并给出了水下激波和气泡相互作用以及多相Richtmyer Meshkov不稳定性的计算结果.     

应用多介质PPM方法计算斜激波与物质交界面的相互作用

利用多介质PPM方法研究斜激波与物质交界面的相互作用.采用与体积分数耦合的Euler方程组作为计算模型,用双波近似来求解一般刚性气体状态方程Riemann问题.通过体积分数的计算来获得界面的位置,在整个流场采用统一的高阶PPM格式进行计算.文中对斜激波与不同物质界面相互作用进行了数值模拟,并给出了交界面上由于斜压效应产生的涡列的演化过程,特别是强斜激波与不同物质界面的相互作用的情况.     

可压缩多介质流体数值模拟中的Level-Set间断跟踪方法

针对可压缩多介质流体的数值模拟,发展了一种Level-Set间断追踪技术,用LS(Level-Set)函数追踪激波和捕捉界面,用Riemann问题解构造带状区域内的虚拟流体状态,对物理量的外推方法、间断附近虚拟流体的构造、间断推进速度的计算等问题进行了研究.最后对可压缩多介质流体一维和二维守恒律方程组进行数值模拟,数值计算采用通量重构的高精度WENO格式,计算结果令人满意.     

在直角坐标系用NGFM模拟复杂计算域水下高压气泡膨胀问题

采用NGFM(New version of Ghost Fluid Method)处理复杂计算域的固壁边界,用RGFM(Real Ghost Fluid Method)求解气-水界面附近网格节点的状态参数,从而在直角坐标系下对复杂计算域的水下高压气泡膨胀问题进行数值模拟。流场控制方程选用Euler方程,用五阶WENO格式离散空间导数项,二阶Runge-Kutta法离散时间导数项;气-水界面追踪使用Level Set方法,对Level Set方程,用五阶HJ-WENO(Hamilton-Jacobi WENO)和三阶Runge-Kutta法求解。将计算结果与任意坐标系下的结果进行对比,验证了NGFM在笛卡尔网格中处理复杂形状固壁边界的可行性。得到了水下流场压力等值线图、高压气泡的演变过程以及特定点处的压力-时间曲线。计算结果表明,高压气泡在固壁反射激波的作用下,膨胀过程受到抑制;强激波在固壁的反射会导致固壁附近出现大范围的空化流动。     

一维多介质可压缩流动数值方法

应用高精度界面追踪方法计算一般状态方程的多介质可压缩流动问题;应用LevelSet技术捕捉界面位置,在界面附近采用守恒数值离散,用双波近似求解一般状态方程Riemann问题,并采用统一高阶PPM格式进行内点和交界面点的计算.一维算例表明,该方法对于光滑区域以及多介质交界面具有二阶精度,能准确地模拟交界面的位置,交界面计算无数值振荡和数值耗散,并能处理一般状态方程的多介质可压缩流动问题.     

多介质流动数值计算中的界面处理方法

 求解Riemann问题得到界面接触间断的流动状态,并以此构造带状区域的虚拟流体状态,对于多维问题设计了一种方便有效的算法。同时求解耦合的守恒形式欧拉方程组和非守恒界面捕捉方程,并用Level-Set函数捕捉界面,数值计算采用高分辨率MWENO格式。最后对可压缩多介质流动问题进行了数值模拟。     

DG方法求解可压缩气固两相流动

给出求解双向耦合可压缩气固两相流的间断有限元方法,对所得到的气固两相流方程组不需要采用分裂的方法离散,对气相、颗粒相方程及其对流部分和源项可以统一处理,两相都采用基于近似Riemann解的数值通量.数值模拟低压含尘激波管内的两相非平衡流动,并与平衡流、冻结流的结果进行比较.分析颗粒相的存在对气体运动的影响,及激波后松弛区域内两相间相互作用规律.发现颗粒质量比决定两相平衡后的最终状态,而颗粒直径决定两相流从非平衡到平衡的过渡过程,即不同尺寸颗粒对应的驰豫时间、松弛距离不同.结果表明：本文提出的计算方法对求解可压缩气固两相流是可行的,为研究复杂的气固两相流动问题奠定了基础.     

An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces

This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.     

基于求解Riemann问题的界面处理方法

通过在界面处构造Riemann问题,根据流体的法向速度和压力在界面(接触间断)处连续的特性,利用Riemann问题的解不仅定义了ghost流体的值,而且对真实流体中邻近界面的点值进行了更新,使得在界面处的流体的状态满足接触间断的性质,给出了更加精确的界面边界条件,守恒误差分析表明该方法在界面计算过程中引入较小的误差.数值试验表明该方法能准确地捕捉界面和激波的位置.     

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.     

A systematic approach for constructing higher-order immersed boundary and ghost fluid methods for fluid–structure interaction problems

A systematic approach is presented for constructing higher-order immersed boundary and ghost fluid methods for CFD in general, and fluid–structure interaction problems in particular. Such methods are gaining popularity because they simplify a number of computational issues. These range from gridding the fluid domain, to designing and implementing Eulerian-based algorithms for challenging fluid–structure applications characterized by large structural motions and deformations or topological changes. However, because they typically operate on non body-fitted grids, immersed boundary and ghost fluid methods also complicate other issues such as the treatment of wall boundary conditions in general, and fluid–structure transmission conditions in particular. These methods also tend to be at best first-order space-accurate at the immersed interfaces. In some cases, they are also provably inconsistent at these locations. A methodology is presented in this paper for addressing this issue. It is developed for inviscid flows and prescribed structural motions. For the sake of clarity, but without any loss of generality, this methodology is described in one and two dimensions. However, its extensions to flow-induced structural motions and three dimensions are straightforward. The proposed methodology leads to a departure from the current practice of populating ghost fluid values independently from the chosen spatial discretization scheme. Instead, it accounts for the pattern and properties of a preferred higher-order discretization scheme, and attributes ghost values as to preserve the formal order of spatial accuracy of this scheme. It is illustrated in this paper by its application to various finite difference and finite volume methods. Its impact is also demonstrated by one- and two-dimensional numerical experiments that confirm its theoretically proven ability to preserve higher-order spatial accuracy, including in the vicinity of the immersed interfaces.     

运动激波和气泡串相互作用的初步数值模拟

通过对激波和流体界面相互作用诱导的大变形界面演化的数值模拟,验证Level set方法精确模拟多个流体界面的有效性.采用2阶迎风TVD求解欧拉方程得到流场解,采用5阶WENO求解Level set方程追踪多流体界面,采用GFM方法处理流体内界面.利用文[1]的计算结果校核本文程序.在此基础上,对运动激波和气泡串相互作用过程进行了初步数值模拟,得到了不同时刻运动激波和圆管内的两个气泡作用后的演化图象,包括压力和密度等值线分布.计算结果表明:针对推广后的多界面Level set方程,该方法仍可高质量地捕捉多个流体界面.     

Deforming composite grids for solving fluid structure problems

We describe a mixed Eulerian–Lagrangian approach for solving fluid–structure interaction (FSI) problems. The technique, which uses deforming composite grids (DCG), is applied to FSI problems that couple high speed compressible flow with elastic solids. The fluid and solid domains are discretized with composite overlapping grids. Curvilinear grids are aligned with each interface and these grids deform as the interface evolves. The majority of grid points in the fluid domain generally belong to background Cartesian grids which do not move during a simulation. The FSI-DCG approach allows large displacements of the interfaces while retaining high quality grids. Efficiency is obtained through the use of structured grids and Cartesian grids. The governing equations in the fluid and solid domains are evolved in a partitioned approach. We solve the compressible Euler equations in the fluid domains using a high-order Godunov finite-volume scheme. We solve the linear elastodynamic equations in the solid domains using a second-order upwind scheme. We develop interface approximations based on the solution of a fluid–solid Riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids. The FSI-DCG approach is verified for three problems with known solutions, an elastic-piston problem, the superseismic shock problem and a deforming diffuser. In addition, a self convergence study is performed for an elastic shock hitting a fluid filled cavity. The overall FSI-DCG scheme is shown to be second-order accurate in the max-norm for smooth solutions, and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters.     

Rayleigh-Taylor不稳定性的Runge-Kutta间断有限元模拟

 采用发展后的间断有限元方法,对Rayleigh-Taylor不稳定性进行了数值模拟。在计算中采用Level-Set方法进行界面追踪,用虚拟流体方法（Ghost Fluid Method,GFM）对界面附近物理量进行等压装配。对两个典型的Rayleigh-Taylor不稳定性算例的数值研究结果表明,采用该方法计算含有接触间断的多介质流体力学问题是有效的,在交界面附近不出现伪振荡,具有较高的分辨率。