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。     

Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction

The modified ghost fluid method (MGFM) provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction (FSI) simulations. However, this methodology for one specific class of FSI problems, where the structure is plate, remains to be developed. This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate. In order to take into account the influence of simultaneous interaction at the interface, a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states. Then, ghost fluid states and plate load can be defined by utilizing the obtained interfacial states. A type of acceleration strategy in the coupling process is presented to pursue higher efficiency. Several one-dimensional examples are used to highlight the utility of this method over loosely-coupled method and validate the acceleration techniques. Especially, this method is applied to compute the underwater explosions (UNDEX) near thin elastic plates. Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated. Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.     

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.     

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.     

界面不稳定性数值模拟中的虚拟流动方法

研究了流体界面不稳定性的一类数值模拟方法——虚拟流动方法(Ghost Fluid Method).在算法中直接针对多维问题设定虚拟区域的流动参数,在流体力学方程的计算中采用了非分裂型的高分辨SCB格式,最后利用该方法完成了R-M和R-T不稳定性问题的数值计算,得到了满意的计算结果.     

SPH方法气-液界面边界条件研究

针对界面附近粒子光滑函数截断和非物理穿透问题,提出一种气-液界面边界条件的处理方法.当界面附近支持域出现不同材料粒子,每步计算可在支持域设置虚粒子,按照密度分配方法给虚粒子物理量赋值,并对界面附近粒子引入气-液两相阻力.采用SPH方法和Level-Set方法,计算运动激波对气-液界面作用问题,两者计算结果一致,初步验证了气-液界面边界条件处理的适用性.用SPH方法分别计算超声速气流中的圆截面液柱绕流和下落问题,界面两侧粒子压力和法向速度连续,给出弓形激波、回流区和下游回流区等定性合理结果.表明本文方法可适度避免界面附近流体粒子光滑截断和粒子非物理穿透现象、界面附近流场数值振荡.     

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.     

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。     

虚拟流体方法的设计原则

研究模拟可压缩多介质流的虚拟流体方法,建立一般状态方程下定义虚拟流体状态的基本原则.根据波系结构和使用的自由变量分别推导虚拟流体状态的定义方式.结果表明在这些方式下求解多介质Riemann问题理论上完全精确.进一步总结几种简单有效的虚拟流体方法,这些定义方式不依赖于虚拟流体区域可能产生的波系结构.其中一种类似于反射边界条件,只是界面速度需要首先精确预测出来.数值算例验证了研究结果的合理性.     

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.     

弹性板水下爆炸冲击载荷的修正虚拟流体方法分析

研究非接触水下爆炸中板结构厚度和密度对冲击载荷和空化演变的影响.将近期发展的修正的虚拟流体方法推广应用于处理可压缩流体与弹性板结构的非线性相互作用.研究发现,假设结构不发生断裂破坏,较小的板厚度或密度可以减弱爆炸波对结构的冲击,冲击载荷随着厚度或密度的增大非线性地趋向于固壁边界下的结果.而且较小的板厚度或密度可以促使空化较早形成,产生较大的空化区,并推迟和减弱空化破裂对结构的二次冲击.     

一种基于多矩的有限体积浸入边界法

基于多矩VSIAM3格式及浸入边界法,提出一套在复杂计算区域内求解不可压缩流动的数值格式.不可压N-S方程使用VSIAM3格式进行离散,引入浸入边界法处理复杂、移动边界,使用虚拟网格方法计算动量方程修正项,同时还考虑了对连续方程的修正.使用标准算例对数值模式进行验证.     

Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem

Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas–water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve “third-order accuracy” in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most “first-order accuracy” for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint.     

虚拟流体方法中界面处Riemann问题定义方式的改进

对RGFM中定义Riemann问题的方式进行改进,取距离界面适当远处的插值点处的状态作为Riemann问题的初值.并用数值算例对改进前后的RGFM进行比较.     

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.     

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.     

A fixed-mesh method for incompressible flow–structure systems with finite solid deformations

A fixed-mesh algorithm is proposed for simulating flow–structure interactions such as those occurring in biological systems, in which both the fluid and solid are incompressible and the solid deformations are large. Several of the well-known difficulties in simulating such flow–structure interactions are avoided by formulating a single set of equations of motion on a fixed Eulerian mesh. The solid’s deformation is tracked to compute elastic stresses by an overlapping Lagrangian mesh. In this way, the flow–structure interaction is formulated as a distributed body force and singular surface force acting on an otherwise purely fluid system. These forces, which depend on the solid elastic stress distribution, are computed on the Lagrangian mesh by a standard finite-element method and then transferred to the fixed Eulerian mesh, where the joint momentum and continuity equations are solved by a finite-difference method. The constitutive model for the solid can be quite general. For the force transfer, standard immersed-boundary and immersed-interface methods can be used and are demonstrated. We have also developed and demonstrated a new projection method that unifies the transfer of the surface and body forces in a way that exactly conserves momentum; the interface is still effectively sharp for this approach. The spatial convergence of the method is observed to be between first- and second-order, as in most immersed-boundary methods for membrane flows. The algorithm is demonstrated by the simulations of an advected elastic disk, a flexible leaflet in an oscillating flow, and a model of a swimming jellyfish.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

On Symplectic and Multisymplectic Structures and Their Discrete Versions in Lagrangian Formalism

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively.We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire grometric object and the noncommutative differential calculus on regular lattice.In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations,the Euler-Lagrange cohomological concepts and content in the configuration space are employed.     

二维GEL耦合方法的研究及对爆炸容器的数值模拟

 将以Euler方法为基础的MF PPM（Piecewise-Parabolic Method）程序和以Lagrange方法为基础的DEFEL（2-D Finite Elements Code,二维流体弹塑性动力有限元）程序,根据压力和法向速度连续准则进行耦合,发展了基于Level Set的GEL（Ghost-Fluid Euler-Lagrange）方法。该方法在处理大变形流场与小变形结构以及复杂流动与多物体相互作用等问题具有优越性。通过二维算例的计算结果与文献比较,检验了GEL方法和耦合程序的正确性,并对球形和椭球封头的爆炸容器进行了数值模拟,通过与实验结果的比较分析,表明本研究程序可以比较好地处理内爆引起的壳体流固耦合问题。