基于level set的Eulerian-Lagrangian耦合方法及其应用

提出了一种基于水平集的Eulerian-Lagrangian耦合方法,其中Lagrangian方法采用相容显式有限元拉氏方法,Eulerian方法采用基于近似Riemann解的有限体积Eulerian方法,多介质界面处理采用新的水平集和Ghost方法计算. 给出了若干数值算例,包括激波管问题以及金属和气体的运动界面及其大变形问题,并分别与精确解和相容显式有限元拉氏方法的计算结果进行了对比. 数值结果表明,该方法计算结果正确,精度较高,能够准确捕捉物质界面,适用于处理大变形问题.      

近似黎曼解对高超声速气动热计算的影响研究

高超声速流场计算一般采用TVD型格式,这些格式中,大多采用了不同形式的近似黎曼解. 通过分析和数值验证,论述了激波捕捉格式中近似黎曼解的耗散性质,说明其对高超声速热流计算的影响. 数值实验证明,采用低耗散格式可大大提高热流计算精度,降低热流计算对网格的依赖程度,从而获得精确的热流数值解.      

Navier-Stokes方程间断Galerkin有限元方法研究

通过引入全局提升算子和局部提升算子,发展了求解Navier-Stokes方程的间断Galerkin(discontinuousGalerkin,DG)有限元方法的一般框架,并在此框架下给出了几种典型黏性离散格式的具体表达形式.对局部提升算子的求解给出了详细的计算步骤.同时还给出了一种简单有效的计算方法来对物面边界进行高阶近似.为了能够对NS方程进行精度测试,采用对原始系统添加源项的方法构造精确解.二维Euler和NS系统的精度测试表明该方法达到了DG方法的理论精度.二维圆柱无黏绕流的计算结果表明关于物面边界的高阶近似方法能够保持DG方法原有的精度.卡门涡街数值模拟则进一步验证了该方法的正确性并且显示出DG方法较高的计算精度和分辨率.     

高精度边界格式的研究

利用有精确解的Ｒｉｎｇｌｅｂ流动，构造了对流场数值解精度进行检验的“Ｒｉｎｇｌｅｂ机器”．重点讨论了边界格式对流场数值解的影响及高精度边界格式的建立．计算表明，在场内应用二阶精度格式情况下，采用二阶精度的边界格式所得到的流场解精度将大大高于采用一阶边界格式所得到的精度．为提高流场解的精度，不仅需要高精度的边界格式，还必须注意边界格式与场内格式的匹配．计算还表明，采用特征线修正的方法能有效地提高边界处理的精度     

环形激波绕射、反射和聚焦流场的间断有限元模拟

采用间断有限元方法对环形激波在圆柱形激波管内绕射、反射和聚焦流场进行了数值模拟。将二维守恒方程的间断有限元方法发展到轴对称Euler方程,并对环形激波绕后台阶流动进行了数值计算。计算结果表明,采用间断有限元方法能够有效地捕捉运动激波在圆柱形激波管内传播的复杂流场结构;在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力,在聚焦点附近不会产生振荡或抹平间断现象。     

用隐式方法和WENO格式计算悬停旋翼跨声速无粘流场

寻找一种能够准确计算以涡为主要特征的复杂流场和克服尾迹耗散问题的数值方法,一直是旋翼空气动力学研究的热点和难点。本文发展了一种基于高阶迎风格式计算悬停旋翼无粘流场的隐式数值方法。无粘通量采用Roe通量差分分裂格式,为提高精度,使用五阶WENO格式进行左右状态插值,并与MUSCL插值进行比较。为提高收敛到定常解的效率,时间推进采用LU-SGS隐式方法。用该方法对一跨声速悬停旋翼无粘流场进行了数值计算,数值结果表明WENO-Roe的激波分辨率高于MUSCL-Roe,体现出了格式精度的提高对计算结果的改善,LU-SGS隐式方法的计算效率比5步Runge-Kutta显式方法的高。     

Level set方法在自适应Cartesian网格上的应用

采用基于自适应Cartesian网格的level set方法对多介质流动问题进行数值模拟。采用基于四叉树的方法来生成自适应Cartesian网格。采用有限体积法求解Euler方程,控制面通量的计算采用HLLC（Hartern, Lax, van Leer, Contact）近似黎曼解方法。level set方程也采用有限体积法求解,采用Lax-Friedchs方法计算通量,通过窄带方法来减少计算量,界面的处理采用ghost fluid方法。Runge-Kutta显式时间推进,时间、空间都是二阶精度。对两种不同比热比介质激波管问题进行数值模拟,其结果和精确解吻合;对空气/氦气泡相互作用等问题进行模拟,取得令人满意的结果。     

Euler-Lagrange耦合计算的GEL方法

研究了一种Euler-Lagrange耦合数值方法ghost-fluid Euler-Lagrange(GEL)方法,编写了GEL二维计算程序。其中Euler流场计算采用以SCB格式编制的二阶计算程序,Lagrange域计算采用DEFEL二维动力有限元程序。通过一维黎曼问题的计算结果与高精度PPM方法进行的比较,以及二维移动边界cylinder lift-off problem的计算结果与文献的对比,验证了GEL方法和本文程序的正确性。     

进化算法与确定性算法在优化控制问题中的收敛性对比

对比了进化算法(基因算法)与确定性算法(共轭梯度法)在优化控制问题中的优化效率．两种方法都与分散武优化策略-Nash对策进行了结合，并成功地应用于优化控制问题。计算模型采用绕NACA0012翼型的位流流场．区域分裂技术的引用使得全局流场被分裂为多个带有重叠区的子流场，使用4种不同的方法进行当地流场解的耦合，这些算法可以通过当地的流场解求得全局流场解。数值计算结果的对比表明．进化算法可以得到与共轭梯度法相同的计算结果．并且进化算法的不依赖梯度信息的特性使其在复杂问题及非线性问题中具有广泛的应用前景。     

陷落腔的流场数值计算研究

本文对有限分析解法的近似计算方法及其对计算精度的影响进行了数值计算和分析讨论；然后采用有限分析解法，对前、后壁壁缘高度不同的三种腔内流场运动发展过程及腔口剪切层运动情况作了数值计算，得到的腔口剪切层上腔口随边相互作用情况与对应腔的流场显示实验结果进行了比较，两者一致，计算结果表明，采用本文发展的近似方法计算可靠，可以较大地提高计算效率。     

On the numerical convergence and performance of different spatial discretization techniques for transient elastodynamic wave propagation problems

We present a systematic investigation of several discretization approaches for transient elastodynamic wave propagation problems. This comparison includes a Finite Difference, a Finite Volume, a Finite Element, a Spectral Element and the Scaled Boundary Finite Element Method. Numerical examples are given for simple geometries with normalized parameters, for heterogeneous materials as well as for structures with arbitrarily shaped material interfaces. General conclusions regarding the accuracy of the methods are presented. Based on the essential numerical examples an expansion of the results to a wide range of problems and thus to numerous fields of application is possible.     

流体与结构相互作用问题的FE-SPH耦合模拟

应用有限元(FE)-光滑粒子流体动力学(SPH)耦合法模拟了具有自由表面的不可压流体与结构的相互作用问题.流体和结构分别采用SPH法和有限元法同时求解,两者在交界面处的相互作用通过接触算法进行处理.为了避免隐式计算压力,通过引入人工压缩率,将不可压流体近似为人工可压缩流体.采用FE-SPH耦合法对弹性板在随时间变化的水压作用下的变形以及倒塌水柱冲击弹性结构两个问题进行了模拟.模拟结果与实验结果以及其他已有数值结果符合良好,说明FE-SPH耦合法用于流体与结构相互作用问题的模拟是可行和有效的.     

ALE有限元方法研究及应用

将ALE（Arbitrary Lagrangian-Eulerian)描述引入到有限元方法中， 从而使有限元方法在解决大范围自由移动边界问题，特别是液体大幅晃动、流－固耦合、加工成型、接触、大变形等问题时获得极大成功。本文综述了ALE有限元方法的研究现状以及在不同领域的应用，并对 今后的研究及应用做了展望。     

A numerical comparison of two different approximations of the error in a meshless method

Meshless methods still require considerable improvement before they equal the prominence of finite elements in computer science and engineering. In the Element Free Galerkin (EFG) method, it is obviously important that the error of approximation should be estimated, as it is in the Finite Element Method (FEM).In this paper we compare two different procedures to approximate the a posteriori error for the EFG method, both procedures are recovery based errors. The performance of the two different approximations of the error is illustrated by analysing different examples for 2-D potential and elasticity problems with known analytical solutions, using regular and irregular clouds of points. For irregular clouds of points, it is recommended to use smooth transition of nodes, thus creating areas of decreasing nodal densities.     

透平叶栅跨音速流动计算中的新型有限元法

将Ｔａｙｌｏｒ－Ｇａｌｅｒｋｉｎ有限元法和多级有限元的思想结合起来，构成了在收敛速度和稳定性两方面均较好的新型有限元算法：多级广义有限元。利用这一方法，分别基于Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和Ｅｕｌｅｒ方程，研究了透平跨音速叶栅无粘流动和粘性流动，并将计算结果与实验结果作了比较。计算结果表明，本方法是透平机械内部跨音速流动计算的强有力的手段。     

固体力学应力分析中的有限域法

本文给出了用有限域法进行了和学应力分析的一般原理，并与目前广泛采用的有限元不做了比较。文中的研究表明：有限域法与有限元法极为相似，前者使用单位位移加权，后者从虚位移原理出发；两种方法的实施过程也有共同点，它们都进行网络部分及逼近。     

A regular boundary element method for fluid flow

The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.¹ In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non-conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non-conforming boundary elements for two-dimensional inviscid laminar fluid flow problems having regular and singular solutions.     

Fluctuation Splitting Schemes for the Compressible and Incompressible Euler and Navier-Stokes Equations

Introduced in the late eighties by Roe, fluctuation splitting (or residual distribution) schemes have recently emerged as a viable alternative to Finite Volume and Finite Element methods for PDE based, fluid dynamics simulations using unstructured meshes. Their application to the numerical approximation of the compressible and incompressible Euler and Navier-Stokes equations is described, emphasizing low Mach number and incompressible applications. The advantages provided by time-preconditioning techniques are discussed and details of the implementation are given.     

Dealing with extremely large deformation by Nearest-Nodes FEM with algorithm for updating element connectivity

In the recently developed Nearest-Nodes Finite Element Method (NN-FEM), elements are mainly used for numerical integration; while shape functions are constructed in a similar way as in meshless methods. Based on this strategy, NN-FEM inherits major merits from both the classical Finite Element Method and meshless methods. One of them is that NN-FEM is nearly not affected by element distortion. So NN-FEM is more efficient than the classical FEM on dealing with large deformation problems. Nevertheless, NN-FEM still has a requirement on finite element meshes, that is, elements in a mesh are required not to overlap or penetrate to each other, to avoid difficulty in numerical integration. To eliminate overlapped elements, NN-FEM is supplemented with an algorithm for updating element connectivity. With this supplement, NN-FEM is able to deal with extremely large deformation. In updating element connectivity, element nodes are kept not changed and all information associated with nodes are not touched. Therefore, there is no need to transfer solution data, and error introduced by solution transfer is avoided.     

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations.