Calculation of a hypersonic flow over bodies of complex configuration on unstructured tetrahedral meshes using the AUSM scheme

An approach to solving the three-dimensional Navier-Stokes equations on tetrahedral computational meshes on the basis of splitting by physical processes is considered. An algorithm of numerical implementation of the suggested method for solving three-dimensional problems of aerothermodynamics of freeconfiguration hypersonic flying vehicles (HFVs) is elaborated. The finite-volume method is applied to approximate the gasdynamics equations. The fluxes on the boundaries of the computational elements are calculated using the AUSM scheme. A computer code aimed at numerical simulation of the three-dimensional aerothermodynamics of the structural elements and the integral configurations of the HFV on the basis of the Euler and Navier-Stokes equations is developed. The algorithms developed are tested using the benchmark problem of a viscous hypersonic perfect gas flow over a sphere. The results of comparison of the computational data found using the suggested approach on the unstructured different-size meshes with the numerical solutions found on structured grids with application of the computational code NERAT are presented. The computational model of the flow of viscous and inviscid perfect gas developed is applied to investigate the aerothermodynamics of a model of an unmanned experimental aircraft X-43 of complex configuration.     

基于双三次曲面片的三维接触面光滑方法

该文提出了一种基于双三次曲面片的适用于结构和非结构网格的三维接触面光滑方法。此光滑方法中,仅仅依靠网格节点坐标和法向定义了双三次曲面片,并由此构造出曲面片之间切平面连续,曲面片内C1连续的三维光滑接触面。在构造的光滑接触面上,设计了接触搜索方法用以确定接触发生的位置,并且依据罚函数接触算法,计算节点的穿透深度和接触作用力。算例结果显示光滑接触面确保了滑动节点的接触力的连续变化,提高了计算的收敛性。     

A gradient smoothing method (GSM) with directional correction for solid mechanics problems

A novel gradient smoothing method (GSM) is proposed in this paper, in which a gradient smoothing together with a directional derivative technique is adopted to develop the first- and second-order derivative approximations for a node of interest by systematically computing weights for a set of field nodes surrounding. A simple collocation procedure is then applied to the governing strong-from of system equations at each node scattered in the problem domain using the approximated derivatives. In contrast with the conventional finite difference and generalized finite difference methods with topological restrictions, the GSM can be easily applied to arbitrarily irregular meshes for complex geometry. Several numerical examples are presented to demonstrate the computational accuracy and stability of the GSM for solid mechanics problems with regular and irregular nodes. The GSM is examined in detail by comparison with other established numerical approaches such as the finite element method, producing convincing results.     

Variational generation of prismatic boundary‐layer meshes for biomedical computing

Boundary‐layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary‐layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary‐layer meshes for such complex geometries. Our method computes a feature size of the geometry, adapts the surface mesh based on the feature size, and then generates the prismatic layers by propagating the triangulated surface using the face‐offsetting method. We derive a new variational method to optimize the prismatic layers to improve the triangle shapes and edge orthogonality of the prismatic elements and also introduce simple and effective measures to guarantee the validity of the mesh. Coupled with a high‐quality tetrahedral mesh generator for the interior of the domain, our method generates high‐quality hybrid meshes for accurate and efficient numerical simulations. We present comparative study to demonstrate the robustness and quality of our method for complex biomedical geometries. Copyright © 2009 John Wiley & Sons, Ltd.     

Discrete dipole moment method for calculation of the T matrix for nonspherical particles

A computational method, based on a moment solution to the discrete dipole approximation (DDA) interaction equations, is proposed for calculation of the T matrix of arbitrary-shaped particles. It is shown that the method will automatically provide the conservation-of-energy and origin-invariance properties required of the T matrix. Furthermore, the method is significantly faster than a T-matrix calculation by direct inversion of the DDA equations. Because the method retains the dipole lattice representation of the particle, it can be applied with relative ease to particles with irregular shapes-although in the same respect it will not automatically simplify for axisymmetric particles. Calculations of scattering matrix distributions, in fixed and random orientations, are made for tetrahedron, cylindrical, and prolate spheroid particle shapes and compared with DDA and extended boundary condition method results.     

The generation of arbitrary order curved meshes for 3D finite element analysis

A procedure for generating curved meshes, suitable for high-order finite element analysis, is described. The strategy adopted is based upon curving a generated initial mesh with planar edges and faces by using a linear elasticity analogy. The analogy employs boundary loads that ensure that nodes representing curved boundaries lie on the true surface. Several examples, in both two and three dimensions, illustrate the performance of the proposed approach, with the quality of the generated meshes being analysed in terms of a distortion measure. The examples chosen involve geometries of particular interest to the computational fluid dynamics community, including anisotropic meshes for complex three dimensional configurations.     

Hierarchical tree‐based finite element mesh generation

Hierarchical grid generation and its use as a basis for finite element mesh generation are considered in this paper. The hierarchical grids are generated by recursive subdivision using quadtrees in two dimensions and octrees in three dimensions. A numbering system for efficient storage of the quadtree grid information is examined, tree traversal techniques are devised for neighbour finding, and accurate boundary representation is considered. It is found that hierarchical grids are straightforward to generate from sets of seeding points which lie along domain boundaries. Quadtree grids are triangularized to provide finite element meshes in two dimensions. Three‐dimensional tetrahedral meshes are generated from octree grids. The meshes can be generated automatically to model complicated geometries with highly irregular boundaries and can be adapted readily at moving boundaries. Examples are given of two‐ and three‐dimensional hierarchical tree‐based finite element meshes and their application to modelling free surface waves. Copyright © 1999 John Wiley & Sons, Ltd.     

Application of transmission-line modelling (TLM) to thermal diffusion in bodies of complex geometry

The use of the TLM method for modelling thermal diffusion in bodies of complex geometries is described. Both regular and irregular orthogonal meshes are used. Results are compared with those obtained using finite element analysis.     

A DEM-based method for predicting the wear evolution of structural boundary composed of spherical boundary elements

In the discrete element method (DEM) simulation for wear prediction, structural boundary is now represented extensively by triangular meshes with high resolution, which brings a huge computational cost. A DEM-based method for predicting the wear evolution of structural boundary has been developed for computational efficiency. The structural boundary subjected to wear is represented by the spherical boundary elements in the DEM simulation in combination with the inside triangles and fitting curved surface in wear prediction. Wear prediction is performed through a series of evolution steps. In each evolution step, the collision energies by particles at structural boundary are collected via the DEM simulation and assigned to the boundary elements. Then, the volume losses of structural boundary are predicted across each relevant boundary element. Finally, the new geometry of structural boundary in response to wear is described by moving the boundary elements along the depths of wear individually. Through converting the contact detection between structural boundary and particles into between spherical boundary elements and particles, our method greatly reduces the computational cost in the DEM simulation. Through two numerical tests, our method has been verified to be an efficient and accurate method for the wear prediction of structural boundaries with different resolutions.     

Finite difference energy techniques for arbitrary meshes applied to linear plate problems

A new energy based finite difference analytical technique is introduced. The method incorporates certain energy concepts and the ability to use arbitrary, irregular meshes within the framework of the Finite Difference Method. This formulation reduces any governing partial differential equations to a set of difference equations containing partial derivatives up to and including the second order. Further, certain strong similarities with the popular Finite Element Method are shown and the ability to solve problems with irregular boundaries is discussed. To demonstrate the Finite Difference Energy Method several plate bending problems are solved.     

A 3D contact smoothing method using Gregory patches

In this work, a method is developed for smoothing three‐dimensional contact surfaces. The method can be applied to both regular and irregular meshes. The algorithm employs Gregory patches to interpolate finite element nodes and provide tangent plane continuity between adjacent patches. The resulting surface interpolation is used to calculate gaps and contact forces, in a variationally consistent way, such that contact forces due to normal and frictional contact vary smoothly as slave nodes transition from one patch to the next. This eliminates the ‘chatter’ which typically occurs in a standard contact algorithm when a slave node is situated near a master facet edge. The elimination of this chatter provides a significant improvement in convergence behaviour, which is illustrated by a number of numerical examples. Furthermore, smoothed surfaces also provide a more accurate representation of the actual surface, such that resulting stresses and forces can be more accurately computed with coarse meshes in many problems. This fact is also demonstrated by the numerical examples. Published in 2002 by John Wiley & Sons, Ltd.     

A geometrically non-linear tensorial formulation of a skewed quadrilateral thin shell finite element

A 48-degree-of-freedom (d.o.f.) skewed quadrilateral thin shell finite element, including the effect of geometrical non-linearity, is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures. The element surface is described by a variable-order polynomial in curvilinear co-ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co-ordinates. The directions of the curvilinear co-ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element. In the present case of a skewed quadrilateral with non-orthogonal curvilinear coordinates, the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish, such as in the case of orthogonal co-ordinates. The tensor form is used in the setup of the shape functions, geometric derivatives, stiffness matrix and computer code. This allows for the treatment of shells with irregular shapes and variable curvatures. To evaluate the efficiency and accuracy of this formulation, a systematic list of examples is chosen: (i) linear and non-linear static analysis of square and rhombic plates, cylindrical and spherical shells; (ii) linear vibrations of trapezoidal flat and curved plates; (iii) large amplitude vibrations of a rhombic plate. For the square plate and cylindrical and spherical shell, shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element. All results are compared with alternative available solutions including those obtained using regular rectangular meshes. Pinched thin cylindrical and spherical shells are studied using different skewed meshes and various Gauss integration meshes, and no membrane locking phenomenon is observed.     

强化有限元的考虑界面滑移的组合梁数值模拟

该文针对组合梁结构连接界面的非线性效应,采用物理区域与单元网格相独立的策略,并引入无厚度界面单元模拟界面的非连续变形,建立了基于强化有限元的考虑界面滑移的组合梁分析模型。该文所采用的物理区域与单元网格相独立的强化有限元,数学单元和物理单元在空间上重合不再是必要条件,可以根据物理单元力学描述的需要选择数学单元的大小和形状。同时一个单元内可以分成多个区域,各分区可以是不同的材料,可以具有不同的几何形状,可以具有不同的受力特点,如板、梁等,从而可以大大减少复杂结构的网格数量。该文方法可以快速便捷得到剪切连接件抗剪刚度从零变化到无穷大时所对应的挠度、界面滑移以及截面应力的变化,可以直观地确定出抗剪刚度能够充分发挥作用的区间,为实际工程设计中确定经济合理的抗剪刚度提供依据。该文方法计算效率高,可以适用于实际工程复杂变截面及空间结构的计算分析,尤其是规模庞大、受力分析繁琐的桥梁结构。     

Numerical simulation of the gas flow in a circuit-breaker

A computational methodology for the solution of unsteady two-dimensional/axisymmetric Euler equations within geometries with moving boundaries is presented. The flow simulation is carried out by applying a finite-volume method which makes use of a Lagrangian-Eulerian version of Roe's approximate Riemann solver. The domain discretization is handled via unstructured triangular grids. Grid adaptation is applied on the basis of geometric and physical requirements. The importance of the implicit treatment of the space conservation laws, based on geometric analysis, is evoked. The procedure for reconstructing Roe's method for moving meshes is described and validated. Finally, the ability of the method for the prediction of the transient flow in a circuit-breaker during its opening phase is illustrated.     

A locally analytic technique applied to grid generation by elliptic equations

One technique for obtaining grids for irregular geometries is to solve sets of elliptic partial differential equations. The solution of the partial differential equations yields a grid which discretizes the physical solution domain and also a transformation for the irregular physical domain to a regular computational domain. Expressing the governing equation of interest in the computational domain requires the derivatives of the physical to computational domain transformation, i.e., the metrics. These metrics are typically determined by numerical differentiation, which is a potential source of error. The locally analytic method uses the analytic solution of the locally linearized equation to develop numerical stencils. Thus, the locally analytic method allows numerical differentiation with no loss of accuracy. In this paper, the locally analytic method is applied to the solution of the Poisson and Brackbill–Saltzman equations. Comparison with an exact solution shows the locally analytic method to be more accurate than the finite difference method, both in solving the partial differential equation and evaluating the metrics. However, it is more computationally expensive.     

Finite cover method with mortar elements for elastoplasticity problems

Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.     

Discrete transfinite mappings for the description and meshing of three-dimensional surfaces using interactive computer graphics

A system for describing three-dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real-time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are described.     

A method to model realistic particle shape and inertia in DEM

A simple and fast original method to create irregular particle shapes for the discrete element method using overlapping spheres is described. The effects of its parameters on the resolution of the particle shape are discussed. Overlapping spheres induce a non-uniform density inside the particle leading to incorrect moments of inertia and therefore rotational behaviour. A simple method to reduce the error in the principal moments of inertia which acts on the individual densities of the spheres is also described. The pertinence of the density correction is illustrated by the case of free falling ballast particles forming a heap on a flat surface. In addition to improve behaviour, the correction reduces also computational time. The model is then used to analyse the interaction between ballast and geogrid by simulating pull-out tests. The pulling force results show that the model apprehends better the ballast geogrid interlocking than models with simple representation of the shape of the particles. It points out the importance of modelling accurately the shape of particles in discrete element simulations.