Mesh Regeneration Research Articles

The performance of a high-frequency thermoacoustic-Stirling engine

A thermoacoustic-Stirling engine that operates at 400 Hz with a working fluid of 1-MPa helium is constructed. For proper acoustic phasing in this engine’s regenerator, an acoustic power feedback path exists in the form of an annulus surrounding the regenerator. This feedback path is obtained by suspending an insulated, stainless steel sleeve containing a wire mesh regenerator, which is flanked by two heat exchangers, a short distance from one end of the larger diameter resonator. The ambient heat exchanger is a shell and tube exchanger, while the hot heater consists of nichrome ribbon wound on an aluminum silicate frame. Gedeon streaming is prevented by a diaphragm covering the end of the stainless steel sleeve adjacent to the ambient heat exchanger. A variable acoustic load provides a convenient means of testing this engine at various hot heater temperatures, while operating at different acoustic pressure amplitudes effects the acoustic power generated by the engine. [Work supported by ONR.]

A novel meshing algorithm for dynamic finite element analysis

This paper describes a new algorithm to handle problems in dynamic finite element analysis and run-time simulation, where mesh re-generation or dynamic adjustment is required. Based on a concept called coded box cell (CBC) substitution, this algorithm can be applied to both initial mesh generation and dynamic mesh adjustment along the border zones of multiple primitives that form an entire model. During the initial mesh generation, appropriate labels are assigned to the nodes and the faces of each finite element. These labels are used to facilitate decision-making in dynamic mesh adjustment. A mapping technique is adopted to transform curved surfaces to plain surfaces for the ease of automatic mesh adjustment while still using the same algorithm. The results of a case study show that a finite element mesh can be adjusted dynamically and locally around its border zone; and the algorithm can be utilized effectively to simulate the thermal behavior of a device under real operating conditions.

Implementation of the finite deformation plastic theory Tensor derivative and metal forging simulation

Abstract It has been shown that the traditional small deformation plasticity can be transplanted to the finite deformation plasticity by using the logarithmic strain measure only. In this way the mathematical problem of how to find the derivative of a tensor function arises. In this paper a general method for finding the derivative of a tensor function is proposed. Several metal forging examples are given. During the calculation the mesh regeneration is not even invoked.

Shape optimization of periodic structures

This paper describes a numerical approach to the optimization of effective properties of periodic perforations in an infinite body, in the frameworks of heat conduction and of linear elasticity. We implement a special finite element mesh in order to deal with the periodic nature of the problem. We compute the gradient of the functional to be minimized. We describe the process of mesh deformation and mesh regeneration. We give several numerical examples, some of them having practical relevance.

506 ファジィ制御と局所細分割を用いたアダプティブ 6 面体要素生成

3-D finite element method (FEM) is widely used as an effective numerical simulation technique. Accuracy of FEM is affected by number of freedom and shape of each element. Local mesh refinement technique is used in order to avoid failure of mesh regeneration. Local hexahedral mesh refinement and adaptive technique are very useful for dynamic contact problems, dynamic large-deformation problems and so on. On the other hand, number of freedoms of analyzing model is restricted by computer environment. An export of FEM analysis can create appropriate models for his analysis and computer environment. Therefore we propose an effective adaptation technique for hexahedral mesh using error estimation, fuzzy control and local hexahedral mesh refinement.

Numerical techniques in finite element analysis of eddy current testing problem

Several types of finite element methods have been developed and shown the validity and the effectiveness for eddy current testing (ECT) problem. However, it is difficult to analyze the finite element model including two or more objects whose positions relatively change, such as conductor plate and ECT probe. Furthermore, it takes a large amount of computer resources to compute an accurate finite element model for a natural crack, because of the complex shapes and the narrow gap. In this paper, a superposition method to avoid the finite element mesh regeneration for the relative position change is presented, and the method is applied to the ECT probe with a ferrite core. Furthermore, the finite element model for the natural crack is shown and the model is applied to the ECT problem with the fatigue crack.

An adaptive finite element procedure for solidification problems

An adaptive mesh regeneration procedure for transient solidification problems has been presented in this paper. The method is based on the local minimum and maximum values of second derivatives of velocity and temperature fields. A numerical example of alloy solidification in a square enclosure is presented for demonstration. Extension to more complicated and odd-shaped problems is straight forward.

An automated process for 3D hexahedral mesh regeneration in metal forming

This paper describes the method for automatic remeshing of the distorted hexahedral finite elements and its application in metal forming processes. It first generates a regular mesh inside the bounding box that circumscribes the given volume to be meshed. Secondly extra elements of the regular mesh that lie outside the volume are removed from the regular mesh. Then, the geometric features of the old mesh (i.e. sharp edges and corners nodes) are determined by established criteria and corresponding features of the new mesh are traced down to guarantee geometric consistency between the two meshes. After that, a Boundary Element Layer (BEL) is constructed to form new hex mesh. By classification of all surface nodes of the regular mesh into face nodes, edge nodes and corner nodes and by the corresponding treatment to different types of surface nodes, the resulted new mesh gives much-improved hex elements that best suit local geometry. Finally a smoothing process is done to reposition the edge nodes, face nodes and internal nodes sequentially before the new mesh is exported for use in continued calculation. The density of the new mesh can be controlled to be adaptive to strain gradient during smoothing.

Development of a grid‐based mesh generation technique and its application to remeshing during the finite element simulation of a metal forming process

An easy and robust grid‐based approach is proposed to construct the fully hexahedral mesh in three‐dimensional case and its application for the mesh regeneration or remeshing during the finite element simulation of a metal forming process is presented to show the validity and effectiveness of the scheme. The proposed scheme enables the construction of the provisional mesh by superimposing the regular cubical grid over the object to be meshed and removing the exterior grid points and cells. Because the constructed provisional mesh has the discrete rugged boundary that is quite different from the boundary geometry of the object to be meshed, the nodes on the boundary of the provisional mesh are projected onto the object boundary. The main disadvantage of the mesh constructed by grid‐based approaches is its severely distorted elements on the boundary owing to the projection of the rugged boundary onto the object boundary. In order to improve the quality of boundary elements, some layers of elements on the boundary surface are constructed and the nodes are repositioned by mesh smoothing. Consequently, the quality of boundary elements is effectively improved.

Automatic remeshing of 2D quadrilateral elements and its application to continuous deformation simulation: part II. applications

Abstract In this paper, the techniques for automatic mesh regeneration of quadrilateral elements, which was developed by Zhu and Gotoh and presented by the same authors in part I of the same titled paper, are integrated with a 2D rigid-plastic FEM program and application examples of the whole system to practical forming processes are given. The first example is the typical axisymmetric compression of a cylinder by a flat-bottomed punch, and the second is an optimized forging process of a door component of an automobile. The remeshing programs developed exhibit good performance during intermediate remeshing in the simulation process, and the deforming behaviour of the metal either in simple compression or in filling into complex die cavities can be simulated smoothly by the present system without human interruption. The results of simulation are given and discussions are made.

H-Adaptive finite element computation of time-harmonic exterior acoustics problems in two dimensions

In this paper we carry out adaptive finite element computations of the Helmholtz equation in two dimensions, in the context of time-harmonic exterior acoustics. The purpose is to demonstrate potentially significant cost savings engendered through adaptivity for propagating solutions at moderate wave numbers ( ka = 2 π, 4 π). The computations are performed on meshes of linear triangles, and are adapted to the solution by locally changing element sizes ( h-refinement). The adaptive procedure involves applying an explicit, residual-based a posteriori error estimator and an h-adaptive strategy, which were derived in a previous paper. The adaptive meshes are then obtained through global mesh regeneration using an advancing front mesh generator. Two different finite element formulations are considered: The Galerkin and Galerkin Least-Squares (GLS) methods. The infinite physical domain is truncated by an artificial exterior boundary, on which a fully coupled Dirichlet-to-Neumann (DtN) boundary condition is applied. Two different problems are computed: Plane wave scattering by a rigid infinite surface (circular and square cross sections), and nonuniform radiation from an infinite circular cylinder. Detailed cost studies with respect to an active column direct solver are performed. For the nonuniform radiation problem, the adaptive mesh is twenty times more cost effective than a uniform mesh (for Galerkin). When coupled with the GLS formulation, the adaptive mesh is forty times more efficient than Galerkin computations on a uniform mesh.

Adaptive solutions for viscoelastic flows

This work describes the implementation of an adaptive procedure for viscoelastic flows. Finite element simulations are conducted using a Taylor-Galerkin/pressure correction scheme. The constitutive equations considered are those for an Oldroyd-B and a Phan-Thien/Tanner model. The adaptive meshing technique is h-refined by grid remeshing, based on a Delaunay procedure. Results are presented for two benchmark problems, namely flow past a sphere in a cylindrical tube and flow in an annular converging tube. It is concluded from the results that the use of an adaptive procedure with mesh regeneration enables an optimized mesh to be devised and a predicted accuracy to be attained.

Airfoil design via transpiration and optimal control theory

In airfoil design, one of the problems of great interest is to find the target airfoil profile to achieve a given target velocity distribution. This problem can be formulated as an optimal control problem, and there are different ways of formulating and solving it numerically [14]. The transpiration technique provides a very powerful tool to simulate airfoil profile geometry movement without the need for mesh regeneration. On the other hand, the least-squares technique proposed in [8] provides a robust and efficient algorithm for solving the full potential equation. Here, these two techniques will be employed to give a new design method. Both the analysis and the design problem are formulated as a single optimal control problem and the conjugate gradient method is applied to solve the problem iteratively.

2D Mesh Generation Scheme for Adaptive Remeshing Process in Finite Element Method

The discretization of a whole domain is a prerequisite process for Finite Element Method (FEM). Since manual mesh generation is tedious, mesh generation schemes have been studied in recent years. In iterative analyses, the geometry of the domain is drastically changed by each iteration. It is known that mesh regeneration eliminates mesh distortion caused by the geometry change, which greatly affects the convergence of the whole analysis. If error control in the analysis is additionally considered in the mesh regeneration, such a process should be adaptive ; adaptive remeshing is required for a reliable solution. There are many mesh generators available, however, most of them require interaction with the user, and thus cannot be used for adaptive remeshing. In this paper, a sophisticated mesh generation scheme for the adaptive remeshing in the 2D FEM is discussed in detail. After comparison with other schemes, it is concluded that our scheme is superior to the others in terms of flexibility and time complexity.

An adaptive Petrov-Galerkin formulation for the compressible Euler and Navier-Stokes equations

In this paper we combine a stable Petrov-Galerkin formulation for the compressible Euler and Navier-Stokes equations with an h-adaptive remeshing refinement, including directional stretching and stretching ratio in the mesh regeneration procedure. The result is an accurate and efficient scheme appropriated to solve problems presenting shocks and boundary-layers.

Refinement of 3D meshes at surface intersections

Refinement of curved boundaries is an important problem in the modelling of solid objects through the use of faceted triangular or quadrilateral elements. Finite element meshes of 3D solids frequently use faceted triangular and quadrilateral elements on their surfaces. Hence several techniques used in geometric modelling have wide ranging applications to finite element modelling. Large numbers of elements are required in finite element analysis in regions where solution variable gradients are high —regions such as corners, surface intersections and surface discontinuities. Creating finite element meshes for analysis can be time consuming, particularly for complex geometries. By employing an adaptive procedure to perform the finite element analysis, the rigorous task of accurately modelling the geometry using finite elements can be simplified. The paper presents an application of previously published work in surface and surface-surface intersection refinement techniques to h-adaptive finite element analysis. The algorithm presented in this paper refines a crude initial mesh on the basis of solution error indicators or other suitable error measures. The refinement procedure strictly maintains the integrity of the geometry by placing newly generated nodes on the true boundary of the solid and also maintains the physical conditions of the problem such as loads and boundary conditions. A geometric and numerical technique is used to refine tetrahedral element meshes in arbitrarily oriented intersecting cylindrical, spherical or conical surfaces. The transformation matrices are computed symbolically and are implemented in the program in order to reduce computational time. Extension of this procedure to surfaces that are other than cylindrical, spherical or conical can be achieved simply by employing an appropriate definition of the surface. The mesh refinement procedure presented in the paper utilizes data structures to store a comprehensive definition of the finite element model and the geometric model at all mesh levels. This allows the mesh density to be improved in any region of the solid, at any mesh level, without a mesh regeneration beinq required. Several examples are presented to show the meshes that are generated by adaptive refinement.

An adaptive finite element algorithm for a two-dimensional stationary Stefan-like problem

An efficient adaptive algorithm is presented for a stationary regularized Stefan problem in 2D. The adaptive criteria relies upon a posteriori estimates based on the residual equation. Since the problem we are studying is a non-linear diffusion-convection problem, these error estimates are relatively crude in the sense that the constant relating the true error to the error indicator is unknown, Thus, instead of trying to build a mesh such that the true error is below a given tolerance, the local error indicator is equidistributed in a way such that the final number of triangles is close to a desired value. At each iteration of the adaptive algorithm, the new triangulation is obtained from the previous one by adding or deleting vertices according to the error indicator and a global mesh regeneration is performed using a Delaunay mesh generator. Numerical experiments for two practical situations show the efficiency and the robustness of our approach.

Aspects of the transpiration model for aerofoil design

AbstractTranspiration is a technique in which extra non‐physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co‐ordinates are adjusted or to find shape corrections in inverse design methods. A first‐order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.

Mesh enrichment against mesh regeneration using quadrilateral elements

AbstractAn adaptive refinement procedure using a new automatic quadrilateral element mesh generator is presented. The performance of the adaptive procedure in achieving a given accuracy with different mesh refinement strategies is compared. It is found that when using bilinear or biquadratic quadrilateral elements refinement strategies of both mesh enrichment and mesh regeneration can lead to a prescribed accuracy being achieved by the Zienkiewicz–Zhu adaptive procedure1 with the optimal rate of convergence. However, fewer mesh refinement steps are needed if the strategy of mesh regeneration is employed with the newly developed automatic quadrilateral element mesh generator2.

Flow in the Stirling Regenerator Characterized in Terms of Complex Admittance Part 1: Theoretical Development

A wire mesh regenerator is studied, with one end closed and the other subject to a harmonic variation of flow. The methods of linear wave analysis are used to determine acomplex input admittance, Y, for the system. Y is the ratio of volume flow to pressure excess for a given frequency, and permits piston face pressure waveform to be determined directly in terms of prescribed velocity waveform. A computational procedure is developed for finding the pressure waveform at the closed end. Computed waveforms are presented and discussed. Energy dissipated per cycle is calculated.