Adaptive tetrahedral meshing in free-surface flow

An efficient finite element mesh generation methodology based on μCT images of multi-layer woven composites

Truncation error expressions for 1D and 2D Burgers’ equations are derived in generalized coordinates. Examination of these truncation error expressions provides insight into the effects of mesh quality (mesh stretching in 1D and mesh stretching, skewness, aspect ratio and curvature in 2D) on the discretization error. For a 1D model function, mesh adaption based upon function equidistribution is explored with different relocation techniques. For 1D and 2D Burgers’ equation, mesh adaption is performed with different adaption monitors based upon truncation error and solution features. The results for two different Reynolds number are presented and discussed.

formula omitted]MST: A robust unified algorithm for quadrilateral mesh adaptation in 2D and 3D

Effect of Mesh Size on Calculation of Strain Non-uniformity Index in Drawn Sheet Metal Parts

Carbon fiber composites as pantograph slide materials are in the development stage, in which copper is the conductive phase, and the addition form and size need to be designed. Herein, the effects of the copper morphology, the size of the copper mesh on the performance, and the influence of the contact mode between the sliding plate and bracket on the temperature rise were compared and analyzed. The resistivity is 11.2 μΩ·m with the addition of 20 wt% copper mesh, a relative reduction of 91.77%. Importantly, the impact strength is increased by 14.19%, and the wear is reduced by 13.21%; hence, the copper mesh laid in layers is the ideal structure. Further study of the distribution and quality of the copper mesh shows that the resistivity is related only to the quality of the copper mesh; in addition, the number of layers of the copper mesh cannot exceed 16, and it is determined that the best type of copper mesh is 5#. Notably, the performance can be improved by appropriately reducing the thickness of the copper mesh and increasing the aperture while the sliding plate and the bracket are connected by copper mesh with conductive adhesive, which has the slowest heating rate of 2.27 °C/min and the smallest resistance. Therefore, the influence of copper content and distribution on the electrical conductivity are systematically investigated, and the mechanical properties and electrical conductivity are optimized through the design of the laminate structure of the compound material.

<p>A density control based adaptive hexahedral mesh generation algorithm for three dimensional models is presented in this paper. The first step of this algorithm is to identify the characteristic boundary of the solid model which needs to be meshed. Secondly, the refinement fields are constructed and modified according to the conformal refinement templates, and used as a metric to generate an initial grid structure. Thirdly, a jagged core mesh is generated by removing all the elements in the exterior of the solid model. Fourthly, all of the surface nodes of the jagged core mesh are matching to the surfaces of the model through a node projection process. Finally, the mesh quality such as topology and shape is improved by using corresponding optimization techniques.</p>

A fuzzy logic knowledge-based approach, FUZZYMESH, for finite element mesh generation and analysis is presented. The proposed approach initiates the adaptive process with a high quality initial mesh that is more refined around the critical points/regions in the problem domain. In order to create high quality initial meshes, the heuristic knowledge, past experience, common sense, and ad hoc methods of finite element specialists are incorporated into the knowledge base of the fuzzy system. Using the linguistic variable concept and approximate reasoning techniques, the fuzzy system makes expert decisions about the initial mesh design by considering the geometric information, as well as the boundary and loading conditions. The decision process includes the determination of priority of critical points/regions and the prediction of mesh sizes for them. According to the mesh size information, a near-optimal initial mesh is created with an automatic mesh generator that is based on the advancing front mesh generation technique. The performance of the proposed approach was measured and evaluated in terms of efficiency and accuracy. The evaluation included comparison between the results of a code based on the proposed fuzzy logic knowledge-based approach, FUZZYMESH, and the conventional approach, which starts the finite element analysis with different meshes, by solving various problems. The global as well as local errors of different solutions were examined and compared. The CPU times for different approaches to achieve a particular accuracy were also measured and compared. The results showed that due to better quality of initial meshes, FUZZYMESH results in lower levels and more accurate error estimates. In turn, the proposed approach is able to solve the problem with a more accurate solution at less cost.

Combining improvement and refinement techniques: 2D Delaunay mesh adaptation under domain changes

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

A priori mesh quality metric error analysis applied to a high-order finite element method

We present a novel algorithm for adaptive triangular mesh coarsening. The algorithm has two stages. First, the input triangular mesh is refined by iteratively applying the adaptive subdivision operator that performs a so-called red-green split. Second, the refined mesh is simplified by a clustering algorithm based on centroidal Voronoi tessellations (CVTs). The accuracy and good quality of the output triangular mesh are achieved by combining adaptive subdivision and the CVTs technique. Test results showed the mesh coarsening scheme to be robust and effective. Examples are shown that validate the method.

Algebraic mesh quality metrics for unstructured initial meshes

Regarding mesh convergence studies, which report conclusions on the mesh quality in reference to some problem characteristic, Ko et al. (2011) relate the required panel size to depend on the incident wave length, and so does DNV (2010). The latter gives a set of general directives regarding the panels: diagonal length less than 1/6 of the shortest wave length analysed; refined mesh in the areas of abrupt geometrical change; and increased refinement of the mesh in the vicinity of the waterline. Faltinsen (1994) also emphasizes the nuclear importance of proper panel distribution around the intersection of the hull with the waterline and points to a wave length divisor as the value of reference. Application of element size and distribution directives in an automatic way, through mesh generation or modification, has been proposed by several authors. One of the most recent algorithms is the one by Rodrigues and Guedes Soares (2014) where a new adaptive quadrilateral type mesh based solution, to be applied in seakeeping problems, is presented, together with an extensive review on the subject.

Freeform surface models are conventionally used to model sheet metal components, such as automobile body parts. Finite element meshes generated automatically for such models have poor quality around small detailed features. Manual correction of the mesh is extremely tedious. An approach presently receiving attention in industry aims to alleviate this problem by automatically simplifying these features in the surface model such that an acceptable mesh is automatically generated. Simplification involves recognition of the feature and modification of its geometry or complete suppression of the feature. Since features such as holes, notches, etc. are punched after the basic shape has been formed, such a simplification will also help in the modelling of forming dies and molds. The ability to detect features will also allow part comparison and classification in surface models. This paper proposes techniques to directly query the CAD data structure to recognize and suppress two basic features, viz. holes and fillets in freeform surface models. It further demonstrates how these techniques can be extended to suppress compound features that are composed of a combination of basic features. Results of a software implementation for the same are discussed with suitable examples and the improvement in mesh quality is demonstrated.

The ban of lead in electronics solder by EU directives results in the technological challenge to develop lead-free alternatives with comparable life span and processing properties. Numerical simulations of the microstructure evolution may contribute to identify promising candidates and thus focus the immense experimental effort. Aim of this work is on the one hand to develop a numerical framework for the efficient and robust simulation of the microstructure evolution in binary alloys combining adaptive finite element methods with fast solvers for the Cahn-Hilliard model. On the other hand we will extend the existing fast solvers for the discrete scalar Cahn-Hilliard equation to the vector-valued case. After some preliminary remarks on phase diagrams, phase separation, and phasefield models in Chapter 1 we will firstly discuss anisotropic Allen-Cahn equations in Chapter 2. Alle-Cahn-like problems arise as subproblems in the Nonsmooth Schur-Newton (NSNMG) method for Cahn- Hilliard equations in Chapters 3 and 4. Here we prove existence and uniqueness of solutions to the anisotropic Allen-Cahn equation with logarithmic potential using the theory of maximal monotone operators. For the numerical solution we introduce an adaptive spatial mesh refinement cycle for evolution problems and several variants of implicit Euler time discretization. We prove stability for the latter and numerical experiments conclude the chapter. Chapter 3 combines existing and newly developed numerical tools to a simulation software for microstructure evolution in binary alloys. Key ingredients are the adaptive mesh refinement cycle of Chapter 2, the NSNMG solver, a quantification algorithm for measuring "coarseness" of microstructures and a quotient space multigrid method for indefinite problems. An application of this software to simulate the microstructure evolution in a eutectic AgCu alloy shows only marginal impact of elastic stresses on coarsening in the setting considered; while the use of a smooth interpolant of the logarithmic potential affects the coarsening dynamics considerably. In the final chapter we consider the multicomponent Cahn-Hilliard equation and derive a unified formulation for the discrete problems which allows a direct application of the NSNMG method. Existence and uniqueness of discrete solution are proved and numerical examples illustrate the robustness of the scheme with respect to temperature, mesh size, and number of components.