Semi-structured Meshes Research Articles

Electromagnetic force calculation within finite volume framework

ABSTRACT In this research, the comparison of force calculation methods in magnetostatic simulations within a cell-centered finite volume framework is presented. Various procedures for postprocessing of the magnetic vector potential field are laid out to obtain the surface and volume integrals of Maxwell’s stress tensor and the Lorentz force density. Two different magnetostatic problems with multiple operating points were modeled with the AVL FIRETM M. The force results have been verified by comparing them to the Ansys Maxwell and were validated on a benchmark case from a Testing Electromagnetic Analysis Methods (TEAM) workshop. The interpolation of the magnetic flux density on a multi-material interface is presented, and it is used in conjunction with the surface integral of Maxwell’s stress tensor for an efficient global force computation. For all observed cases, the calculated results correspond well to the results found in the literature. It was found that the accuracy of the volume integral of Maxwell’s stress tensor is dependent on the mesh quality and gradient calculation scheme. Employing the semi-structured mesh with Gauss’s gradient scheme results in force discrepancies of less than 3% between the surface and volume integral of Maxwell’s stress tensor. The convergence of the iterative solver is observed to be slower in the case of the materials with permeability jump, where discontinuities between the tangential component of the magnetic flux density and the normal component of the magnetic field intensity occur.

Mesh dependence analysis for simulating unsteady cavitation around a plane convex hydrofoil

The mesh significantly influences the quality of the numerical results in computational fluid dynamics (CFD) problems due to its correlation with turbulence models. In the present paper a structured mesh was generated using Gmsh and two semi-structured meshes were generated using snappyHexMesh to determine the suitable mesh distribution for simulating unsteady cavitation around a plane convex hydrofoil. The numerical simulation was conducted by using the software OpenFOAM with the k-ω SST SAS turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. Besides, the experimental results obtained by the Laboratory for Hydraulic Machines of École Polytechnique Fédérale de Lausanne were used to validate the numerical results. The results showed that both structured and semi-structured meshes predicted the cavitation pattern and the maximum cavity length. The semi-structured mesh with suitable refinement reproduced in detail the dynamic behavior of unsteady cavitation, while the structured mesh efficiently reproduced the phenomenon.

NonInvasive Multigrid For SemiStructured Grids

Multigrid solvers for hierarchical hybrid grids (HHG) have been proposed to promote the efficient utilization of high performance computer architectures. These HHG meshes are constructed by uniformly refining a relatively coarse fully unstructured mesh. While HHG meshes provide some flexibility for unstructured applications, most multigrid calculations can be accomplished using efficient structured grid ideas and kernels. This paper focuses on generalizing the HHG idea so that it is applicable to a broader community of computational scientists, and so that it is easier for existing applications to leverage structured multigrid components. Specifically, we adapt the structured multigrid methodology to significantly more complex semi-structured meshes. Further, we illustrate how mature applications might adopt a semi-structured solver in a relatively non-invasive fashion. To do this, we propose a formal mathematical framework for describing the semi-structured solver. This formalism allows us to precisely define the associated multigrid method and to show its relationship to a more traditional multigrid solver. Additionally, the mathematical framework clarifies the associated software design and implementation. Numerical experiments highlight the relationship of the new solver with classical multigrid. We also demonstrate the generality and potential performance gains associated with this type of semi-structured multigrid.

The development of a computational tool for generation of high quality FE models of pipelines with corrosion defects

Corrosion is one of the most common causes of accidents involving pipelines. Unfortunately, the semi-empirical methods currently available are overly conservative for the assessment of some types of corrosion defects in pipelines. Fortunately, the computational simulations through finite element (FE) method are a very efficient and reliable approach to quantify the remaining strength of corroded pipes. However, the process of computational modeling demands intense manual labor from the engineer, and it is also slow and extremely repetitive, especially in cases of multiple defects. The main purpose of this work was to describe an original methodology for the automatic generation of FE models of pipes with corrosion defects (single or multiple). The model discretization uses semi-structured mesh and specific mesh transitions, which demanded even more manual labor. Also, the computational modeling process needs to be robust and efficient to ensure accuracy without excessive number of degrees of freedom. Thus, the tool allows the pre-configuration of mesh transitions and other parameters related to the mesh refinement. This program, called PIPEFLAW, is built-in as a software extension into the MSC.PATRAN commercial software and is written with Patran Command Language. The PIPEFLAW program has a friendly graphical user interface, which allows the user to provide the main parameters of the pipe and defect (or a series of defects), considering several different configurations and geometries. This paper is focused on the automatic generation of 3D FE models of pipelines with a single or a colony of idealized defects with rectangular or elliptical shapes. As result, some examples of FE pipe models with defects generated automatically by the program are shown and some element shape tests were performed to evaluate the final mesh quality of the FE pipe model. The methodology is validated through the comparison of the internal failure pressure of a pipeline with two rectangular defects, obtained using experimental burst test, manually generated FE models, semi-empirical methods and PIPEFLAW generated model. The developed tools lead to a reduction in the modeling procedure in the case presented from 2 weeks, using non-automatic standard procedure normally used in the industry, to 1 min.

Anisotropic boundary layer mesh generation for immersed complex geometries

This paper proposes a new method to build boundary layer meshes over an immersed complex geometry. It allows to generate an anisotropic semi-structured mesh with a smooth gradation of mesh size from a geometry immersed into an arbitrary coarse domain, while capturing and keeping the interface. The idea is to generate an a priori mesh fitting the geometry boundary layer which is ready for simulations. The mesh size distribution is driven by a levelset distance function and is determined using physical parameters available before the simulation, based on the boundary layer theory. The aspect ratio is then determined knowing the shape of the geometry, and all is applied in a metric tensor field using a gradation thanks to the new multi-levelset method. Then, the mesh generator adapt the initial mesh on the given metric field to create the desired boundary layer mesh.

Optimization of the multigrid-convergence rate on semi-structured meshes by local Fourier analysis

In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother is presented as an efficient choice for regular tetrahedral grids, whereas line and plane relaxations are needed for poorly shaped tetrahedra. A novel partitioning of the Fourier space is proposed to analyze the four-color smoother. Numerical test calculations validate the theoretical predictions. A multigrid method is constructed in a block-wise form, by using different smoothers and different numbers of pre- and post-smoothing steps in each tetrahedron of the coarsest grid of the domain. Some numerical experiments are presented to illustrate the efficiency of this multigrid algorithm.

Automatic decomposition and efficient semi-structured meshing of complex solids

In this paper, a novel approach to automatically sub-divide a complex geometry and apply an efficient mesh is presented. Following the identification and removal of thin-sheet regions from an arbitrary solid using the thick/thin decomposition approach developed by Robinson et al. [1], the technique here employs shape metrics generated using local sizing measures to identify long-slender regions within the thick body. A series of algorithms automatically partition the thick region into a non-manifold assembly of long-slender and complex sub-regions. A structured anisotropic mesh is applied to the thin-sheet and long-slender bodies, and the remaining complex bodies are filled with unstructured isotropic tetrahedra. The resulting semi-structured mesh possesses significantly fewer degrees of freedom than the equivalent unstructured mesh, demonstrating the effectiveness of the approach. The accuracy of the efficient meshes generated for a complex geometry is verified via a study that compares the results of a modal analysis with the results of an equivalent analysis on a dense tetrahedral mesh.

Sweeping of unstructured meshes over generalized extruded volumes

An algorithm for the discretization of general extrudable volumes into semi-structured meshes is presented in this paper. The set of considered extrudable volumes is limited to volumes formed by two opposite topologically identical and geometrically similar cap surfaces, from which one is identified as the source and the other one as the target surface, and by the set of lateral quad-mappable surfaces. The source cap surface is discretized by an appropriate unstructured surface mesh which is projected onto the target cap surface using an affine mapping defined between the parametric spaces of the cap surfaces. This mapping is established by a least-squares fit of boundary nodes on the target surface. The structured quad meshes on lateral surfaces are obtained by transfinite interpolation. The volume interior nodes used to form inner layer of elements are defined by the mapping derived from a least-squares approximation of all boundary nodes. The obtained mesh is then subjected to a specific two-phase smoothing. The capabilities of the proposed algorithm are demonstrated by several examples.

Adaptive boundary layer meshing for viscous flow simulations

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.

MOAB-SD: integrated structured and unstructured mesh representation

Structured and semi-structured (a.k.a. swept or extruded) hexahedral meshes are used in many types of engineering analysis. In finite element analysis, regions of structured and semi-structured mesh are often connected in an unstructured manner, preventing the use of a globally consistent parametric space to represent these meshes. This paper describes a method for mapping between the parametric spaces of such regions, and methods for representing these regions and interfaces between them. Using these methods, a 57% reduction in mesh storage cost is demonstrated, without loss of any information. These methods have been implemented in the MOAB mesh database component, which provides access to these meshes from both structured and unstructured functions. The total cost for representing structured mesh in MOAB is less than 25 MB per million elements using double-precision vertex coordinates; this is only slightly larger than the space required to store vertex coordinates alone.

Semi-structured meshes for axial turbomachinery blades

This paper describes the development and application of a novel mesh generator for the flow analysis of turbomachinery blades. The proposed method uses a combination of structured and unstructured meshes, the former in the radial direction and the latter in the axial and tangential directions, in order to exploit the fact that blade-like structures are not strongly three-dimensional since the radial variation is usually small. The proposed semi-structured mesh formulation was found to have a number of advantages over its structured counterparts. There is a significant improvement in the smoothness of the grid spacing and also in capturing particular aspects of the blade passage geometry. It was also found that the leading- and trailing-edge regions could be discretized without generating superfluous points in the far field, and that further refinements of the mesh to capture wake and shock effects were relatively easy to implement. The capability of the method is demonstrated in the case of a transonic fan blade for which the steady state flow is predicted using both structured and semi-structured meshes. A totally unstructured mesh is also generated for the same geometry to illustrate the disadvantages of using such an approach for turbomachinery blades. Copyright © 2000 John Wiley & Sons, Ltd.