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Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems
This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.
Construction of Hexahedral Elements Mesh Capturing Realistic Geometries of Bayou Choctaw SPR Site
The three-dimensional finite element mesh capturing realistic geometries of Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh is consisting of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time with maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill, Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for not only various civil and geological structures but also biological applications such as artificial limbs.
Unstructured Euler flow solutions using hexahedral cell refinement
An attempt is made to extend grid refinement into three dimensions by using unstructured hexahedral grids. The flow solver is developed using the TIGER (topologically Independent Grid, Euler Refinement) as the starting point. The program uses an unstructured hexahedral mesh and a modified version of the Jameson four-stage, finite-volume Runge-Kutta algorithm for integration of the Euler equations. The unstructured mesh allows for local refinement appropriate for each freestream condition, thereby concentrating mesh cells in the regions of greatest interest. This increases the computational efficiency because the refinement is not required to extend throughout the entire flow field.
Refinement Of Hexahedral Cells In Euler Flow Computations
Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.
Local Decomposition of Hexahedral Singular Nodes into Singular Curves
Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. Hex meshes with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. In conclusion, with this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.
An efficient second-order adaptive procedure for inserting CAD geometries into hexahedral meshes using volume fractions
Here, this paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The procedure consists of two steps. The first step performs spatial acceleration using a k-d tree. The second step involves subdividing individual hexahedra in an adaptive mesh refinement (AMR)-like fashion and approximating the CAD geometry linearly (as a plane) at the finest subdivision. The procedure requires only two geometric queries from a CAD kernel: determining whether or not a queried spatial coordinate is inside or outside the CAD geometry and determining the closest point on the CAD geometry’s surface from a given spatial coordinate. We prove that the procedure is second-order accurate for sufficiently smooth geometries and sufficiently refined background meshes. We demonstrate the expected order of accuracy is achieved with several verification tests and illustrate the procedure’s effectiveness for several exemplar CAD geometries.
Communication: A density functional investigation of structure-property evolution in the tetrakis hexahedral C{sub 4}Al{sub 14} nanocluster
Nanoclusters are prime objects of study in modern nanotechnology and offer a variety of applications promoted by their properties tunable by size, shape, and composition. DFT calculations are employed to analyze structure, stability, and selected electronic properties of a core-shell C{sub 4}Al{sub 14} species. With insertion of the carbon core, the original low-symmetry aluminum cluster is predicted to undergo a considerable reshaping and acquire a striking D{sub 4h} tetrakis-hexahedral geometry, with proportions controlled by a near-degenerate spin state or charge. The system also becomes more stable to dissociation. Surprisingly, other properties such as ionisation energy and electron affinity do not change significantly, although still exhibit some interesting features including opposite variations for vertical and adiabatic values. The stability and property evolutions are analyzed in terms of contributions from reshaping of the shell and its further interaction with the core. The system thus has potential applications as a symmetric building unit and a molecular device for nano-electronics/spintronics.
Generalization of two-dimensional DDL schemes of the GQ method for three-dimensional arbitrary hexahedral spatial mesh
The DDL schemes of the GQ3D method for the approximation of the radiation transport operator on arbitrary hexahedral meshes is developed and tested.
A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes
In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.
A 3-D CE/SE Navier-Stokes Solver With Unstructured Hexahedral Grid for Computation of Near Field Jet Screech Noise
A 3-D space-time CE/SE Navier-Stokes solver using an unstructured hexahedral grid is described and applied to a circular jet screech noise computation. The present numerical results for an underexpanded jet, corresponding to a fully expanded Mach number of 1.42, capture the dominant and nonaxisymmetric 'B' screech mode and are generally in good agreement with existing experiments.
A template-based approach for parallel hexahedral two-refinement
Here, we provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3 prior to smoothing.
Construction of hexahedral finite element mesh capturing realistic geometries of a petroleum reserve
Abstract not provided.
Sculpt: Automatic Parallel Hexahedral Mesh Generation
Sculpt is a companion application to Cubit designed to run in parallel for generating all-hex meshes of complex geometry. It uses a unique overlay-grid procedure that extracts surfaces from a volume-fraction representation of the geometry. This allows for fast, automatic, fault-tolerant meshing in a high-performance computing (HPC) environment. Although Sculpt can be driven from Cubit as a GUI front-end, Sculpt was developed as a separate application so that it can be run independently from Cubit on HPC computing platforms. It was also designed as a separable software library so it can be easily integrated as an in-situ meshing solution within other codes. This work provides a brief technical discussion of the algorithms used in Sculpt as well as a complete user's manual. It includes details of the Cubit interface to Sculpt and the complete manual for the stand-alone application, including examples.
Shape Matching for 3D CAD Models for Hexahedral Meshing Workflows [Slides]
Abstract not provided.
Voronoi or hexahedral meshing for simulation accuracy and speed?
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Diel variations of the attenuation, backscattering and absorption coefficients of four phytoplankton species and comparison with spherical, coated spherical and hexahedral particle optical models
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