Accurate Cell-Centered Discretizations for Modeling Multiphase Flow in Porous Media on General Hexahedral and Simplicial Grids
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A technique for conforming an interface between a first mesh and a second mesh is disclosed. A first interface surface in the first mesh and a second interface surface in the second mesh residing along the interface are identified. The first and second interface surfaces are initially non-conforming along the interface. Chords within the first and second interface surfaces that fall within a threshold separation distance of each other are paired. Sheets having chords that reside within the first or second interface surfaces are recursively inserted into or extracted from one or both of the first and second meshes until all remaining chords within the first interface surface are paired with corresponding chords in the second interface surface and all remaining chords within the second interface surface are paired with corresponding chords in the first interface surface.
A technique for conforming an interface between a first mesh and a second mesh is disclosed. A first interface surface in the first mesh and a second interface surface in the second mesh residing along the interface are identified. The first and second interface surfaces are initially non-conforming along the interface. Chords within the first and second interface surfaces that fall within a threshold separation distance of each other are paired. Sheets having chords that reside within the first or second interface surfaces are recursively inserted into or extracted from one or both of the first and second meshes until all remaining chords within the first interface surface are paired with corresponding chords in the second interface surface and all remaining chords within the second interface surface are paired with corresponding chords in the first interface surface.
A techniques for coarsening a hexahedral mesh is described. The technique includes identifying a coarsening region within a hexahedral mesh to be coarsened. A boundary sheet of hexahedral elements is inserted into the hexahedral mesh around the coarsening region. A column of hexahedral elements is identified within the boundary sheet. The column of hexahedral elements is collapsed to create an extraction sheet of hexahedral elements contained within the coarsening region. Then, the extraction sheet of hexahedral elements is extracted to coarsen the hexahedral mesh.
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.
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.
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.
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.
The DDL schemes of the GQ3D method for the approximation of the radiation transport operator on arbitrary hexahedral meshes is developed and tested.
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.
Abstract not provided.
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.
Abstract not provided.
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