Publications

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Local topological modification is widely used to improve mesh quality after automatic generation of tetrahedral and quadrilateral meshes. These same techniques are also used to support adaptive refinement of these meshes. In contrast, few methods are known for locally modifying the topology of hexahedral meshes. Most efforts to do this have been based on fixed transition templates or global refinement. In contrast, a dual-based 'pillowing' method has been used which, while local, is still quite restricted in its application, and is typically applied in a template-based fashion. In this presentation, I will describe the generalization of a dual-based approach to the local topological modification of hex meshes and its application to clean up hexahedral meshes. A set of three operations for locally modifying hex mesh topology has been shown to reproduce the so-called 'flipping' operations described by Bern et. al as well as other commonly-used refinement templates. I will describe the implementation of these operators and their application to real meshes. Challenging aspects of this work have included visualization of a hex mesh and its dual (especially for poor-quality meshes); the incremental modification of both the primal (i.e. the mesh) and the dual simultaneously; and the interactive steering of these operations with the goal of improving hex meshes which would otherwise have unacceptable quality. These aspects will be discussed in the context of improving hex meshes generated by curve contraction-based whisker weaving. Application of these techniques for improving other hexahedral mesh types, for example those resulting from tetrahedral subdivision, will also be discussed.

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The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.

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Much progress has been made through these years to achieve automatic hexahedral mesh generation. While general meshing algorithms that can take on general geometry are not there yet; many well-proven automatic meshing algorithms now work on certain classes of geometry. This paper presents a feature based volume decomposition approach for automatic Hexahedral Mesh generation. In this approach, feature recognition techniques are introduced to determine decomposition features from a CAD model. The features are then decomposed and mapped with appropriate automatic meshing algorithms suitable for the correspondent geometry. Thus a formerly unmeshable CAD model may become meshable. The procedure of feature decomposition is recursive: sub-models are further decomposed until either they are matched with appropriate meshing algorithms or no more decomposition features are detected. The feature recognition methods employed are convexity based and use topology and geometry information, which is generally available in BREP solid models. The operations of volume decomposition are also detailed in the paper. The final section, the capability of the feature decomposer is demonstrated over some complicated manufactured parts.

The finite element method is being used today to model component assemblies in a wide variety of application areas, including structural mechanics, fluid simulations, and others. Generating hexahedral meshes for these assemblies usually requires the use of geometry decomposition, with different meshing algorithms applied to different regions. While the primary motivation for this approach remains the lack of an automatic, reliable all-hexahedral meshing algorithm, requirements in mesh quality and mesh configuration for typical analyses are also factors. For these reasons, this approach is also sometimes required when producing other types of unstructured meshes. This paper will review progress to date in automating many parts of the hex meshing process, which has halved the time to produce all-hex meshes for large assemblies. Particular issues which have been exposed due to this progress will also be discussed, along with their applicability to the general unstructured meshing problem.

Current hexahedral mesh generation techniques rely on a set of meshing tools, which when combined with geometry decomposition leads to an adequate mesh generation process. Of these tools, sweeping tends to be the workhorse algorithm, accounting for at least 50% of most meshing applications. Constraints which must be met for a volume to be sweepable are derived, and it is proven that these constraints are necessary but not sufficient conditions for sweepability. This paper also describes a new algorithm for detecting extruded or sweepable geometries. This algorithm, based on these constraints, uses topological and local geometric information, and is more robust than feature recognition-based algorithms. A method for computing sweep dependencies in volume assemblies is also given. The auto sweep detect and sweep grouping algorithms have been used to reduce interactive user time required to generate all-hexahedral meshes by filtering out non-sweepable volumes needing further decomposition and by allowing concurrent meshing of independent sweep groups. Parts of the auto sweep detect algorithm have also been used to identify independent sweep paths, for use in volume-based interval assignment.

Considerable progress has been made on automatic hexahedral mesh generation in recent years. Several automatic meshing algorithms have proven to be very reliable on certain classes of geometry. While it is always worth pursuing general algorithms viable on more general geometry, a combination of the well-established algorithms is ready to take on classes of complicated geometry. By partitioning the entire geometry into meshable pieces matched with appropriate meshing algorithm the original geometry becomes meshable and may achieve better mesh quality. Each meshable portion is recognized as a meshing feature. This paper, which is a part of the feature based meshing methodology, presents the work on shape recognition and volume decomposition to automatically decompose a CAD model into meshable volumes. There are four phases in this approach: (1) Feature Determination to extinct decomposition features, (2) Cutting Surfaces Generation to form the ''tailored'' cutting surfaces, (3) Body Decomposition to get the imprinted volumes; and (4) Meshing Algorithm Assignment to match volumes decomposed with appropriate meshing algorithms. The feature determination procedure is based on the CLoop feature recognition algorithm that is extended to be more general. Results are demonstrated over several parts with complicated topology and geometry.

The Dicer algorithm generates a fine mesh by refining each element in a coarse all-hexahedral mesh generated by any existing all-hexahedral mesh generation algorithm. The fine mesh is geometry-conforming. Using existing all-hexahedral meshing algorithms to define the initial coarse mesh simplifies the overall meshing process and allows dicing to take advantage of improvements in other meshing algorithms immediately. The Dicer algorithm will be used to generate large meshes in support of the ASCI program. The authors also plan to use dicing as the basis for parallel mesh generation. Dicing strikes a careful balance between the interactive mesh generation and multi-million element mesh generation processes for complex 3D geometries, providing an efficient means for producing meshes of varying refinement once the coarse mesh is obtained.

The use of feature recognition as part of an overall decomposition-based hexahedral meshing approach is described in this paper. The meshing approach consists of feature recognition, using a c-loop or hybrid c-loop method, and the use of cutting surfaces to decompose the solid model. These steps are part of an iterative process, which proceeds either until no more features can be recognized or until the model has been completely decomposed into meshable sub-volumes. This method can greatly reduce the time required to generate an all-hexahedral mesh, either through the use of more efficient meshing algorithms on more of the geometry or by reducing the amount of manual decomposition required to mesh a volume.

This paper describes the techniques used to resolve invalid connectivity created as a natural part of the whisker weaving algorithm. These techniques rely on the detection of {open_quotes}repeated hexes{close_quotes} in the STC data, which indicate face pairs which share two edges. The {open_quotes}repeated hex{close_quotes} case is described in detail, including the resolution technique by which a self-intersecting whisker sheet with two independent face loops are created. The algorithm used to construct the primal of an all-hexahedral mesh (i.e. the actual nodes and hex elements) from the connectivity data contained in the STC is also described. The primal is constructed using a {open_quotes}gift-wrapping{close_quotes} algorithm, where all the mesh edges and hexes containing a particular node are found by traversing between hexes already known to share the node. This algorithm is implemented inside the CUBIT code and is used to generate meshes for several example problems.

Adaptive finite element analysis demands a great deal of computational resources, and as such is most appropriately solved in a massively parallel computer environment. This analysis will require other parallel algorithms before it can fully utilize MP computers, one of which is parallel adaptive meshing. A version of the paving algorithm is being designed which operates in parallel but which also retains the robustness and other desirable features present in the serial algorithm. Adaptive paving in a production mode is demonstrated using a Babuska-Rheinboldt error estimator on a classic linearly elastic plate problem. The design of the parallel paving algorithm is described, and is based on the decomposition of a surface into {open_quotes}virtual{close_quotes} surfaces. The topology of the virtual surface boundaries is defined using mesh entities (mesh nodes and edges) so as to allow movement of these boundaries with smoothing and other operations. This arrangement allows the use of the standard paving algorithm on subdomain interiors, after the negotiation of the boundary mesh.

MELCOR is a fully integrated, engineering-level computer code being developed at Sandia National Laboratories for the USNRC, that models the entire spectrum of severe accident phenomena in a unified framework for both BWRs and PWRs. As a part of an ongoing assessment program, MELCOR has been used to model the MP-1 and MP-2 experiments, which provided data for late-phase melt progression in PWR geometries. Core temperature predicted by MELCOR were within 250--500 K of measured data in both MP-1 and MP-2. Relocation in the debris bed and metallic crust regions of MP-2 was predicted accurately compared to PIE data. Temperature gradients in lower portions of the test bundle were not predicted well in both MP-1 and MP-2, due to the lack of modeling of the heat transfer path to the cooling jacket in those portions of the test bundles. Fifteen sensitivity studies were run on various core (COR), control volume hydrodynamics (CVH) and heat structures (HS) package parameters. No unexpected sensitivities were found, and in particular there were no sensitivities to reduced time step, finer nodalization or to computer platform. Calculations performed by the DEBRIS and TAC2D codes for MP-1 and MP-2 showed better agreement with measured data than those performed by MELCOR. This was expected, through, due to the fully 2-dimensional modeling used in the other codes.

MELCOR is a fully integrated, engineering-level computer code being developed at Sandia National Laboratories for the USNRC, that models the entire spectrum of severe accident phenomena in a unified framework for both BWRs and PWRs. As a part of an ongoing assessment, program, MELCOR has been used to model the ACRR in-pile DF-4 Damaged Fuel experiment. DF-4 provided data for early phase melt progression in BWR fuel assemblies, particularly for phenomena associated with eutectic interactions in the BWR control blade and zircaloy oxidation in the canister and cladding. MELCOR provided good agreement with experimental data in the key areas of eutectic material behavior and canister and cladding oxidation. Several shortcomings associated with the MELCOR modeling of BWR geometries were found and corrected. Twenty-five sensitivity studies were performed on COR, HS and CVH parameters. These studies showed that the new MELCOR eutectics model played an important role in predicting control blade behavior. These studies revealed slight time step dependence and no machine dependencies. Comparisons made with the results from four best-estimate codes showed that MELCOR did as well as these codes in matching DF-4 experimental data.