Frame Fields for Hexahedral Mesh Generation

As a discretized representation of the volumetric domain, hexahedral meshes have been a popular choice in computational engineering science and serve as one of the main mesh types in leading industrial software of relevance. The generation of high quality hexahedral meshes is extremely challenging because it is essentially an optimization problem involving multiple (conflicting) objectives, such as fidelity, element quality, and structural regularity. Various hexahedral meshing methods have been proposed in past decades, attempting to solve the problem from different perspectives. Unfortunately, algorithmic hexahedral meshing with guarantees of robustness and quality remains unsolved. The frame field based hexahedral meshing method is the most promising approach that is capable of automatically generating hexahedral meshes of high quality, but unfortunately, it suffers from several robustness issues. Field based hexahedral meshing follows the idea of integer-grid maps, which pull back the Cartesian hexahedral grid formed by integer isoplanes from a parametric domain to a surface-conforming hexahedral mesh of the input object. Since directly optimizing for a high quality integer-grid map is mathematically challenging, the construction is usually split into two steps: (1) generation of a feature-aligned frame field and (2) generation of an integer-grid map that best aligns with the frame field. The main robustness issue stems from the fact that smooth frame fields frequently exhibit singularity graphs that are inappropriate for hexahedral meshing and induce heavily degenerate integer-grid maps. The thesis aims at analyzing the gap between the topologies of frame fields and hexahedral meshes and developing algorithms to realize a more robust field based hexahedral mesh generation. The first contribution of this work is an enumeration of all local configurations that exist in hexahedral meshes with bounded edge valence and a generalization of the Hopf-Poincaré formula to octahedral (orthonormal frame) fields, leading to necessary local and global conditions for the hex-meshability of an octahedral field in terms of its singularity graph. The second contribution is a novel algorithm to generate octahedral fields with prescribed hex-meshable singularity graphs, which requires the solution of a large non-linear mixed-integer algebraic system. This algorithm is an important step toward robust automatic hexahedral meshing since it enables the generation of a hex-meshable octahedral field. In the collaboration work with colleagues [BRK+22], the dataset HexMe consisting of practically relevant models with feature tags is set up, allowing a fair evaluation for practical hexahedral mesh generation algorithms. The extendable and mutable dataset remains valuable as hexahedral meshing algorithms develop. The results of the standard field based hexahedral meshing algorithms on the HexMesh dataset expose the fragility of the automatic pipeline. The major contribution of this thesis improves the robustness of the automatic field based hexahedral meshing by guaranteeing local meshability of general feature aligned smooth frame fields. We derive conditions on the meshability of frame fields when feature constraints are considered, and describe an algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite the fact that local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 57%, when compared on the challenging HexMe dataset

Parallelization of the Advancing Front Local Reconnection Mesh Generation Software Using a Pseudo-Constrained Parallel Data Refinement Method

Preliminary results of a long-term project entailing the parallelization of an industrial strength sequential mesh generator, called Advancing Front Local Reconnection (AFLR), are presented. AFLR has been under development for the last 25 years at the NSF/ERC center at Mississippi State University. The parallel procedure that is presented is called Pseudo-constrained (PsC) Parallel Data Refinement (PDR) and consists of the following steps: (i) use an octree data-decomposition scheme to divide the original geometry into subdomains (octree leaves), (ii) refine each subdomain with the proper adjustments of its neighbors using the given refinement code, and (iii) combine all subdomain data into a single, conforming mesh. Parallelism was achieved by implementing Pseudo-constrained Parallel Data Refinement AFLR (PsC.AFLR) on top of a runtime system called Parallel Runtime Environment for Multi-computer Applications (PREMA). During run time, the PsC.AFLR method exposes data decomposition information (number of subdomains waiting to be refined) to the underlying runtime system. In turn, this system facilitates work-load balancing and guides the program’s execution towards the most efficient utilization of hardware resources. Preliminary results, on the mesh refinement operation, show that the end-user productivity (measured in terms of elements refined per second) increases as the number of cores in use are increased. When using approximately 16 cores, PsC.AFLR outperforms the serial AFLR code by about 11 times. PsC.AFLR also maintains its stability by generating meshes of comparable quality. Although it offers good end-user productivity, PsC.AFLR suffers in its capability to generate meshes with the same level of density or quality as that of the serial AFLR software due to the constraints set by subdomain boundaries that are required to successfully execute AFLR. These constraints demonstrate that it is not ideal to use AFLR in a black box manner when parallelizing the software. Its source code must be modified to a non-trivial extent if one wishes to remove these constraints and maximize the end-user productivity and potential scalability

The EMCC / DARPA Massively Parallel Electromagnetic Scattering Project

The Electromagnetic Code Consortium (EMCC) was sponsored by the Advanced Research Program Agency (ARPA) to demonstrate the effectiveness of massively parallel computing in large scale radar signature predictions. The EMCC/ARPA project consisted of three parts

Nearfield Summary and Statistical Analysis of the Second AIAA Sonic Boom Prediction Workshop

A summary is provided for the Second AIAA Sonic Boom Workshop held 8-9 January 2017 in conjunction with AIAA SciTech 2017. The workshop used three required models of increasing complexity: an axisymmetric body, a wing body, and a complete configuration with flow-through nacelle. An optional complete configuration with propulsion boundary conditions is also provided. These models are designed with similar nearfield signatures to isolate geometry and shock/expansion interaction effects. Eleven international participant groups submitted nearfield signatures with forces, pitching moment, and iterative convergence norms. Statistics and grid convergence of these nearfield signatures are presented. These submissions are propagated to the ground, and noise levels are computed. This allows the grid convergence and the statistical distribution of a noise level to be computed. While progress is documented since the first workshop, improvement to the analysis methods for a possible subsequent workshop are provided. The complete configuration with flow-through nacelle showed the most dramatic improvement between the two workshops. The current workshop cases are more relevant to vehicles with lower loudness and have the potential for lower annoyance than the first workshop cases. The models for this workshop with quieter ground noise levels than the first workshop exposed weaknesses in analysis, particularly in convective discretization

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Propulsion system integration and modelling synthesis

Concerns over fuel costs, along with the ever increasing requirement to reduce the impact of emissions, means that the world's airlines continue to introduce low-noise and more fuel-efficient aircraft into their fleet. Increasing the engine bypass ratio is one way to improve propulsive efficiency. However, historically an increase in the bypass ratio (BPR) has usually been associated with an increase in the fan diameter. Consequently, there can be a notable increase in the impact of the engine installation on the overall aircraft performance. For example, although the typical increase in fan diameter is generally beneficial to the uninstalled engine specific fuel consumption, the increase in the nacelle drag and weight are detrimental to the aircraft performance. There is also likely to be a stronger aerodynamic coupling between the engine and the airframe. Overall there is a risk that the gains in uninstalled engine performance are wholly or partly lost due to adverse engine-airframe installation and interference effects as well as additional nacelle weight. It is clear that the quantification of the elements of installation drag is a key aspect in the assessment of the likely developments in engine design as well as on the installation requirements for future airframe architectures. The overall aim of this research is to determine the effect of nacelle size, weight, geometry and installation on flight efficiency. This aim has been addressed through the development of a framework which combines the engine thermodynamic model, aircraft performance, engine installation aspects and a flight trajectory approach. This framework has been developed to assess the relative importance of various engine installation aspects on the overall flight fuel burn for a range of short-haul and long-haul configurations

The Winonan

https://openriver.winona.edu/thewinonan1960s/1000/thumbnail.jp

A parallel advancing front grid generation scheme

A parallel advancing front scheme has been developed. The domain to be gridded is first subdivided spatially using a relatively coarse octree. Boxes are then identified and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only considering the boxes of the active front that generate small elements. The procedure has been implemented on the SGI origin class of machines using the shared memory paradigm. Timings for a variety of cases show speedups similar to those obtained for flow codes. The procedure has been used to generate grids with tens of millions of elements.&nbsp

The Winonan

https://openriver.winona.edu/thewinonan1950s/1014/thumbnail.jp