Mesh generation and optimization from digital rock fractures based on neural style transfer
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58 GEOSCIENCES↗
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CrossLink: General Overview [Slides]
Problem: Traditional mesh generation approaches are labor intensive and have limited robustness when applied to parametric design exploration and optimization of complex geometries. While automatic mesh generation approaches exist, they tend to generate tetrahedral or mixed-hybrid meshes which are generally unsuitable for physics applications with strong shock waves, thin boundary layers, and strong gradients. In addition, simulations sizes in the billions of cells are becoming more common with traditional mesh generation methods quickly reaching scalability limits. Solution: CrossLink offers a topology-based mesh generation approach with unstructured block-filling methods and a scalable mesh generation engine. In addition, CrossLink incorporates a python-based API for seamless workflow integration and robust repeatability of the geometry handling and mesh generation process. This makes it ideal for parametric design study and optimization of complex geometries. Finally, future versions of CrossLink will offer a parametric mesh capability that optimizes a high-order mesh and enables reconstruction of the final mesh in memory by the physics solver.
97 MATHEMATICS AND COMPUTING↗
Level-set topology optimization with PDE generated conformal meshes
This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.
42 ENGINEERING↗
Incremental Interval Assignment by Integer Linear Algebra with Improvements
Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.
97 MATHEMATICS AND COMPUTING↗
Analysis of cell-based diffusion acceleration for the slice balance approach
In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)
42 ENGINEERING↗
Parallel transport sweeps on two-dimensional cartesian and hexagonal grids
This paper aims to provide a proof of concept for parallel transport sweeps on two-dimensional hexagonal grids for the discrete ordinates transport equation. While the method is an extension of the popular and well-established Koch-Baker-Alcoulffe (KBA) algorithm, there are significant differences between the cartesian and hexagonal grid and thereafter sweep. The most important is the three-way connectivity of hexagons within the grid which creates greater dependencies between the elements. The KBA method in structured orthogonal grids was first implemented in the DRAGON5 code and the method is first described here. The differences in implementation for the hexagonal grid are also described. Benchmark results are also presented, showing roughly 10 times speedup in computational times with roughly 100 processors, in both cases. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Application of linear prolongation to coarse mesh finite difference acceleration in CASMO5
The Coarse-Mesh Finite Difference (CMFD) method has been used for over a decade to accelerate the convergence of the Method of Characteristics (MOC) solution to the two- dimensional particle transport equation in CASMO5. Numerical testing, along with widespread use in production-level calculations, have shown that the current CMFD implementation provides stability and robustness for a wide range of realistic reactor physics problems. However, the recent development of linear prolongation has attracted attention from the community as a way to further improve the performance and stability of CMFD. Two interpolation methods for linear prolongation are presented in this work and implemented into a test version of CASMO5. The performance of the proposed interpolations, referred to as the bilinear and linear directional schemes, is evaluated in terms of runtime relative to the default constant or uniform scaling update. Numerical results indicate that the use of linear prolongation can reduce the transport solver runtime on average by approximately 10% when tested with two hundred randomly selected cases. The new directional linear interpolation, combined with default constant boundary updates, is found to provide the highest reduction in runtime for the cases analyzed. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Shape design sensitivities using fully automatic 3-D mesh generation
Previous work in three dimensional shape optimization involved specifying design variables by associating parameters directly with mesh points. More recent work has shown the use of fully-automatic mesh generation based upon a parameterized geometric representation. Design variables have been associated with a mathematical model of the part rather than the discretized representation. The mesh generation procedure uses a nonuniform grid intersection technique to place nodal points directly on the surface geometry. Although there exists an associativity between the mesh and the geometrical/topological entities, there is no mathematical functional relationship. This poses a problem during certain steps in the optimization process in which geometry modification is required. For the large geometrical changes which occur at the beginning of each optimization step, a completely new mesh is created. However, for gradient calculations many small changes must be made and it would be too costly to regenerate the mesh for each design variable perturbation. For that reason, a local remeshing procedure has been implemented which operates only on the specific edges and faces associated with the design variable being perturbed. Two realistic design problems are presented which show the efficiency of this process and test the accuracy of the gradient computations.
Botkin, M. E.↗
Improving the Mesh Optimization Capabilities in Crosslink, a Topology Based Mesh Generator [Slides]
The nodes, edges, faces, and blocks that define the connectivity of a multi-block mesh. This is equivalent to a coarse unstructured mesh with global numbering. The topology is approximate.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Overlap Preservation Using Loosely-Coupled Boundary Conditions for Body-Fitted Structured Overset Grids
Several improvements are made to overlap preservation in the automated approach to generating overset structured meshes. A loosely-coupled boundary condition (LCBC) is introduced to maintain optimal overlap for surface meshes generated from overlapping initial curves. Extension of the LCBC scheme to three-dimensional volume meshing is also presented. Test cases include various rotary wing vehicles from NASA’s Revolutionary Vertical Lift Technology (RVLT) project, and the wing-body geometry from the NASA Juncture Flow Experiment. Results demonstrate improvements in donor stencil quality from the enhanced overlap between neighboring surface and volume meshes.
TTT↗
CrossLink: Advancements in Scalable Unstructured Mesh Generation [Slides]
Traditional mesh generation approaches are labor intensive and have limited robustness when applied to parametric design exploration and optimization of complex geometries. While automatic mesh generation approaches exist, they tend to generate tetrahedral or mixed-hybrid meshes which are generally unsuitable for physics applications with strong shock waves, thin boundary layers, and strong gradients. In addition, simulations sizes in the billions of cells are becoming more common with traditional mesh generation methods quickly reaching scalability limits. CrossLink offers a topology-based mesh generation approach with unstructured block-filling methods and a scalable mesh generation engine. In addition, CrossLink incorporates a python based API for seamless workflow integration and robust repeatability of the geometry handling and mesh generation process. This makes it ideal for parametric design study and optimization of complex geometries. Finally, future versions of CrossLink will offer a parametric mesh capability that optimizes a high-order mesh and enables reconstruction of the final mesh in memory by the physics solver.
97 MATHEMATICS AND COMPUTING↗
Variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes
This work presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.
42 ENGINEERING↗
Shape optimization of three-dimensional stamped and solid automotive components
The shape optimization of realistic, 3-D automotive components is discussed. The integration of the major parts of the total process: modeling, mesh generation, finite element and sensitivity analysis, and optimization are stressed. Stamped components and solid components are treated separately. For stamped parts a highly automated capability was developed. The problem description is based upon a parameterized boundary design element concept for the definition of the geometry. Automatic triangulation and adaptive mesh refinement are used to provide an automated analysis capability which requires only boundary data and takes into account sensitivity of the solution accuracy to boundary shape. For solid components a general extension of the 2-D boundary design element concept has not been achieved. In this case, the parameterized surface shape is provided using a generic modeling concept based upon isoparametric mapping patches which also serves as the mesh generator. Emphasis is placed upon the coupling of optimization with a commercially available finite element program. To do this it is necessary to modularize the program architecture and obtain shape design sensitivities using the material derivative approach so that only boundary solution data is needed.
Botkin, M. E.↗
Box truss analysis and technology development. Task 1: Mesh analysis and control
An analytical tool was developed to model, analyze and predict RF performance of box truss antennas with reflective mesh surfaces. The analysis system is unique in that it integrates custom written programs for cord tied mesh surfaces, thereby drastically reducing the cost of analysis. The analysis system is capable of determining the RF performance of antennas under any type of manufacturing or operating environment by integrating together the various disciplines of design, finite element analysis, surface best fit analysis and RF analysis. The Integrated Mesh Analysis System consists of six separate programs: The Mesh Tie System Model Generator, The Loadcase Generator, The Model Optimizer, The Model Solver, The Surface Topography Solver and The RF Performance Solver. Additionally, a study using the mesh analysis system was performed to determine the effect of on orbit calibration, i.e., surface adjustment, on a typical box truss antenna.
Bachtell, E. E.↗
Coupled Target-Beam-Moderator Optimization for the Second Target Station
This report describes the results for a coupled target-beam-moderator optimization analysis for the Second Target Station (STS) at ORNL's Spallation Neutron Source. This study is a continuation of the optimization analysis for the moderators in the preliminary design of STS performed in 2022. In the 2022 analysis the dimensions of the moderators are parameterized, while the target and the proton beam profile are kept constant. In this analysis the target height and the proton beam profile are added as parameters. This allows to study the coupled effects of changing target, moderator and beam dimensions. Similar to the 2022 analysis, this work is performed with an automated optimization workflow that uses the optimization toolbox DAKOTA, parameterized geometries in CREO and SpaceClaim, the unstructured mesh generation in Attila4MC, and the particle transport code MCNP6.2©. This workflow enables an efficient optimization using high-fidelity geometries. The main conclusions of this analysis are the following: • Coupled beam-target-moderator optimization provides a few additional percent performance gain over stand-alone moderator optimization. • The moderator performance is not very sensitive to the target height (between ≈60 and ≈80 mm) as long as the beam profile is chosen adequately. • The moderator performance is sensitive to the choice of beam spatial standard deviations, even when the footprint is kept constant. • The optimal moderator radius is the same for a beam footprint of 30 cm 2 , 62.5 cm 2 , and 90 cm 2 . Also the slope of the super-gaussian beam profile does not significantly impact the optimal moderator radius. • The optimal parameters and sensitivities are very similar to the 2022 optimization analysis. These results only indicate a a difference in the optimal radius of the cylindrical moderator, however, this has been corrected in the final design moderator optimization. The main purpose of this report is to document the simulations, results and lessons learned. The most impactful results are summarized in. We also note that the target geometry used in this work is not the final design.
43 PARTICLE ACCELERATORS↗
Time-dependent grid adaptation for meshes of triangles and tetrahedra
This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.
Russ D Rausch↗
Optimization of the moderators in the STS preliminary design
This report details the results for an optimization of the dimensions of the moderators in the preliminary design of the Spallation Neutron Source Second Target Station (STS). This study uses the optimization algorithms of Dakota and an unstructured mesh model for the moderators in MCNP. More details on the unstructured mesh model and the automated mesh generation can be found in [3]. Parallel to this effort, the same moderator geometries have been optimized using a constructive solid geometry (CSG) MCNP model. More details on this model and its results can be found in [4]. Three optimal designs are selected for each moderator: one that is optimized for maximum peak brightness, one for maximum time-integrated brightness, and one for a combination of peak and time-integrated brightness. The backbone of the optimization work flow is provided by Dakota. For each set of design parameters requested by Dakota, a new solid geometry is automatically built in Creo and SpaceClaim, and subsequently exported to Attila4MC to generate an unstructured mesh geometry for MCNP. After the MCNP calculation is finished, the objective function (e.g., brightness metric) is returned to Dakota. After the new design has been evaluated, a result-file is written, and Dakota proposes the next set of design parameters to be evaluated. The loop continues until a specified convergence criterion has been met. The design parameters of the cylindrical (upper) moderator include the hydrogen radius, the premoderator thickness (top, bottom, radial), the beryllium radius and the horizontal position of the moderator. The crucial design choice is the hydrogen radius. A radius of 62 mm is shown to provide the maximum time-integrated brightness. The maximum peak brightness occurs with a radius of 40 mm. A combined (middle) design, which balances peak and time-integrated brightnesses, is obtained with a hydrogen radius of 50 mm. The premoderator thicknesses and the beryllium radius are slightly larger in the design optimized for time-integrated brightness than in the design optimized for peak brightness. The sensitivity to these two parameters is relatively small close to the optimal configurations. The hydrogen vessel and vacuum vessel wall thicknesses are dependent on the radius of the liquid hydrogen due to structural integrity requirements. The increased wall thicknesses for larger vessels significantly penalize the time-integrated brightness, with the maximum obtainable value reduced by more than 10% relative to earlier studies which used fixed vessel wall thicknesses. The impact of the variable wall thicknesses is much less for the peak brightness and combined brightness designs. The design parameters of the tube (lower) moderator selected for the optimization are the tube length, the annular premoderator thickness, the beryllium radius and the horizontal position of the moderator. The tube length is the crucial parameter and is chosen large (210 mm) and small (125 mm) in the designs optimized for time-integrated and peak brightness respectively. A combined optimal design has a tube length of 170 mm. The premoderator thickness and the beryllium radius are chosen larger in the design optimized for time-integrated brightness.
42 ENGINEERING↗