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41 records · Page 3

Gravitation and Mesh Adaption

The Gravitation and Mesh Adaptation (GaMA) toolbox consists of a set of Matlab classes for modeling the environment around asteroids and comets. A variety of gravitational models and supporting algorithms from are consolidated alongside a custom meshing utility tailored for the application. This allows the user to work within a single streamlined environment to import and manipulate surface definitions, probe the dynamical environment, integrate trajectories, and post-process results. For other applications, modified surface meshes can be exported. Gravity Models: 1) Werner's analytic polyhedron model 2) Mascon model 3) Gottlieb's spherical harmonic model 4) Approximate polyhedron models 5) Curvilinear surface models 6) Custom composite models Meshing Features: 1) Array-based half-edge data structure 2) Supports curvilinear surface definitions up to degree 4 3) Ray-tracing 4) Coarsening 5) Feature-based refinement 6) Projection 7) Smoothing 8) Mesh quality validity tests 9) Mesh repair Additional Features: 1) Solar radiation pressure model 2) Distant 3rd body model 3) Collision detection 4) Trajectory integration and post-processing 5) Visualization of surface fields

Pearl, Jason↗

Multiscale graph neural network autoencoders for interpretable scientific machine learning

The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) autoencoding architecture with demonstrations on complex fluid flow applications. To address the first goal of interpretability, the GNN autoencoder achieves reduction in the number nodes in the encoding stage through an adaptive graph reduction procedure. Further, this reduction procedure essentially amounts to flowfieldconditioned node sampling and sensor identification, and produces interpretable latent graph representations tailored to the flowfield reconstruction task in the form of so-called masked fields. These masked fields allow the user to (a) visualize where in physical space a given latent graph is active, and (b) interpret the time-evolution of the latent graph connectivity in accordance with the time-evolution of unsteady flow features (e.g. recirculation zones, shear layers) in the domain. To address the goal of unstructured mesh compatibility, the autoencoding architecture utilizes a series of multi-scale message passing (MMP) layers, each of which models information exchange among node neighborhoods at various lengthscales. The MMP layer, which augments standard single-scale message passing with learnable coarsening operations, allows the decoder to more efficiently reconstruct the flowfield from the identified regions in the masked fields. Analysis of latent graphs produced by the autoencoder for various model settings are conducted using unstructured snapshot data sourced from large-eddy simulations in a backward-facing step (BFS) flow configuration with an OpenFOAM-based flow solver at high Reynolds numbers.

97 MATHEMATICS AND COMPUTING↗

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗

The importance of properties in modeling

Casting and welding of superalloys, stainless steel and titanium alloys are processes which can be improved through modeling of heat flow, fluid flow, residual stress development, and microstructural evolution. These simulations require inputs of thermophysical data, some of which involves the partially or totally liquid state. In particular, these processes involve melting, flow in the liquid, and solidification. Modeling of such processes can lead to an improved understanding of defects such as shrinkage, inclusions, cracks, incomplete filling (or penetration), macrosegregation, improper grain structure, and deviations from dimensional specifications. Effective modeling can shorten process development time and improve quality. An approach to these problems is to develop efficient models; validate through correlations with thermal, distortion, and microstructural data; run parametric studies; extract knowledge based rules; and apply to adaptive closed loop control systems. With the appropriate pre- and post-processing, such analyses can be made 'user friendly'. This would include graphical user interfaces as well as realistic images and color maps. In such form, these models can be used for sensitivity analyses, which are useful in defining appropriate sensors and in the development of control strategies. Such modeling can be done at several levels, e.g., the MARO level, modeling large scale phenomena such as heat and fluid flow or material deformation; the MICRO level, modeling the development of dendrites, grains or precipitates; or at the NANO level, modeling point defects, dislocations, stacking faults, etc. There are many computational issues associated with these simulations, e.g. computational efficiency and accuracy. In addition, there are many materials issues, not the least of which is the availability of accurate high temperature thermophysical data for complex alloys. This would include latent heat of fusion, temperature dependent heat capacity and thermal conductivity (for liquid and solid), viscosity, surface tension, thermal expansion, mechanical properties, etc. Preliminary data is frequently gathered from the literature; however, this is often not available for modern alloys. If additional data are required, measurements can be used; however, these are costly, time consuming and can be erroneous due to a lack of testing standards or impure materials. Microstructural predictors can be extracted from thermal information, e.g. cooling rate and thermal gradient; the prediction of microstructure is dependent on solidus and liquidus temperature, mushy zone permeability, the solidification curve, volume changes, phase transformations, alloying effects (such as surface tension or viscosity), mold/metal reactions, metal/environment reactions, etc. Defect maps may be needed to predict the onset of shrinkage, hot cracking or 'freckling'. Constants may be needed for stress relaxation, dendrite coarsening, vaporization, etc. Visualization was used as a tool to better comprehend complex data sets associated with the analysis of directional solidification (including crystal growth) and welding. Examples include not only isotherms, but also cooling rate, growth rate and thermal gradient. The latter two are not single valued scalars, but rather time and space dependent vector fields. Efficient models were developed for both casting and welding to predict heat flow and the relationship to dendrite and grain growth. These codes include many of the non-linear effects, e.g. radiation, which dominate these processes. The home-built FDM code(s) were designed to be useful not only to the scientist, but also to the process engineer. Special output can be requested to compare directly to experimental data. Visualization procedures were developed to visualize critical results, e.g. fusion zone width at the surface opposite that where the arc is applied ('penetration'). Both elaborate and simplified distortion analyses were carried out. It is clear that extensive mechanical property data are critical in order to accurately predict residual stress patterns. A scheme is currently being developed to integrate these modeling tools into a set of control algorithms; however, the success of this approach is critically dependent on the availability of accurate high temperature thermophysical data.

Giamei, A. F.↗