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At least 451 records · Page 25

AMReX: Block-structured adaptive mesh refinement for multiphysics applications

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

Zhang, Weiqun↗

CFD Verification and Validation of Wire-Wrapped Pin Assemblies

TerraPower is participating in a cooperative project among industry, the national lab system, and academia to perform Verification and Validation (V and V) of Computational Fluid Dynamics (CFD) methods for predicting the flow and heat transfer within liquid-metal-cooled nuclear fuel assemblies with wire-wrapped fuel pins. This project, consisting of both experimental and numerical components, uses surrogate fluids and electrically heated fuel pins to substitute for the liquid metal coolant and the nuclear heat source. The experiments include both unheated assemblies to measure the flow velocities with Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV), as well as heated assemblies to measure the temperatures of the fluid and the simulated fuel pins with thermocouples. Both sets of experiments also measure the pressure at multiple locations in the system. The numerical component of this work involves high-fidelity Large-Eddy Simulation (LES) modeling and industry-standard Reynolds-Averaged Navier-Stokes (RANS) modeling of the experiments. Furthermore, the experiments and simulations will be conducted on two duct geometries: the first is a non-deformed hexagonal duct that has flat internal duct faces that represents a beginning of life geometry. The other is a deformed duct where the internal hexagonal flow area enlarges then decreases along the axial height to represent the changes that occur to the duct geometry from pressure and irradiation effects in the core. This paper describes the methods and results of the industrial, RANS-based CFD code verification, solution verification, and solution validation. The V and V simulations are being performed for the following experiment test geometries: - Isothermal non-deformed bundle; - Heated non-deformed bundle; - Isothermal deformed bundle; - Heated deformed bundle. These flows have been computed at first with the pre-test design specifications, without the aid of any experimental results. Later, post-test calculations will be performed incorporating the actual test conditions and input from some of the experimental results. These RANS simulations of helically wire-wrapped fuel assemblies employ meshes of bare pins without the wire-wrap in the bundle. The effect of wire-wrap on the flow is accounted for by introducing a momentum source into the governing fluid equations. The momentum source is only applied to cells corresponding to the location of the wire-wrap, and its components in each cell are based on the local flow field. This methodology simplifies the geometry and mesh generation and reduces the cell count, while still capturing the effects of the wire-wrap. The momentum source approach is used for all of the assembly simulations performed in this study. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

An MCNP6 Version of the Visual Editor - Paper 2

The Visual Editor is a graphical user interface for working with the MCNP computer code developed at Los Alamos National Laboratory. It consists of a graphical user interface written in C++ that is linked directory to the MCNP Fortran code. Work on the original Visual Editor started in 1992 and was first published in 1993. The original version of the Visual Editor was created on Unix/Linux operating systems and was linked to the MCNP computer code. The Visual Editor was adapted to the Windows operating system in 1999. In 2008 the Visual Editor was adapted to work with the MCNPX computer code. This paper discusses the latest upgrade of the Visual Editor to be compatible with the MCNP6 computer code. Two graphical user interfaces have been created, the Visual MCNP6 Plotter and the Visual MCNP6 Editor. The Visual MCNP6 Plotter includes all of the standard plotting features available in the default MCNP6 plotting package including geometry plotting, tally plotting, cross section plotting, mesh tally plotting and weight window mesh plotting. The Visual MNCP6 Editor has additional capabilities to allow for the creation of MCNP input files with graphical tools. The Visual MCNP6 Editor allows user to create and modify the input file within the Editor. Modifications are not allowed in the Visual MCNP6 Plotter. Both graphical user interfaces allow for advanced plotting features including 3D geometry plots and particle track plotting. Complete details on these tools along with their current status can be found at the Visual Editor website (www.mcnpvised.com). (author)

61 RADIATION PROTECTION AND DOSIMETRY↗

Rotor Airloads Prediction Using Unstructured Meshes and Loose CFD/CSD Coupling

The FUN3D unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been modified to allow prediction of trimmed rotorcraft airloads. The trim of the rotorcraft and the aeroelastic deformation of the rotor blades are accounted for via loose coupling with the CAMRAD II rotorcraft computational structural dynamics code. The set of codes is used to analyze the HART-II Baseline, Minimum Noise and Minimum Vibration test conditions. The loose coupling approach is found to be stable and convergent for the cases considered. Comparison of the resulting airloads and structural deformations with experimentally measured data is presented. The effect of grid resolution and temporal accuracy is examined. Rotorcraft airloads prediction presents a very substantial challenge for Computational Fluid Dynamics (CFD). Not only must the unsteady nature of the flow be accurately modeled, but since most rotorcraft blades are not structurally stiff, an accurate simulation must account for the blade structural dynamics. In addition, trim of the rotorcraft to desired thrust and moment targets depends on both aerodynamic loads and structural deformation, and vice versa. Further, interaction of the fuselage with the rotor flow field can be important, so that relative motion between the blades and the fuselage must be accommodated. Thus a complete simulation requires coupled aerodynamics, structures and trim, with the ability to model geometrically complex configurations. NASA has recently initiated a Subsonic Rotary Wing (SRW) Project under the overall Fundamental Aeronautics Program. Within the context of SRW are efforts aimed at furthering the state of the art of high-fidelity rotorcraft flow simulations, using both structured and unstructured meshes. Structured-mesh solvers have an advantage in computation speed, but even though remarkably complex configurations may be accommodated using the overset grid approach, generation of complex structured-mesh systems can require months to set up. As a result, many rotorcraft simulations using structured-grid CFD neglect the fuselage. On the other hand, unstructured-mesh solvers are easily able to handle complex geometries, but suffer from slower execution speed. However, advances in both computer hardware and CFD algorithms have made previously state-of-the-art computations routine for unstructured-mesh solvers, so that rotorcraft simulations using unstructured grids are now viable. The aim of the present work is to develop a first principles rotorcraft simulation tool based on an unstructured CFD solver.

Biedron, Robert T.↗

Mesh Convergence Issues

(U) This document is written to describe issues that impact on the ability of codes to converge to a unique answer. Several issues that could be discussed in the area of mesh convergence and resolution the topics include the resolution of geometry, stress gradients, shock propagation, material softening, and localization of deformation. After a quick discussion of what mesh convergence means, this paper presents a review of some of the criteria for mesh convergence. With an introductory level understanding of these criteria, two problems are presented to demonstrate convergence and non-­convergence. The first example is a simple convergent hemisphere of gas, known as the Noh problem. With this problem convergence is shown. The Noh problem is also used to investigate the impact of mesh stiffening, or viscosity. The second problem is that of an explosively driven hemisphere. The hemisphere made of U6Nb with an inner radius of 40 mm and an outer radius of 41 mm was filled with PBX9501 and tested. Test results included surface temperature and information on the breakup, such as distribution of fines. Convergence computational methods are discussed along with some proposals for obtaining mesh convergence for a wide range of applications.

36 MATERIALS SCIENCE↗

Offset Compound Gear Drive

The Offset Compound Gear Drive is an in-line, discrete, two-speed device utilizing a special offset compound gear that has both an internal tooth configuration on the input end and external tooth configuration on the output end, thus allowing it to mesh in series, simultaneously, with both a smaller external tooth input gear and a larger internal tooth output gear. This unique geometry and offset axis permits the compound gear to mesh with the smaller diameter input gear and the larger diameter output gear, both of which are on the same central, or primary, centerline. This configuration results in a compact in-line reduction gear set consisting of fewer gears and bearings than a conventional planetary gear train. Switching between the two output ratios is accomplished through a main control clutch and sprag. Power flow to the above is transmitted through concentric power paths. Low-speed operation is accomplished in two meshes. For the purpose of illustrating the low-speed output operation, the following example pitch diameters are given. A 5.0 pitch diameter (PD) input gear to 7.50 PD (internal tooth) intermediate gear (0.667 reduction mesh), and a 7.50 PD (external tooth) intermediate gear to a 10.00 PD output gear (0.750 reduction mesh). Note that it is not required that the intermediate gears on the offset axis be of the same diameter. For this example, the resultant low-speed ratio is 2:1 (output speed = 0.500; product of stage one 0.667 reduction and stage two 0.750 stage reduction). The design is not restricted to the example pitch diameters, or output ratio. From the output gear, power is transmitted through a hollow drive shaft, which, in turn, drives a sprag during which time the main clutch is disengaged.

Stevens, Mark A.↗

The optimization of high resolution topographic data for 1D hydrodynamic models

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domain and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.

97 MATHEMATICS AND COMPUTING↗

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Mavriplis, Dimitri J.↗

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Mavriplis, D. J.↗

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Here, this paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

42 ENGINEERING↗

Status of the framework for research in nuclear science and engineering - 25460

The Framework for Research in Nuclear Science and Engineering (FRENSIE) is a collection of packages written in C++ that are designed primarily to aid in methods development. New features are continually being added to the various packages and as a result, the Forward Adjoint Continuous Energy Monte Carlo (FACEMC) tool provided by FRENSIE continues to undergo verification and validation. While FRENSIE is not currently open source, the ultimate goal is for it to be released as such. A few of the more recent developments in FRENSIE include the addition of combinatorial geometry capabilities using ROOT, tet and hex meshing, support for thermal neutron S (α; β) data, photon Doppler broadening, electron interactions using basic analog electron physics models as well as an elastic moment-preserving model, and atomic relaxation. Preliminary verification results for much of the newly added physics models show good agreement between FACEMC and MCNP6. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Verification of Advective Bar Elements Implemented in the Aria Thermal Response Code.

A verification effort was undertaken to evaluate the implementation of the new advective bar capability in the Aria thermal response code. Several approaches to the verification process were taken : a mesh refinement study to demonstrate solution convergence in the fluid and the solid, visually examining the mapping of the advective bar element nodes to the surrounding surfaces, and a comparison of solutions produced using the advective bars for simple geometries with solutions from commercial CFD software . The mesh refinement study has shown solution convergence for simple pipe flow in both temperature and velocity . Guidelines were provided to achieve appropriate meshes between the advective bar elements and the surrounding volume. Simulations of pipe flow using advective bars elements in Aria have been compared to simulations using the commercial CFD software ANSYS Fluent (r) and provided comparable solutions in temperature and velocity supporting proper implementation of the new capability. Verification of Advective Bar Elements iv Acknowledgements A special thanks goes to Dean Dobranich for his guidance and expertise through all stages of this effort . His advice and feedback was instrumental to its completion. Thanks also goes to Sam Subia and Tolu Okusanya for helping to plan many of the verification activities performed in this document. Thank you to Sam, Justin Lamb and Victor Brunini for their assistance in resolving issues encountered with running the advective bar element model. Finally, thanks goes to Dean, Sam, and Adam Hetzler for reviewing the document and providing very valuable comments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell’s equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE Φ and TM Φ polarizations on the finite element (primal) mesh. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE Φ polarized fields, (E z , E ρ , B Φ ) and (2) D and H of TM Φ polarized fields, (D Φ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). Here, a cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMΦ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling Interfacial Fracture in Sierra

This report summarizes computational efforts to model interfacial fracture using cohesive zone models in the SIERRA/SolidMechanics (SIERRA/SM) finite element code. Cohesive surface elements were used to model crack initiation and propagation along predefined paths. Mesh convergence was observed with SIERRA/SM for numerous geometries. As the funding for this project came from the Advanced Simulation and Computing Verification and Validation (ASC V&V) focus area, considerable effort was spent performing verification and validation. Code verification was performed to compare code predictions to analytical solutions for simple three-element simulations as well as a higher-fidelity simulation of a double-cantilever beam. Parameter identification was conducted with Dakota using experimental results on asymmetric double-cantilever beam (ADCB) and end-notched-flexure (ENF) experiments conducted under Campaign-6 funding. Discretization convergence studies were also performed with respect to mesh size and time step and an optimization study was completed for mode II delamination using the ENF geometry. Throughout this verification process, numerous SIERRA/SM bugs were found and reported, all of which have been fixed, leading to over a 10-fold increase in convergence rates. Finally, mixed-mode flexure experiments were performed for validation. One of the unexplained issues encountered was material property variability for ostensibly the same composite material. Since the variability is not fully understood, it is difficult to accurately assess uncertainty when performing predictions.

Brown, Arthur A.↗

Wedgehog Manual and Interface Guide, Jayenne-7_0_0

Wedgehog is an IMC package developed by the CCS–2’s Monte Carlo Team1 . Wedgehog is designed to interface with a time-split radiation-hydrodynamics (rad-hydro) code and supports one-dimensional R, two-dimensional RZ or three dimensional XY Z geometry. The geometry is confined to logically rectangular Adaptive Mesh Refinement (AMR) meshes with unit aspect ratios and 2:1 refinement between adjacent cells. Wedgehog supports both two and three temperature simulations. Available scattering models for photon-electron interaction include Compton and isotropic scattering. It maintains a census of particles in between time steps to preserve the contents of the radiation field. Wedgehog can accommodate frequency dependence by using a “Multigroup” (MG) approximation that essentially averages the frequency-dependent opacity information into discrete bins. Additionally, Wedge hog includes a capability to use Opacity Distribution Factors (ODFs) that may be generated with the XCP-5 code TOPS. A previous version of Wedgehog that utilizes IBM’s Cell chip is available for the Roadrunner petascale computer at Los Alamos National Laboratory (circa 2006-2013, estimated). However, as Roadrunner is going out of service in the near future, we have dropped support for the interfaces that were deprecated in Jayenne 6 4 0 and removed in Jayenne-7 0 0. The Roadrunner version had the same interface as the mainline code and is available in RZ and XYZ geometry with all the same features except for flux tallies across a surface (i.e., tally sphere and RZ line-segment).

79 ASTRONOMY AND ASTROPHYSICS↗

A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

In this work, we propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.

97 MATHEMATICS AND COMPUTING↗