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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Large-scale parametric modeling of spent nuclear fuel dynamics in the 30 cm package drop scenario

Packages used to transport spent nuclear fuel (SNF) are required by the U.S. Code of Federal Regulations 10 CFR 71.71 to demonstrate satisfactory performance during a drop scenario. While the CFR is meant to ensure safe package function, it does not evaluate survival of the SNF within. The U.S. Department of Energy Spent Fuel and Waste Science and Technology program is working on closing the knowledge gap related to the response of SNF to external mechanical loads, including the hypothetical 30 cm package drop scenario in the CFR. In support of this effort, LS-DYNA finite element simulations were developed by Pacific Northwest National Laboratory (PNNL) to model generic drop scenarios at both the package and fuel assembly level. The models were validated against one-third scale package and full scale fuel assembly drop test data and were exercised to predict fuel cladding strains in a narrow range of model configurations. This work describes a large-scale parametric study conducted by PNNL using the previously developed and validated PWR finite element model, with the addition of a new generic BWR assembly model. The motivation for the parametric study was to characterize the broad range of SNF responses in the 30 cm package drop scenario. This was accomplished by varying the drop orientation, fuel assembly type (17x17 PWR and 10x10 BWR), burnup, cladding temperature, spacer grid buckling load, package mass, impact limiter stiffness, and mechanical gap conditions within the basket. A MATLAB framework was developed to automate LS-DYNA model generation and execution on PNNL institutional computing resources. In total, over 2000 simulations were performed. For each simulation, the SNF response was quantified in terms of permanent grid deformation, fuel rod contact pressure, and strains within the fuel rods, guide tubes, and water rods. The results provide valuable insight into the range of responses that could be reasonably expected from SNF in the hypothetical drop scenario, as well as the sensitivity to each input parameter. The results of this parametric study are a key component of the testing and modeling strategy the Spent Fuel and Waste Science and Technology program is using to close the external loads knowledge gap.

Kadooka, Kevin↗
DOE OSTI2021

Spent Nuclear Fuel Mechanical Loads in the General Package Drop Scenario

The US Department of Energy Spent Fuel and Waste Science and Technology program is performing research to determine the mechanical loading conditions applied to spent nuclear fuel (SNF) during normal conditions of transportation to inform mechanical tests of SNF and close an important knowledge gap related to the practical disposition of SNF in the US. A recent multi-national collaborative test campaign measured SNF assembly impact response to the 30 cm horizontal package drop scenario, which is a common regulatory basis test of SNF package design. Researchers at Pacific Northwest National Laboratory (PNNL) are using the test data to validate explicit finite element models to calculate the mechanical loads and structural response of spent nuclear fuel assemblies in the as-tested 30 cm horizontal package drop scenario. Once the as-tested package drop model is validated, the next step is to apply the model to the general 30 cm drop scenario, which includes all impact angles, all fuel assembly types, and all burnup conditions. PNNL is developing a damage model that will incorporate the results of finite element parametric studies to establish trends in SNF mechanical loading to various input parameters, like impact orientation and burnup. The damage model will have the capability to estimate mechanical loads for any single set of input parameters, but it will first be used to describe the upper bounds of potential SNF loading in the 30 cm drop scenario. This paper describes PNNL’s progress toward developing the general solution to the problem of spent nuclear fuel mechanical loads in the 30 cm package drop scenario and it describes the next steps in closing the knowledge gap.

Klymyshyn, Nicholas A.↗
DOE OSTI2022

A novel post-processing method for progressive failure analysis of brittle composite compression

Finite element analysis of brittle materials in axial compression typically uses element deletion to allow continued global deformation post-element-failure. However, element deletion produces cyclic load-displacement curves that underestimate energy absorption and are not representative of a continuum system. Two key observations support the conclusion that results from an appropriately discretized model can be an adequate representation of a continuum system. Specifically, the frequency of the oscillations in the load-displacement curve is directly dependent upon element length in the loading direction, and the peak amplitudes of oscillations are mesh size independent. A method of post-processing the analysis results, by connecting the peak amplitudes of oscillations, is proposed and applied to a series of continuous carbon fiber composite crush tubes. The load-displacement curve, stable crushing load, and specific energy absorption of the post-processed results compare well to an experimental study of crush tubes with similar layups.

Materials Science↗
DOE OSTI2021

Mechanical Loads on Spent Nuclear Fuel in the General 30 cm Package Drop Scenario

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) Spent Fuel and Waste Science & Technology (SFWST) research program is guided by the high-level goal of closing prioritized knowledge gaps related to spent nuclear fuel (SNF) storage and transportation, which are summarized by Saltzstein et al. (2020). One of the high-priority knowledge gaps is the identification and quantification of mechanical loads that are expected to affect SNF during normal conditions of transportation and storage to inform the range of physical SNF test programs. This report uses modeling and analysis methods to estimate the mechanical loads on spent nuclear fuel (SNF) in the general 30 cm package drop scenario. The drop scenario assumes impact limiters are in place in the transportation configuration and the impact surface is perfectly rigid. The goal of this analysis is to consider the universe of potential mechanical loading conditions that can happen to SNF and present the results in a manner that is useful for materials testing, decision making, and regulatory rule making purposes. This study uses validated finite element models and methods to perform a broad parametric study of key variables that can affect the mechanical loads on SNF during a hypothetical package free drop scenario. Physical drop test data from a cask and fuel assembly drop test campaign is the basis for model validation. Additionally, the results of the parametric study are used to inform a damage model, which uses multiple nonlinear regression to estimate the relationships between input variables and output response. The parametric finite element analyses consider thousands of input variable combinations, while the damage model estimates millions of combinations. The breadth of this study provides confidence that the potential range of mechanical loads that SNF might experience during the general 30 cm package drop scenario are characterized well enough to consider this knowledge gap closed. While this report documents the overall peak values calculated in this study, the 95 th percentile values, the histograms, and the observed trends are equally important. This study covered a large range of SNF temperatures, room temperature to 300°C, and burnups, 10 GWd/MTU to 62 GWd/MTU. Each temperature and burnup combination has a different cladding yield strain, so it is more meaningful to summarize the calculated cladding strain response as its factor of safety, which is defined relative to the yield strain. The factor of safety is calculated as the yield strain divided by the peak cladding strain. A factor of safety greater than unity indicates that the cladding remains below yield, whereas a value less than unity is indicative of plastic deformation. In all cases of this study a safety factor over 1.0 was calculated, although in the most limiting case at 300°C the safety factor was only 1.01, which suggests that yielding could occur when additional loads like rod internal pressure are included. When the temperature is restricted to 200°C the limiting safety factor increases to 1.28, which has significant margin to accommodate internal pressure and potential local cladding defects that could cause a local stress concentration. An important trend in the calculated fuel rod mechanical loads is that the 2 nd highest loaded fuel rod in an assembly tends to be significantly lower than the highest loaded rod. The implication is that even if one rod in an assembly experiences a failure the loads would have to be significantly higher to cause two or more rods to fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Effect of Diphenyl Content on Viscoelasticity of Poly(dimethyl- co -diphenyl)siloxane Melt and Network

Polydimethylsiloxane (PDMS) is one of the most widely used polymeric materials for sealants, adhesives, lubricants, and thermal as well as electrical insulation. At low temperatures, however, PDMS is subject to crystallization that can cause deterioration in mechanical function. A common way to suppress such crystallization is through the incorporation of phenylsiloxane into the backbone of polysiloxane. Nevertheless, the introduction of phenyl components, even in small quantities, could potentially change the properties of the siloxane in a significant way. In this work, a series of mechanical tests and finite element simulations were performed to study the macroscale viscoelasticity of two poly(dimethyl-co-diphenyl)siloxane formulations in order to understand the effects of a few percent diphenyl contents on the viscoelasticity of the polysiloxane material. Here, we utilized the small-angle X-ray scattering to investigate the microscopic structures of the copolymers and broadband dielectric spectroscopy and rheology to probe the chain dynamics at the microscale. The results of these characterizations were used to inform the finite element simulations. We found that the degree of cross-linking does not significantly alter the microstructure but can profoundly affect the viscoelastic response of the copolymer networks. The corresponding hysteretic behavior is interpreted in terms of reptation-like motion and relaxation of the effective free chains in the cured polymer network. The relaxation of the copolymer chains is slowed significantly by even a small increase in the molar ratio of the diphenyl component.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Validation of high-fidelity ion cyclotron range of frequencies antenna coupling simulations in full 3D geometry against experiments in the ASDEX Upgrade tokamak

We address the validation of finite elements ion cyclotron range of frequencies (ICRF) antenna coupling simulation against experiments performed in the ASDEX Upgrade tokamak. Measurements of the loading resistance in ICRF-heated, magnetically-perturbed 3D plasma discharges are compared against numerical predictions of the RAPLICASOL code. To this end, the 3D induction field and the 3D density profile are modeled by concatenating the PARVMEC, BMW and EMC3-EIRENE codes. The 3D density is input to RAPLICASOL, where full-wave simulations are performed on a finite element mesh retaining full 3D geometry in the ICRF antenna model and the plasma description. The results are further compared with RAPLICASOL simulations using a 1D density profile as measured at the outboard midplane in the same experiments. We find that simulations using a 1D density profile overestimate the change in loading resistance by a factor of ~197 -248%, while simulations using the full 3D density profile are in agreement with experiments within a factor ~16%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Silicon Carbide Multilayer Piping for High Temperature sCO 2 Brayton Cycle

Efficiencies of greater than 50% in supercritical carbon dioxide (sCO 2 ) Brayton power cycle systems can be achieved only at turbine inlet temperatures of above 700°C. In support of the push to higher temperatures, a finite element model was developed by Materials Research & Design, Inc. (MR&D) with support from Ceramic Tubular Products, LLC. (CTP) to guide the refinement of CTP’s high temperature ceramic multilayer piping. The multilayer technology combines the advantages of a monolithic silicon carbide (SiC) tube and a SiOC f /SiOC ceramic matrix composite (CMC), the result of which is a material with high-temperature strength and stability, high mechanical and thermal shock resistance, and high corrosion resistance. In addition to fabricating test specimens to refine the finite element model, long-duration, high temperature CO 2 exposure tests were performed by Sandia National Laboratories (SNL) on two varieties of inner monolithic SiC.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Multiphysics modeling of printed surface acoustic wave thermometers

Surface acoustic wave (SAW) transducers are a class of sensors and actuators that operate on the fundamental principle of piezoelectricity. Aerosol jet printing and other additive manufacturing techniques have resulted in the low-cost fabrication of low-power and small-footprint SAW devices that are suitable for sensing in high-temperature and radioactive environments. In this work, we developed a series of temperature-dependent finite element models for a SAW transducer consisting of printed silver interdigitated transducers (IDTs) deposited onto piezoelectric lithium niobate. Modeling accuracy was evaluated experimentally from room temperature to 200 °C using an aerosol-jet-printed SAW thermometer. A time-domain study enabled visualization of the wave propagation and successfully guided the denoising of the scattering parameter measurement. Additionally, frequency-domain models using traditional modal analysis or the unique port boundary condition feature in COMSOL Multiphysics accurately predicted the temperature-driven natural frequency drift in the SAW thermometer. The finite element models developed in this study serve to facilitate the computer-aided design of future SAW transducers for applications in harsh environments.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantifying the Impacts of Grain-scale Heterogeneity on Mechanical Response

Driven by the exceedingly high computational demands of simulating mechanical response in complex engineered systems with finely resolved finite element models, there is a critical need to optimally reduce the fidelity of such simulations. The minimum required fidelity is constrained by error tolerances on the simulation results, but error bounds are often impossible to obtain a priori. One such source of error is the variability of material properties within a body due to spatially non-uniform processing conditions and inherent stochasticity in material microstructure. This study seeks to quantify the effects of microstructural heterogeneity on component- and system-scale performance to aid in the choice of an appropriate material model and spatial resolution for finite element analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2021

SCEPTRE 2.2 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general- purpose C++ code for solving the li near Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates and spherical harmonics. Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Part y Libraries (TPL) to be available, and example scripts for building these TPLs are provided. The TPLs needed by SCEPTRE are Trilinos, boost, and netcdf. SCEPTRE uses an autotools build system , and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

SCEPTRE 2.1 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general purpose C++ code for solving the Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates and spherical harmonics. Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Party Libraries (TPL) to be available, and example scripts for building these TPL's are provided. The TPL's needed by SCEPTRE are Trilinos, boost, and netcdf. SCEPTRE uses an autoconf build system, and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

SCEPTRE 2.3 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general- purpose C++ code for solving the linear Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates (Sn) and spherical harmonics (Pn). Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Party Libraries (TPL) to be available, and example scripts for building these TPL are provided. The TPL needed by SCEPTRE are Trilinos, Boost, and Netcdf. SCEPTRE uses an autotools build system, and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Long range frequency chirping of Alfvén eigenmodes

In this work, a theoretical framework has been developed for an NBI scenario to model the hard non-linear evolution of global Alfvén eigenmodes (GAEs) where the adiabatic motion of phase-space structures (holes and clumps), associated with frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements, which allows an update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper action-angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the non-linear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of the finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long-range adiabatic frequency sweeping events observed for Alfvén gap modes in real experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

THERMAL STRESS ANALYSIS OF A SPENT NUCLEAR FUEL CANISTER

The potential for chloride induced stress corrosion cracking (CISCC) in spent nuclear fuel dry storage canisters is a current topic of research by the US Department of Energy Spent Fuel and Waste Science and Technology program. One of the important prerequisites for CISCC is a tensile residual stress state. This study utilizes computational models to provide an initial analysis of thermal stresses in a generic spent nuclear fuel canister. A STAR-CCM+ thermal fluid model provides a temperature profile analysis of the canister based on four different ambient temperature conditions. An ANSYS APDL finite element model incorporates the temperature profiles to analyze the thermal stresses in the canister. The calculated thermal stress magnitudes are in the range of 10 MPa to 80 MPa, which could be significant for crack propagation through the canister wall. The maximum thermal stress is not a concern for the structural failure of the canister, but it is high enough that it is a significant contribution to the total stress state of the canister wall, which also includes residual stress from fabrication, internal pressure from helium cover gas, and potential transient mechanical loads, such as earthquakes. This paper describes the initial finite element thermal stress analysis that was completed in 2020, reports the initial findings, and identifies areas where model refinement is still needed to complete this work in the future.

Jensen, Ben J.↗
DOE OSTI2025

Macro-micro multiscale modeling to assist the design of HPDC Al castings microstructure and alloys for EV super-large body structures (Phase 1)

Implementation of High Pressure Die Casting (HPDC) Aluminum (Al) body structures for high volume electrified vehicles (EV) to improve electric efficiency remains a key strategy within many original equipment manufacturer (OEM)s. In addition to high strength for safety requirements, superior Self-Piercing Riveting (SPR) performance is demanded for HPDC Al alloys to be compatible with high volume SPR joining. In this work, it is proposed to extend and validate an existing Contractor finite element multiscale macro-micro modeling approach to quantify the influence of the microstructure of HPDC alloys on the fracture strain/displacement under 3-point bend and clinch testing. The success of this work will allow to replace solution treatment stage with low energy consumption heat treatment (HT) processes, or to design new non heat treatable (NHT) HPDC Al alloys to eliminate HT requirements. Ultimately, this project will facilitate the application of HPDC Al alloys for super-large vehicle structures to significantly reduce vehicle weight, and thus improving energy efficiency. The purpose of this project is to extend and validate an existing finite element code, which is based on the Contractor developed macro-micro multi-scale modeling approach, to numerically simulate the three-point bending and clinch test and study the influences of material microstructural characteristics and phase properties on the rivetability. The macro-micro modeling approach begins with a sample scale model and identify the location, which is mostly prone to failure, the deformation history of the boundaries of that location calculated will be used to drive a microstructure-based sub-models where the material microstructure and microscale properties are considered. Using this approach, the wrap-bending failure for two Al alloys are correctly predicted for the first time. This will start with phase I effort of building a framework of macro-micro three point bending test and clinch test of Al10SiMgMn HPDC alloy in the as-cast and T7 heat treated conditions. Those results will then be validated with experimental test results. The phase II effort will involve the utilization of the knowledge learned in phase I to establish the quantitative correlation between the microstructure characteristics and the riveting performance, which will be further used to guide the optimization of HPDC Al alloy microstructure using heat treatment process to achieve sufficient rivetability to join large thin-wall HPDC alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Interface capturing simulations of bubble population effects in PWR subchannels

As the computational power of high-performance computing (HPC) facilities grows, so too does the feasibility of using first principle based simulation to study turbulent two-phase flows within complex pressurized water reactor (PWR) geometries. Direct numerical simulation (DNS), integrated with an interface capturing method, allows for the collection of high-fidelity numerical data using advanced analysis techniques. The research presented here employs the massively parallel, finite-element based, unstructured mesh code, PHASTA, to simulate a set of two-phase bubbly flows through PWR subchannel geometries including auxiliary structures (spacer grids and mixing vanes). The main objective of the presented work is to analyze bubble dynamics and turbulence interactions at varying bubble concentrations to support the development of advanced two-phase flow closure models. Turbulent two-phase flows in PWR subchannels were simulated at hydraulic Reynolds numbers of 81,000 with bubble concentrations of 3%–15% by gas volume fraction (768–3928 resolved bubbles, respectively) and compared against a 1% void fraction case (262 bubbles) that had been previously simulated. The finite element mesh utilized for the study at higher bubble concentrations was composed of 1.55 billion elements, compared to the previous study which employed 1.11 billion elements, ensuring all turbulence scales and individual bubbles within the flow are fully resolved. For each case, the resolved initial bubble size was 0.65 mm in diameter (resolved with 25 grid points across the diameter). The simulations were analyzed to find flow features such as the mean velocity profile, bubble relative velocity and the effect of the bubbles on the turbulent conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Autonomous Inversion of In Situ Deformation Measurement Data for Injection-Induced Stress Change

Geologic carbon storage (GCS) is likely to play a key part of the global effort to dramatically reduce CO2 emissions and perhaps even reduce atmospheric CO2 concentrations through carbon negative operations. A critical part of effort to commercialize and widely deploy this technology is developing the capability to rapidly assimilate real-time monitoring data into a form that will enable site operators to make decisions to manage the safe and efficient operations. Two of the risks associate with GCS are the risk of inducing fractures in the sealing formations that can create leakage pathways and the risk of inducing earthquakes of sufficient magnitude to cause public concern, property damage, or safety risks. To properly manage these risks the site operator needs to know the initial state of stress, the change in stress induced by injection, and the relationship between operational parameters such as injection rate and pressure and the change in stress. Current methods of estimating the change in stress require choosing the type of constitutive model and the model parameters based on core, log, and geophysical data during the characterization phase, with little feedback from operational observations to validate or refine these choices. These characterization methods interrogate the geologic formations using length scales, loading rates or magnitudes that are quite different from those encountered by the actual storage system. It is shown that errors in the assumed constitutive response, even when informed by laboratory tests on core samples, are likely to be common, large, and underestimate the magnitude of stress change caused by injection. Recent advances in borehole-based strain instruments and borehole and surface-based tilt and displacement instruments have now enabled monitoring of the deformation of the storage system throughout its operational lifespan. This data can enable validation and refinement of the knowledge of the geomechanical properties and state of the system, but brings with it a challenge to transform the raw data into actionable knowledge. We demonstrate a method that uses automatic differentiation and a finite-element based geomechanical model perform a gradient-based deterministic inversion of geomechanical monitoring data. This approach allows autonomous integration of the instrument data without the need for time consuming manual interpretation and selection of updated model parameters. Furthermore, only isotropic linear elasticity is considered in this paper, the approach presented is very flexible as to what type of geomechanical constitutive response can be used. The approach is easily adaptable to nonlinear physics-based constitutive models to account for common rock behaviors such as creep and plasticity. The approach also enables training of machine learning-based constitutive models by allowing back propagation of errors through the finite element calculations. This enables strongly enforcing known physics, such as conservation of momentum and continuity, while allowing data-driven models to learn the truly unknown physics such as the constitutive or petrophysical responses.

Burghardt, Jeffrey A.↗