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At least 127 records · Page 7

A hybrid adaptive multiresolution approach for the efficient simulation of reactive flows

Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR codes. In this work a novel hybrid adaptive multiresolution (HAMR) approach to AMR-based calculations is introduced to address this issue. The multiresolution (MR) smoothness indicators are used to identify regions of smoothness on the mesh where the computational cost of individual physics solvers may be decreased by replacing direct calculations with interpolation. We suggest an approach to balance the errors due to the adaptive discretization and the interpolation of physics quantities such that the overall accuracy of the HAMR solution is consistent with that of the MR-driven AMR solution. The performance of the HAMR scheme is evaluated for a range of test problems, from pure hydrodynamics to turbulent combustion.

97 MATHEMATICS AND COMPUTING↗

Improved Creep Testing Approach for Bentonite EBS

In the United States, the nuclear reactor contributes 18.7 percent of the nation’s total electricity generation and produces a significant amount of spent nuclear fuel (SNF) and high-level waste. Because SNF is being stored for longer periods than initially envisioned, the U.S. Department of Energy Office of Nuclear Energy, Office of Spent Fuel and Waste Science and Technology is assessing the technical performance of the SNF storage systems after extended durations. The concept of a sustainable geologic repository for SNF disposal relies heavily on the safety provided by multiple barriers, such as repository host rock, overlying rock formation, and human-made engineered barrier systems (EBS). One of the major components of EBS is bentonite-based buffer materials that isolate the nuclear-waste canisters from the host rock and fill the void left in the horizontally drilled boreholes. The resaturated bentonite has a swelling characteristic, which is useful for self-sealing the microcracks in the host rock and supporting the canister’s heavy weight. However, factors such as nonuniformity in the saturation, swelling pressure of bentonite, and the high temperature at the canister-bentonite interface may lead to instability of the waste canister inside the borehole. Therefore, evaluating the long-term deformation of bentonite-based material is necessary. RESPEC Company, LLC recently completed a preliminary study for the U.S. Department of Energy (DE SC0022804) that is attempting to understand the time-dependent deformation in the consolidated sand/bentonite (SB) specimens through triaxial creep experiments and improve the understanding of EBS performance under anticipated repository conditions. The project included developing a standard testing procedure for preparing the consolidated core specimen from a mixture of sand and bentonite in a 50:50 ratio by weight, fabricating a new pressure vessel in-house, modifying existing creep equipment to perform triaxial creep experiments on consolidated SB specimens, and performing six long-term triaxial creep experiments under low-deviatoric stress at two different temperature conditions, which is representative of hypothetical conditions that might be encountered in a geologic repository within a reasonable rate of success in completing creep experiments. The consolidated SB specimen was prepared using the novel specimen preparation procedure and had physical characteristics (e.g., moisture content and bulk density) reasonably comparable with the properties of bentonite-based buffer, which is proposed to be used in the EBS in the Swedish KBS-3H design and the Swiss design of SNF disposal in the horizontal drifts. The newly fabricated pressure vessel could withstand the confining pressure of up to 15 megapascals (MPa) while maintaining the test temperature of up to 90 degrees Celsius (°C) for long-term creep experiments. The preliminary results from the triaxial creep experiments suggested that the consolidated SB specimen may experience time-dependent deformation at a low-deviatoric stress state and room temperature condition. Based on the deformation recorded in the SB specimen from axial and radial linear variable differential transformers (LVDTs) and physical characteristic changes, it is apparent that the time-dependent deformation is a combination of consolidation and creep, which is influenced by the level of deviatoric stresses and temperature. The systematic creep testing of bentonite-based specimens helped develop a standard testing procedure applicable for analyzing the similar characteristics of shale or clay-like materials in different geologic conditions outside repository science, including in civil engineering and infrastructure projects, underground and open pit mining, and deep drilling.

58 GEOSCIENCES↗

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems

Physics-informed neural network (PINN) is a data-driven approach to solving equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization approximates a multiscale equation by a homogenized equation without multiscale property; it includes solving cell problems and the homogenized equation. The cell problems are periodic, and we propose an oversampling strategy that significantly improves the PINN accuracy on periodic problems. The homogenized equation has a constant or slow dependency coefficient and can also be solved by PINN accurately. We hence proposed a 3-step method, neural homogenization based PINN (NH-PINN), to improve the PINN accuracy for solving multiscale problems with the help of homogenization.

97 MATHEMATICS AND COMPUTING↗

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Goad, Clyde C.↗

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗

Dynamics of electrified liquid metal surface using shallow water model

A shallow water model that incorporates surface tension and electric field effects is developed to investigate the dynamics of an electrified liquid surface. The computational model is verified against the Zakharov–Kuznetsov equation and is applied to study the growth and damping of the electrified liquid surface. A linear wave analysis is performed under a shallow water theory assuming an analytic solution of the electric field, similar to the Tonks–Frenkel instability. The electrified liquid surface grows or dampens based on the balance of the electric field, surface tension, and gravitational forces. As a result, the numerical results obtained from the electrified shallow water solver are in good agreement with the theoretical analysis.

Computational models↗

Multiple ferroelectric nematic phases of a highly polar liquid crystal compound

Ferroelectric nematic liquid crystals represent not only fascinating, fundamental science, but they also hold promise for new technologies including high-density power storage or sub-millisecond switching information displays. In this work, we describe the synthesis and measurements of the physical properties of a new compound, 4-nitrophenyl 4-[(2,4-dimethoxylbenzoyl)oxy]-2-fluorobenzoate (RT11001). This material exhibits multiple, highly polar, ferroelectric nematic phases that have not been previously reported. Here we employ a wide range of physical characterisation methods including differential scanning calorimetry (DSC), mass density measurement, optical birefringence, polarising optical microscopy (POM), dielectric spectroscopy, electric current analysis, electro-optical switching, small-angle and wide-angle x-ray scattering measurements to show that RT11001 has multiple, distinct ferroelectric phases. We argue that the highest temperature phase is a polar nematic fluid with non-polar smectic clusters. Directly below appears to be a transition to another polar nematic phase containing polar positionally ordered clusters. Lastly, there are indications of an additional, polar biaxial liquid crystal phase at lower temperatures.

36 MATERIALS SCIENCE↗

An infrasound source analysis of the OSIRIS-REx sample return capsule hypersonic re-entry

The OSIRIS-REx sample return capsule's hypersonic re-entry into the atmosphere is a rare opportunity to test a variety of sonic boom source models since the projectile dimensions are well characterized. While the as-flown flight path is unknown, the predicted flight path enables a rough approximation of the source Mach number and location. Six infrasound microphones deployed in the boom carpet along the predicted flight path recorded impulsive signals from the OSIRIS-REx re-entry. Using a suite of atmosphere profiles and the geometric acoustics approximation, we estimate locations with uncertainty estimates along the flight path from which the signals were emitted. Acoustic overpressure and signal duration predictions from Whitham's far field theory, Carlson's simplified sonic boom prediction method, and a drag-dominated hypersonic model are analyzed with uncertainty estimates from the location estimate. While the Carlson simplified sonic boom prediction method could be accurate, our preference is for the drag-dominated source model. Using this source model with an inviscid Burgers's equation solver for propagation, we obtained an excellent match to the recorded data. In conclusion, these results will help better inform future sample return capsule re-entry observation campaigns as well as contribute to a better understanding of high altitude infrasonic sources.

58 GEOSCIENCES↗

Marmot V2

MARMOT is a robust numerical tool for mesoscale modeling of fuel performance developed under the NEAMS Fuels technical area to predict the coevolution of microstructure and properties in fuel and cladding materials. MARMOT accomplishes this using the phase field method coupled with finite strain mechanics and heat conduction. MARMOT is based on the open source Multiphysics Object-Oriented Simulation Environment (MOOSE) and solves the coupled partial differential equations defining the physics using the finite element method. MARMOT is being developed in order to facilitate the development of improved materials models for fuel performance, but it is also being developed as a powerful tool in and of itself for the simulation of mesoscale fuel performance.

Aagesen, LarryK.↗

Determining Stellar Elemental Abundances from DESI Spectra with the Data-driven Payne

Abstract Stellar abundances for a large number of stars provide key information for the study of Galactic formation history. Large spectroscopic surveys such as the Dark Energy Spectroscopic Instrument (DESI) and LAMOST take median-to-low-resolution (R≲ 5000) spectra in the full optical wavelength range for millions of stars. However, the line-blending effect in these spectra causes great challenges for elemental abundance determination. Here we employDD-Payne, a data-driven method regularized by differential spectra from stellar physical models, to the DESI early data release spectra for stellar abundance determination. Our implementation delivers 15 labels, including effective temperatureT eff , surface gravity log g , microturbulence velocityv mic , and the abundances for 12 individual elements, namely C, N, O, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, and Ni. Given a spectral signal-to-noise ratio of 100 per pixel, the internal precisions of the label estimates are about 20 K forT eff , 0.05 dex for log g , and 0.05 dex for most elemental abundances. These results agree with the theoretical limits from the Crámer–Rao bound calculation within a factor of 2. The majority of the accreted halo stars contributed by the Gaia–Enceladus–Sausage are discernible from the disk and in situ halo populations in the resultant [Mg/Fe]–[Fe/H] and [Al/Fe]–[Fe/H] abundance spaces. We also provide distance and orbital parameters for the sample stars, which spread over a distance out to ∼100 kpc. The DESI sample has a significantly higher fraction of distant (or metal-poor) stars than the other existing spectroscopic surveys, making it a powerful data set for studying the Galactic outskirts. The catalog is publicly available.

Astronomy & Astrophysics↗

On the integrability cases of the equation of motion for a satellite in an axially symmetric gravitational field.

Investigation of two cases of integrability of a second-order differential equation describing the projection of an axisymmetric satellite orbit on to a plane perpendicular to the rotation axis. It is demonstrated that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the classical plane eikonal equation of geometric optics.

Ghaffari, A.↗

Two-demensional analysis of heat and mass transfer in porous media using the strongly implicit procedure

Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.

Curry, D. M.↗

Mesh generation using algebraic techniques

The solution of partial differential equations which describe physical phenomena by the use of coordinate transformations is described. The constraints of the problems are stated in geometric terms and include boundary constraints, uniformity constraints, and internal constraints. Algebraic mesh generations are very satisfactory for these constraints.

Eiseman, P. R.↗

Partitioning and packing mathematical simulation models for calculation on parallel computers

The development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system is described. Degrees of parallelism (i.e., coupling between the equations) and their impact on parallel processing are discussed. The problem of identifying computational parallelism within sets of closely coupled equations that require the exchange of current values of variables is described. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. An algorithm which packs the equations into a minimum number of processors is also described. The results of the packing algorithm when applied to a turbojet engine model are presented in terms of processor utilization.

Arpasi, D. J.↗

Mathematical model partitioning and packing for parallel computer calculation

This paper deals with the development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system. The identification of computational parallelism within the model equations is discussed. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. Next, an algorithm which packs the equations into a minimum number of processors is described. The results of applying the packing algorithm to a turboshaft engine model are presented.

Arpasi, Dale J.↗

Partitioning And Packing Equations For Parallel Processing

Algorithm developed to identify parallelism in set of coupled ordinary differential equations that describe physical system and to divide set into parallel computational paths, along with parts of solution proceeds independently of others during at least part of time. Path-identifying algorithm creates number of paths consisting of equations that must be computed serially and table that gives dependent and independent arguments and "can start," "can end," and "must end" times of each equation. "Must end" time used subsequently by packing algorithm.

Arpasi, Dale J.↗