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At least 793 records · Page 44

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DOE OSTI2024

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Furthermore, adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Controlling quantum many-body dynamics in driven Rydberg atom arrays

Dynamic stabilization of an array Large-scale systems comprising one-dimensional chains and two-dimensional arrays of excited atoms held in a programmable optical lattice are a powerful platform with which to simulate emergent phenomena. Bluvstein et al. built an array of up to 200 Rydberg atoms and subjected the system to periodic excitation. Under such driven excitation, they found that the array of atoms stabilized, freezing periodically into what looked like time crystals. Understanding and controlling the dynamic interactions in quantum many-body systems lies at the heart of contemporary condensed matter physics and the exotic phenomena that can occur. Science , this issue p. 1355

Science & Technology - Other Topics↗

NASA NTRS1989

Generation of circumferential velocity contours associated with pulsed point suction on a rotating disk

Numerous experimental studies were conducted on the steady, three-dimensional boundary layer over a disk rotating at constant angular speed in an otherwise undisturbed fluid. The subject flow geometry is of interest because it provides a relatively simple way to study the cross-flow instability phenomenon which occurs in three-dimensional boundary layers, as on swept wings. This flow instability results in the formation of a stationary spiral vortex flow field over the disk, as shown by Wilkinson and Malik. Using a hot-wire probe, the spatial wave pattern of stationary vortices, which filled the entire circumference of the disk was mapped. The subject flow instability caused transition-to-turbulent flow as the periphery of the disk was approached. The effect on receptivity and transition of discrete disturbance modes, such as three-dimensional toughness elements and acoustic excitation was investigated. The present study (an extension of the work of Wilkinson and Malik) is focused on the effect of pulsed point suction on flow instability and transition, and consequently, on the classical stationary vortical flow pattern.

Selby, Gregory V.↗

NASA NTRS2011

Evaluating the Application of Multi-Satellite Observations in Hydrologic Modeling

When monitoring local or regional hydrosphere dynamics for applications such as agricultural productivity or drought and flooding events, it is necessary to have accurate, high-resolution estimates of terrestrial water and energy storages. Though in-situ observations provide reliable estimates of hydrologic states and fluxes, they are only capable of accurately capturing the dynamics at relatively discrete points in space and time, which makes them inadequate for characterizing the variability of the water budget across scales. In contrast, satellite-based remote sensing is ideal for providing observations of hydrological states and fluxes because it provides spatially-distributed observations at spatial and temporal scales required for regional land surface process modeling. Due to the continued progress in algorithm development and emerging satellite technology, we now have near-real time monitoring of several components of the water cycle including precipitation, soil moisture, lake and river height, terrestrial water storage, snow cover, and evapotranspiration. As these data become more readily available, their application to hydrologic modeling is becoming more common, however there remains little consensus on the most appropriate method for optimal integration and evaluation in regard to hydrological applications. Here we present two case studies operationally applying several remotely sensed products from AMSR-E, GRACE, and MODIS and discuss assimilation strategies, ease of integration and interpretation, and methods for quantifying the success of the application methodology.

Bolten, John↗

DOE OSTI2020

Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

The discrete ordinates discontinuous Galerkin (SN-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind SN-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original SN-DG method, the low-memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in the scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. Finally, for both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2019

Effect of Spatial Filtering in Implicit Large-Eddy Simulations of Separated Flows

The relatively high Reynolds number of turbulent flows encountered in various applications puts these problems well beyond the reach of direct numerical simulation (DNS) at present. Meanwhile, lower-fidelity Reynolds-averaged Navier-Stokes (RANS) calculations are known to be not accurate enough in complex problems, such as smooth-body flow separation and other flows involving highly-unsteady phenomena. Hence, given the current infeasibility of DNS and the unsatisfactory performance of RANS, intermediate techniques such as large-eddy simulation (LES) and hybrid RANS-LES, whose fidelity lie between RANS and DNS, have received much attention for application to various problems of practical importance. Modeling of the effect of missing scales on resolved scales, also known as subgrid-scale (SGS) modeling, is an important subject for LES. SGS models can be broadly categorized as explicit or implicit approaches. The explicit approach is based on an SGS model that explicitly appears in the governing equations expressed in the form of so-called “filtered Navier-Stokes equations”, which describe the evolution of the turbulence scales resolved by the LES grid. The effect of the scales unresolved by the grid is represented by the SGS model. The implicit modeling approach, on the other hand, does not employ an explicit model but instead treats the intrinsic dissipation of the numerical discretization scheme as an implicit SGS model. An LES without an explicit SGS model is commonly termed as an implicit LES (ILES). The relative merits of one SGS modeling approach over another is a subject of ongoing debate. We have opted to employ an ILES methodology, based on high-order compact finite-difference and spatial filtering schemes, in our recent investigations of separated flow problems [1, 2]. Further discussion of our preference of ILES over explicit LES is provided in Uzun and Malik [2]. The spatial filtering operation, described in the next section, is treated as an implicit SGS model for the ILES. Some observations made during the course of our recent investigations, which pointed out to excessive numerical dissipation in certain parts of the flowfield, prompted us to take a closer look at the potential effect of the spatial filter on ILES predictions. This technical note is therefore devoted to spatial filter effects in the context of a high Reynolds number, transonic shock-induced separated flow.

Ali Uzun↗

DOE OSTI2025

Coupled cluster and dislocation dynamics modeling of microstructure evolution in irradiated materials

We develop here a coupled cluster and dislocation dynamics framework to study the microstructure evolution of irradiated materials. The framework not only accounts for the three dimensional diffusion of radiation-generated clusters, but also their interaction with dislocation networks and the resultant climb motion of discrete dislocations within finite crystals. The framework is solved with a superposition solution scheme, and is applied to investigate the evolution of the irradiation-induced dislocation loops in zirconium (Zr), considering the effects of various bias factors including the diffusion anisotropy difference (DAD) of interstitials and interstitial clusters, the dislocation bias of defects to discrete dislocation segments, and the production bias of defects from the radiation cascade. We find that the DAD is the most critical factor influencing the kinetics of the loop evolution in Zr, while the recombination/interaction of mobile defects can induce a strong spatial dependence of the loop evolution together with the DAD. Here, the method is also adopted to study the evolution of interstitial $\langle$a$\rangle$ and vacancy $\langle$c$\rangle$ dislocation loop ensembles consistent with the microstructure observed during irradiation-induced growth of Zr. Our findings not only reveal the spatial dependence of the size and ellipticity of the dislocation loops, but also suggest a limit on the anisotropy factor of interstitials to reproduce the co-growth of $\langle$a$\rangle$ and $\langle$c$\rangle$ loops in zirconium, in good agreement with experimental observations and other simulation results.

Bias factors↗

DOE OSTI2021

A field–particle correlation analysis of a perpendicular magnetized collisionless shock

Using the field–particle correlation technique, we examine the particle energization in a three-dimensional (one spatial dimension and two velocity dimensions; 1D-2V) continuum Vlasov–Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field–particle correlation technique with the high-fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons arising from the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov–Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field–particle correlation technique to spacecraft measurements of collisionless shocks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1987

Deriving surface albedo measurements from narrow band satellite data

A target calibration procedure for obtaining surface albedo from satellite data is presented. The methodology addresses two key issues, the calibration of remotely-sensed, discrete wavelength, digital data and the derivation of an albedo measurement (defined over the solar short wave spectrum) from spectrally limited observations. Twenty-seven Landsat observations, calibrated with urban targets (building roof-tops and parking lots), are used to derive spatial and seasonal patterns of surface reflectance and albedo for four land cover types: city, suburb, farm and forest.

Brest, Christopher L.↗

NASA NTRS1993

Time-accurate Navier-Stokes calculations with multigrid acceleration

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.

Melson, N. Duane↗

NASA NTRS1996

Multigrid Acceleration of Time-Accurate Navier-Stokes Calculations

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is fully implicit in time and is unconditionally stable (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability. This is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. A multigrid-multiblock, steady-state, three-dimensional Navier-Stokes solver, TLNS3D, was modified to iteratively invert the equations at each physical time step. The implementation of this procedure in TLNS3D is discussed. The implications of applying several popular turbulence models to unsteady flow are also considered. Numerical results are presented to show the application of the scheme to various two-dimensional turbulent flows. The results of a three-dimensional laminar flow calculation are also given.

Melson, N. Duane↗

NASA NTRS2006

The Use of RGPS Kinematic Data to Estimate Nonlinear Sea Ice Motion

In current simulations of the interaction between sea ice and its environment, large significance is placed on the deformation of the sea ice. Sea ice deformation is an important process in determining the sea ice thickness distribution across a wide range of space and time scales. Changes in the sea ice thickness distribution affect energy and mass fluxes between the atmosphere and ocean and also the strength of the ice. While most current ice models assume linear variation in the ice motion field to calculate strain, deformation of sea ice occurs through the opening, closing and shearing of ice along discrete linear features. New numerical models are being developed which explicitly account for discontinuities in ice motion, and the need for requisite data sets for model validation has emerged. Multiple buoy data sets, as well as satellite data, have been used to examine the movement and deformation of sea ice. Generally it has been found that the ice motion field has been represented well by buoy data, as well as satellite data over a broad range of scales. However, the underlying deformation (spatial variation in displacement) as represented by different data sets may vary. For the work presented here, sea ice motion In current simulations of the interaction between sea ice and its environment, large significance is placed on the deformation of the sea ice. Sea ice deformation is an important process in determining the sea ice thickness distribution across a wide range of space and time scales. Changes in the sea ice thickness distribution affect energy and mass fluxes between the atmosphere and ocean and also the strength of the ice. While most current ice models assume linear variation in the ice motion field to calculate strain, deformation of sea ice occurs through the opening, closing and shearing of ice along discrete linear features. New numerical models are being developed which explicitly account for discontinuities in ice motion, and the need for requisite data sets for model validation has emerged. Multiple buoy data sets, as well as satellite data, have been used to examine the movement and deformation of sea ice. Generally it has been found that the ice motion field has been represented well by buoy data, as well as satellite data over a broad range of scales. However, the underlying deformation (spatial variation in displacement) as represented by different data sets may vary. For the work presented here, sea ice motio

Pruis, M.↗

DOE OSTI2021

Tailoring plasticity mechanisms in compositionally graded hierarchical steels fabricated using additive manufacturing

Abstract While there exists in nature abundant examples of materials with site-specific gradients in microstructures and properties, engineers and designers have traditionally used monolithic materials with discrete properties. Now, however, additive manufacturing (AM) offers the possibility of creating structures that mimic some aspects of nature. One example that has attracted attention in the recent years is the hierarchical structure in bamboo. The hierarchical architecture in bamboo is characterized by spatial gradients in properties and microstructures and is well suited to accommodate and survive complex stress states, severe mechanical forces, and large deformations. While AM has been used routinely to fabricate functionally graded materials, this study distinguishes itself by leveraging AM and physical metallurgy concepts to trigger cascading deformation in a single sample. Specifically, we have been successful in using AM to fabricate steel with unique spatial hierarchies in structure and property to emulate the structure and deformation mechanisms in natural materials. This study shows an improvement in the strength and ductility of the nature-inspired “hierarchical steel” compared with conventional cast stainless steels. In situ characterization proves that this improvement is due to the sequential activation of multiple deformation mechanisms namely twinning, transformation-induced plasticity, and dislocation-based plasticity. While significantly higher strengths can be achieved by refining the chemical and processing technique, this study sets the stage to achieve the paradigm of using AM to fabricate structures which emulate the flexibility in mechanical properties of natural materials and are able to adapt to in-service conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Operator dynamics in Floquet many-body systems

We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025

Yoshimura, Takato (ORCID:0000000309159846)↗

NASA NTRS1986

Parameter estimation problems for distributed systems using a multigrid method

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Taasan, S.↗

NASA NTRS1990

Parameter estimation problems for distributed systems using a multigrid method

Ta'asan, Shlomo↗

NASA NTRS1993

An adaptive multigrid model for hurricane track prediction

This paper describes a simple numerical model for hurricane track prediction which uses a multigrid method to adapt the model resolution as the vortex moves. The model is based on the modified barotropic vorticity equation, discretized in space by conservative finite differences and in time by a Runge-Kutta scheme. A multigrid method is used to solve an elliptic problem for the streamfunction at each time step. Nonuniform resolution is obtained by superimposing uniform grids of different spatial extent; these grids move with the vortex as it moves. Preliminary numerical results indicate that the local mesh refinement allows accurate prediction of the hurricane track with substantially less computer time than required on a single uniform grid.

Fulton, Scott R.↗