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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
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 OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗
DOE OSTI2021

Impoverishing Roots Will Improve Wheat Yield and Profitability Through Increased Water and Nitrogen Use Efficiencies

We report that more than a 60% increase in crop production is required by the 2050's to feed a growing world population. Understanding how plant functional traits and field management affect crop yields has the potential to improve agricultural productivity, minimize economic and environmental losses, and maximize food security. We explored the influence of winter wheat root characteristics and management on winter wheat growth, yield, and profit using a mechanistic and well-tested ecosystem and crop model, ecosys. We applied and further tested ecosys at an agricultural farm growing winter wheat in Ardmore, Oklahoma, United States. The model accurately predicted observed shoot carbon (R 2 = 0.95), soil moisture (R 2 = 0.67), soil temperature (R 2 = 0.91), and yield (percent error = 17%). Numerical optimization experiments were conducted to explore potential improvements of winter wheat yield and profit by modifying root characteristics, including root radius and root:shoot carbon transfer conductance, and fertilizer inputs. Our results show the potential for simultaneously improving winter wheat yields and profits. The optimum conditions were found to be in the range of root radius between 0.1 and 0.3 mm, carbon transfer conductance between 0.004 and 0.01 h -1 , and the currently applied fertilizer rate of 112 kg ha -1 . Under these conditions, improvements in yields and profits of up to approximately 25% and 110%, respectively, were modeled compared to those under baseline root traits. These improvements were achieved by impoverishing root structures, thereby increasing nutrient allocation to grains. Our results also demonstrate and motivate model structures that integrate the complex network of plant physiology, soil nutrient biogeochemistry, hydrology, and management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A simple solution to the Rietveld refinement recipe problem

Rietveld refinements are widely used for many purposes in the physical sciences. Conducting a Rietveld refinement typically requires expert input because correct results may require that parameters be added to the fit in the proper order. This order will depend on the nature of the data and the initial parameter values. A mechanism for computing the next parameter to add to the refinement is shown. The fitting function is evaluated with the current parameter value set and each parameter incremented and decremented by a small offset. This provides the partial derivatives with respect to each parameter, along with information to discriminate meaningful values from numerical computational errors. The implementation of this mechanism in the open-source GSAS-II program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Rapid Commissioning of Large Machine Tools Using Finite Element-Based Correction of Geometric Errors

Large computer numerical control (CNC) machine tools derive their stiffness from monolithic cast iron bases or weldments that are sometimes integral to machine motion systems like box ways or guideways. However, the sheer size of castings and even floor flatness deviations result in dimensional errors in these systems, which manifest as machine motion errors. Typical geometric alignment processes rely on an iterative approach, where measurements are taken to assess alignment (straightness, squareness, and parallelism), followed by adjustment of the machine supports (fixators or leveling pads), which can take weeks even for an experienced operator. Conversely, a novel method is proposed to shorten the correction time by eliminating the trial-and-error process in favor of a more deterministic approach guided by a finite element (FE) method. A feasibility study is conducted on a CNC polymer hybrid machine, with a steel weldment frame, supported by six leveling pads. An FE model of the frame is utilized to obtain recommended leveling pad adjustments, based on measurement of machine errors taken using a laser tracker. After a single adjustment cycle, measurements reveal that geometric errors of the machine tool are reduced from 2.22 mm of flatness deviation to 0.32 mm, achieving an 85.6% reduction. Furthermore, the entire process including measurement, adjustment, and assessment is completed in just 6 h by two operators who are not professional service engineers. In conclusion, this methodology demonstrates feasibility for scaling up, especially to large, high-precision CNC machine tools with bases mounted by fixators, offering the capability for bidirectional adjustment.

42 ENGINEERING↗
DOE OSTI2021

Five-day track forecast skills of WRF model for the western North Pacific tropical cyclones

In this study, the characteristics of simulated tropical cyclones (TCs) over the western North Pacific by a regional model (the WRF Model) are verified. We utilize 12-km horizontal grid spacing, and simulations are integrated for 5 days from model initialization. A total of 125 forecasts are divided into five clusters through the k-means clustering method. The TCs in the cluster 1 and 2 (group 1), which includes many TCs moving northward in the subtropical region, generally have larger track errors than for TCs in cluster 3 and 4 (group 2). The optimal steering vector is used to examine the difference in the track forecast skill between these two groups. The bias in the steering vector between the model and analysis data is found to be more substantial for group 1 TCs than group 2 TCs. The larger steering vector difference for group 1 TCs indicates that environmental fields tend to be poorly simulated in group 1 TC cases. Furthermore, the residual terms, including the storm-scale process, asymmetric convection distribution, or beta-related effect, are also larger for group 1 TCs than group 2 TCs. Therefore, it is probable that the large track forecast error for group 1 TCs is a result of unreasonable simulations of environmental wind fields and residual processes in the midlatitudes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1976

Numerical computation of transient coaxial entry tube flows

A numerical program was developed to compute transient laminar flows in two dimensions including multicomponent mixing and chemical reaction. The program can compute both incompressible flows and compressible flows at all speeds, and it is applied to describe transient and steady state solutions for low subsonic, coaxial entry, tue flows. Single component, nonreacting flows comprise most of the solutions, but one steady state solution is presented for trace concentration constituents engaging in a second order reaction. Numerical stability was obtained by adding at each calculation point a correction for numerical diffusion errors caused by truncation of the Taylor series used to finite difference the conservation equations. Transient computations were made for fluids initially at rest, then subjected to step velocity inputs that were uniform across each region of the entry plane and were held constant throughout the computation period. For center tube to annulus velocity ratios of 0.5 and 2.0, the bulk fluid in the tube initially moved in plug flow, but strong radial flows developed near the injection plane which moved the fluid into the high shear region between the jets and away from the tube wall.

Wieber, P. R.↗
NASA NTRS1982

Evaluation of SMART sensor displays for multidimensional precision control of Space Shuttle remote manipulator

An enhanced proximity sensor and display system was developed at the Jet Propulsion Laboratory (JPL) and tested on the full scale Space Shuttle Remote Manipulator at the Johnson Space Center (JSC) Manipulator Development Facility (MDF). The sensor system, integrated with a four-claw end effector, measures range error up to 6 inches, and pitch and yaw alignment errors within + or 15 deg., and displays error data on both graphic and numeric displays. The errors are referenced to the end effector control axes through appropriate data processing by a dedicated microcomputer acting on the sensor data in real time. Both display boxes contain a green lamp which indicates whether the combination of range, pitch and yaw errors will assure a successful grapple. More than 200 test runs were completed in early 1980 by three operators at JSC for grasping static and capturing slowly moving targets. The tests have indicated that the use of graphic/numeric displays of proximity sensor information improves precision control of grasp/capture range by more than a factor of two for both static and dynamic grapple conditions.

Bejczy, A. K.↗
NASA NTRS1982

Linear discriminant analysis with misallocation in training samples

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general appraoch to modeling of mislocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained and the asymptotic first two moments of the two types of error rate given. Certain numerical results for the error rates are presented by considering the random and two non-random misallocation models. It is shown that when the allocation procedure for training samples is objectively formulated, the effect of misallocation on the error rates of the Bayes linear discriminant rule can almost be eliminated. If, however, this is not possible, the use of Fisher rule may be preferred over the Bayes rule.

Chhikara, R.↗
NASA NTRS1986

Spline-based distributed system identification with application to large space antennas

A parameter and state estimation technique for distributed models is demonstrated through the solution of a problem generic to large space antenna system identification. Assuming the position of the reflective surface of the maypole (hoop/column) antenna to be approximated by the static two-dimensional, stretched-membrane partial differential equation with variable-stiffness coefficient functions, a spline-based approximation procedure is described that estimates the shape and stiffness functions from data set observations. For given stiffness functions, the Galerkin projection with linear spline-based functions is applied to project the distributed problem onto a finite-dimensional subspace wherein algebraic equations exist for determining a static shape (state) prediction. The stiffness functions are then parameterized by cubic splines and the parameters estimated by an output error technique. Numerical results are presented for data descriptive of a 100-m-diameter maypole antenna.

Banks, H. T.↗
NASA NTRS1987

Radial orbit error reduction and sea surface topography determination using satellite altimetry

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Engelis, Theodossios↗
NASA NTRS1985

Improved numerical methods for turbulent viscous recirculating flows

The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.

Turan, A.↗
NASA NTRS1986

Interface procedures for overlapping grids

The solution of partial differential equations by means of either implicit or conservative explicit finite-difference methods, on the one hand, or multicomponent overlapping grid schemes on the other, is presently subjected to interpolation at grid boundaries in an attempt to eliminate the time lag. The accuracy of the transient solution of a hyperbolic or parabolic partial differential equation is dependent on the procedures used to transfer information between grids in a composite grid system. The present techniques reduce numerical solution errors.

Mastin, C. Wayne↗