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At least 1,711 records · Page 95

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DOE OSTI2017

A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

Here we present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code

A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

A Full Multigrid Method for the Self-Adjoint Angular Flux Equation Based on Cellwise Block Jacobi Iteration

Previous work by Densmore et al. has demonstrated that multigrid methods for the self-adjoint angular flux (SAAF) equation with cellwise block Jacobi smoothing can be extremely effective at solving for the angular flux in one dimension. The extension of that work to two dimensions demonstrated that while the smoother works well, the use of a direct coarse-grid approximation can severely limit the rate of convergence for optically thin cells. In that paper, this convergence limit was evaded through the use of a partially Galerkin coarse-grid approximation. However, relying on a Galerkin coarse-grid approximation is not ideal as constructing the coarse-grid discretization in this approach is complicated. The motivation for this summary is to find a method that can work without the need for a Galerkin coarse-grid approximation. The Full Multigrid (FMG) method is well known as a method that can theoretically solve a problem to its discretization accuracy with optimal linear computational complexity, that is in just O(N) operations for N unknowns. Indeed, we develop an FMG method for the 2-D SAAF equation that yields discretization accuracy and does not require the use of a Galerkin coarse-grid approximation. Until recently, aside from proofs about the order of the error for FMG, little work had been done in quantifying when and how FMG can obtain discretization accuracy. However, recent work by Rodrigo et al. has introduced a Fourier analysis technique called worst-case right-hand side analysis used to calculate the FMG accuracy measure. The FMG accuracy measure is the upper bound on the constant of proportionality between the error of the FMG solution and the discretization error. In this summary, we develop and implement an FMG method for the 2-D Cartesian SAAF equations. We then perform worst-case right-hand side analysis and give numerical examples that demonstrate under what circumstances the method can solve the 2-D SAAF equations to discretization accuracy, for optically thin cells, without the need for a Galerkin coarse-grid approximation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

CUDO: closed-form universal dwell-time optimization for computer-controlled optical surfacing

Precision optical figuring demands fast and accurate dwell time optimization to reach nanometer- and sub-nanometer-level accuracy in next-generation optical systems. We introduce CUDO (closed-form universal dwell-time optimization), the first, to the best of our knowledge, unified closed-form analytical framework that supports both function-form and matrix-form dwell time models in computer-controlled optical surfacing (CCOS). In contrast to traditional methods, which rely on iterative optimization and hyperparameter tuning, our framework derives direct analytical solutions with no adjustable parameters. This approach unifies the solution principles of existing methods within a single mathematical model, delivering three key advantages: (1) accuracy on par with, or superior to, iterative solvers, (2) substantial reduction in computation time, and (3) numerical robustness. Comparative studies with prior art confirm that closed-form solutions achieve equivalent residual error while removing runtime bottlenecks. By simplifying the implementation and enabling real-time, scalable deployment, CUDO establishes a practical foundation for future deterministic fabrication of large-aperture and high-performance optics.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Improvements of the boundary projection acceleration technique applied to the discrete-ordinates transport solver in XYZ geometries

In this paper we discuss the latest upgrades of the Boundary Projection Acceleration (BPA) applied to the XYZ transport solver of APOLLO3, namely IDT. The acceleration method is a well-known effective technique for the speed-up of the source iterations of the discrete-ordinates method. The BPA in IDT has been improved in three aspects: the taking into account of the residue on boundary conditions as a boundary source for the acceleration problem, the extension of the method to higher order angular moments in the case of anisotropic scattering and, finally, the application of the method to the multigroup iterations for the acceleration of the fission source and k-effective. The spectrum of the method has been Fourier-analyzed to explore the effectiveness. The 3D mock-up geometry of the ZPPR is presented as final study to test the performances of the acceleration on a realistic whole-core 3D calculation. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Planetary Boundary Layer Height derived from MPL data using Sawyer-Li method

Sawyer and Li (2013) developed a technique to derive the PBL height from micropulse lidar (MPL) backscatter measurements using combined wavelet covariance transform and iterative curve-fitting methods. The wavelet covariance transform method applies a Haar wavelet function to MPL backscatter signals (Brooks et al., 2003).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

SU-E-T-175: Clinical Evaluations of Monte Carlo-Based Inverse Treatment Plan Optimization for Intensity Modulated Radiotherapy

Purpose: Pencil-beam or superposition-convolution type dose calculation algorithms are routinely used in inverse plan optimization for intensity modulated radiation therapy (IMRT). However, due to their limited accuracy in some challenging cases, e.g. lung, the resulting dose may lose its optimality after being recomputed using an accurate algorithm, e.g. Monte Carlo (MC). It is the objective of this study to evaluate the feasibility and advantages of a new method to include MC in the treatment planning process. Methods: We developed a scheme to iteratively perform MC-based beamlet dose calculations and plan optimization. In the MC stage, a GPU-based dose engine was used and the particle number sampled from a beamlet was proportional to its optimized fluence from the previous step. We tested this scheme in four lung cancer IMRT cases. For each case, the original plan dose, plan dose re-computed by MC, and dose optimized by our scheme were obtained. Clinically relevant dosimetric quantities in these three plans were compared. Results: Although the original plan achieved a satisfactory PDV dose coverage, after re-computing doses using MC method, it was found that the PTV D95% were reduced by 4.60%–6.67%. After re-optimizing these cases with our scheme, the PTV coverage was improved to the same level as in the original plan, while the critical OAR coverages were maintained to clinically acceptable levels. Regarding the computation time, it took on average 144 sec per case using only one GPU card, including both MC-based beamlet dose calculation and treatment plan optimization. Conclusion: The achieved dosimetric gains and high computational efficiency indicate the feasibility and advantages of the proposed MC-based IMRT optimization method. Comprehensive validations in more patient cases are in progress.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2012

Domain decomposition for the SPN solver MINOS

In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

WE-AB-207A-03: A CBCT Head Scanner for Point-Of-Care Imaging of Intracranial Hemorrhage

Purpose: This work reports the design, development, and first technical assessment of a cone-beam CT (CBCT) scanner developed specifically for imaging of acute intracranial hemorrhage (ICH) at the point of care, with target applications in diagnosis and monitoring of traumatic brain injury, stroke, and postsurgical hemorrhage. Methods: System design employed a task-based image quality model to quantify the influence of factors such as additive noise and high-gain (HG) detector readout on ICH detectability. Three bowtie filters with varying bare-beam attenuation strength and curvature were designed to enable HG readout without detector saturation, and a polyenergetic gain correction was developed to minimize artifacts from bowtie flood-field calibration. Image reconstruction used an iterative penalized weighted least squares (PWLS) method with artifact correction including Monte Carlo scatter estimation, Joseph-Spital beam hardening correction, and spatiotemporal deconvolution of detector glare and lag. Radiation dose was characterized for half-scan and full-scan protocols at various kV, and imaging performance was assessed in a head phantom presenting simulated ICH with diameter ranging 2–12 mm. Results: The image quality model guided system design and was validated by measurements on a CBCT imaging bench. Compared to low-gain readout without a bowtie filter, the combination of HG readout and a modest bowtie improved the contrast-to-noise ratio (CNR per unit square-root dose) by 20% in the center of the image but degraded noise performance near the periphery (20% reduction in CNR). Low-frequency bowtie artifacts (∼100 HU magnitude) were corrected by the polyenergetic gain correction. Image reconstructions on the prototype scanner demonstrate clear visibility of the smallest ICH insert (2 mm diameter) in both HG readout (with a bowtie) and dual-gain readout (without bowtie). Conclusion: Technical assessment of the prototype scanner suggests the capability for reliable visualization of small (2 mm), low-contrast (50 HU) ICH at <20 mGy dose and motivates translation to clinical studies, now underway. Xiaohui Wang and David Foos (co-authors) are employees of Carestream Health. Research funding support from Carestream Health.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including a real utility network, show good scalability on different computing architectures.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2013

A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation

The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltzmann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable iteration scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2009

Optimization of OT-MACH Filter Generation for Target Recognition

An automatic Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter generator for use in a gray-scale optical correlator (GOC) has been developed for improved target detection at JPL. While the OT-MACH filter has been shown to be an optimal filter for target detection, actually solving for the optimum is too computationally intensive for multiple targets. Instead, an adaptive step gradient descent method was tested to iteratively optimize the three OT-MACH parameters, alpha, beta, and gamma. The feedback for the gradient descent method was a composite of the performance measures, correlation peak height and peak to side lobe ratio. The automated method generated and tested multiple filters in order to approach the optimal filter quicker and more reliably than the current manual method. Initial usage and testing has shown preliminary success at finding an approximation of the optimal filter, in terms of alpha, beta, gamma values. This corresponded to a substantial improvement in detection performance where the true positive rate increased for the same average false positives per image.

false alarm reduction↗

DOE OSTI2025

Comprehensive analysis of disruption mitigation methods using gas and pellet-like injections in ITER-like Tokamaks

Abstract Inert-gas shielding could be an effective mechanism for protection of plasma facing surfaces (PFS) against plasma particles impact and photon radiation heat loads during transient events in fusion devices. Neutral gas injection is one promising way to mitigate erosion of tokamak components and contamination. The objective of this work is to study and optimize mitigation methods using neutral gas and pellet-like injections to decrease the heat load to the divertor surfaces and to prevent vaporization of the various internal surfaces due to transient events in ITER-like devices. The integrated self-consistent models implemented in the HEIGHTS package was used for detailed analysis of the potential secondary plasma generation from the injected inert gas, its radiative characteristics, and shielding effectiveness. We varied the density, size, and location of an argon gas cloud to minimize the disruption energy deposited into the divertor components. We also investigated innovative ways for minor changes in ITER-like internal design to mitigate disruptions. We found the optimum parameters to fully protect ITER tokamak surfaces from erosion and vaporization during plasma instabilities. This preliminary analysis showed that using Ar gas injection methods could lead to enhancement in components lifetime in ITER-like and future DEMO devices with minor design changes.

Science & Technology - Other Topics↗

NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗

DOE OSTI2016

Fourier Analysis of the Multilevel QD Method with {alpha}-Approximation For Time-Dependent Radiative Transfer Problems

Thermal radiation transfer (TRT) problems describe interaction of photon radiation with matter. They are defined by the time-dependent radiative transfer (RT) equation for the specific intensity I coupled with the energy balance (EB) equation. This class of problems is characterised by high dimensionality, multiple scales and strong nonlinearity. In this paper we analyze the multilevel quasi-diffusion (QD) method for solving TRT problems. This is a nonlinear method of moments with exact closures. The QD method enables one to reduce dimensionality of the original radiative transfer problem. It is formulated by a nonlinear system of equations consisting of (i) the high-order RT (HORT) equation for the intensity of photon radiation and (ii) low-order equations for the angular and energy moments of the intensity. The nonlinear closures are formulated by means of stable factors. The low-order problem brings the radiative transfer model to the level of multi-physics equations. The multilevel QD (MLQD) method possesses attractive features for efficient multi-physics coupling. To calculate the high-order RT solution we apply the {alpha}-approximation which assumes that the intensity changes exponentially in time over a time step. The {alpha}-approximation leads to the steady-state RT equation with a modified opacity and enables one to avoid storing the high-dimensional solution from the previous time step. The rate of change is evaluated by the solution of the time-dependent low-order QD (LOQD) equations for moments. We note that the HORT equation in the {alpha}-approximation contains an extra nonlinear term. It affects the iterative behaviour of the MLQD method. The obtained computational results indicated that the rate of convergence is slower compared to the rate when the time-dependent HORT is used to calculate the intensity. In this paper we perform an iterative stability analysis of the MLQD method in a discretized form and analyze convergence of outer (transport) iterations on a time step. We consider multigroup TRT problems in 1D slab geometry. The fully implicit scheme is used to discretize equations in time. The HORT equation is approximated with the method of step characteristics. A finite volume method is applied for spatial discretization of multigroup LOQD equations. The grey (one-group) LOQD equations are algebraically consistent with the multigroup LOQD equations. To perform Fourier analysis a model TRT problem in an infinite homogeneous medium is considered. The system of nonlinear equations of the MLQD method is linearized near an equilibrium solution at some given temperature. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Effect of contrast enhancement prior to iteration procedure on image correction for soft x-ray projection microscopy

Soft X-ray microscopy is well recognized as a powerful tool of high-resolution imaging for hydrated biological specimens. Projection type of it has characteristics of easy zooming function, simple optical layout and so on. However the image is blurred by the diffraction of X-rays, leading the spatial resolution to be worse. In this study, the blurred images have been corrected by an iteration procedure, i.e., Fresnel and inverse Fresnel transformations repeated. This method was confirmed by earlier studies to be effective. Nevertheless it was not enough to some images showing too low contrast, especially at high magnification. In the present study, we tried a contrast enhancement method to make the diffraction fringes clearer prior to the iteration procedure. The method was effective to improve the images which were not successful by iteration procedure only.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Chord length sampling method for analyzing VHTR unit cells in continuous energy simulations

The chord length sampling method (CLS) is studied in the continuous energy simulations by applying it to analyzing two types of Very High Temperature Gas-cooled Reactor (VHTR) unit cells: the fuel compact cell in the prismatic type VHTR and the fuel pebble cell in the pebble-bed type VHTR. Infinite multiplication factors of the unit cells are calculated by the CLS and compared to the benchmark simulations at different volume packing fractions from 5% to 30%. It is shown that the accuracy of the CLS is affected by the boundary effect, which is induced by the CLS procedure itself and results in a reduction in the total volume packing fraction of the fuel particles. To mitigate the boundary effect, three correction schemes based on the research of 1) Murata et al. 2) Ji and Martin 3) Griesheimer et al. are used to improve the accuracy by applying a corrected value of the volume packing fraction to the CLS. These corrected values are calculated based on 1) a simple linear relationship, 2) an iterative self-consistent simulation correction method, and 3) a theoretically derived non-linear relationship, respectively. The CLS simulation using the corrected volume packing fraction shows excellent improvements in the infinite multiplication factors for the VHTR unit cells. Ji and Martin's self-consistent correction method shows the best improvement. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2019

Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity

Efficient and accurate poroelasticity models are critical in modeling geophysical problems such as oil exploration, gas-hydrate detection, and hydrogeology. We propose an efficient operator splitting method for Biot’s model of linear poroelasticity based on fixed-point iteration and constrained stress. In this method, we eliminate the constraint on time step via combining our fixed-point approach with a physics-based restraint between iterations. Three different cases are considered to demonstrate the stability and consistency of the method for constant and variable parameters. The results are validated against the results from the fully coupled approach. In case I, a single iteration is used for continuous coefficients. The relative error decreases with an increase in time. In case II, material coefficients are assumed to be linear. In the single iteration approach, the relative error grows significantly to 40% before rapidly decaying to zero. This is an artifact of the approximate solutions approaching the asymptotic solution. The error in the multiple iterations oscillates within 10 − 6 before decaying to the asymptotic solution. Nine iterations per time step are enough to achieve the relative error close to 10 − 7 . In the last case, the hybrid method with multiple iterations requires approximately 16 iterations to make the relative error 5 × 10 − 6 .

Delgado, Paul M.↗