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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Digital Rock Studies of Tight Porous Media

This technical report summarizes some recently developed approaches to studies of rock properties at a pore scale. Digital rock approach is complementary to laboratory and field studies. It can be especially helpful in situations where experimental data are uncertain, or are difficult or impossible to obtain. Digitized binary images of the pore geometries of natural rocks obtained by different imaging techniques are the input data. Computer-generated models of natural rocks can be used instead of images in a case where microtomography data are unavailable, or the resolution of the tools is insufficient to adequately characterize the features of interest. Simulations of creeping viscous flow in pores produce estimates of Darcy permeability. Maximal Inscribed Spheres calculations estimate two-phase fluid distribution in capillary equilibrium. A combination of both produce relative permeability curves. Computer-generated rock models were employed to study two-phase properties of fractured rocks, or tight sands with slit-like pores, too narrow to be characterized with micro-tomography. Various scenarios can simulate different fluid displacement mechanisms, from piston-like drainage to liquid dropout at the dew point. A finite differences discretization of Stokes equation is developed to simulate flow in the pore space of natural rocks. The numerical schemes are capable to handle both no-slip and slippage flows. An upscaling procedure estimates the permeability by subsampling a large data set. Capillary equilibrium and capillary pressure curves are efficiently estimated with the method of maximal inscribed spheres both an arbitrary contact angle. The algorithms can handle gigobytes of data on a desktop workstation. Customized QuickHull algorithms model natural rocks. Capillary pressure curves evaluated from computer-generated images mimic those obtained for microtomography data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Neutronics/Thermal-hydraulics coupling with RMC and CTF for BEAVRS benchmark calculation

As the computational accuracy required for design and safety analysis of current and future nuclear reactors is continuously increasing, high fidelity numerical reactor simulations including different physics raise wide concern of researchers. The interplay between neutronic and thermal-hydraulic (N-TH) effects of a nuclear reactor core plays an important role in reactor design, safety analysis and core performance. Monte Carlo method can provide high fidelity neutronics analysis of different nuclear reactors, owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. Armed with the massively parallel algorithms, the computational cost of Monte Carlo codes can be greatly reduced. Compared to single channel thermal process, sub-channel codes have enormous advantages of detailed modeling of full-core reactor or single assembly and high accuracy of calculation results. Detailed sub-channel modeling of a full-core also needs running in parallel, otherwise the computational cost will be relatively high. In this paper, a new hybrid coupling with continuous-energy Monte Carlo code RMC and the sub-channel code CTF has been developed. The coupling codes are applied to steady-state simulations of BEAVRS benchmark in hot full power condition. In order to deal with the temperature dependence of cross sections for Monte Carlo code, the on-the-fly cross sections treatment has been developed in RMC. The on-the-fly method was applied to the N-TH coupling in this work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Fast and Accurate Intersections on a Sphere

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.

Environmental sciences↗
DOE OSTI2022

A mathematical assessment of the isolation random forest method for anomaly detection in big data

We present the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection, proposed by Liu F.T., Ting K.M. and Zhou Z. H. in their seminal work as a heuristic method for anomaly detection in Big Data. We prove that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved, using the Law of Large Numbers. Here, a couple of counterexamples are presented to show that the method is inconclusive and no certificate of quality can be given, when using it as a means to detect anomalies. Hence, an alternative version of the method is proposed whose mathematical foundation is fully justified. Furthermore, a criterion for choosing the number of sampled trees needed to guarantee confidence intervals of the numerical results is presented. Finally, numerical experiments are presented to compare the performance of the classic method with the proposed one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Preliminary Design of the TEX-MOX Criticality Experimental Program using Optimization Algorithms Implemented in the IRSN PROMETHEE Tool

In the frame of its missions, IRSN is widely involved in design, evaluation and analyses of critical experiments in order to contribute to computer codes and nuclear data validation. The work described in this paper was carried out in the framework of the PRINCESS IRSN research project and is part of the IRSN/LLNL collaboration on the TEX program in the frame of the NCSP. The need for epithermal and intermediate energy range critical benchmarks is an established international criticality safety data need, underpinned by the subsequent use of data assimilation methods like GLLSM to reduce Nuclear Data uncertainties. The goal of the TEX program is to address this need by executing experiments with NCSP fissile assets, which can be used to create critical assemblies that span a wide range of fission energy spectra, from the thermal energy range (below 0.625 eV), through the intermediate energy range (0.625 eV to 100 keV), to the fast one (above 100 keV). The TEX program involves different materials of interest, such as TEX-Ta experiments using plutonium ZPPR plates proposed by LLNL. This paper presents an overview of the studies performed at IRSN using numerical optimization algorithms for the design of critical experiments involving Mixed U and Pu fuel plates, referred to as TEX-MOX program. This program ultimately aims to perform critical experiments to validate the MOX fuel configurations encountered in the MOX fuel fabrication process. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

A divergence-free constrained magnetic field interpolation method for scattered data

An interpolation method to evaluate magnetic fields, given its unstructured and scattered magnetic data, is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergence-free condition is incorporated as a constraint in the cost function, allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Finally, applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

A Dissipation-Based Method for Improving the Accuracy of Computational Fluid Dynamics Simulations of High Level Non-Newtonian Waste - 17351

Analysis of shear rate in dissipative scales of turbulence was performed using a quasi-direct numerical simulation (Q-DNS) of flow through a pipe involving Bingham fluid. Dependency of deformation rate on dissipative scales of turbulence was studied and a modification algorithm was developed and implemented in Reynolds-averaged Navier-Stokes (RANS) modeling of the same flow using the standard k-e model. It was shown that the modification was effective in increasing accuracy of the RANS simulations when the velocity profile was modified to match experimental data. In both the Q-DNS and RANS simulations, the Herschel-Bulkley (HB) rheology equation was used to relate shear stress of the non-Newtonian fluid to shear deformation. Additional analysis of dependency of shear on the turbulent dissipation rate (TDR) was performed using various flow conditions in RANS simulations with a modified viscosity model (alpha model). In the past, the alpha model has been shown to produce accurate simulations for the same flow conditions. Results of the analysis shows that a qualitative agreement exists between shear dependency in the RANS-alpha and Q-DNS-HB simulations when the ratio of velocity to length scale is used. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
DOE OSTI2014

A new solution for the 1D neutral particle transport equation in heterogeneous media - Paper 89

The equation of photon transport in directionally discretized 2N streams has been the subject of various numerical algorithms over the past 65 years since Chandrasekhar first explored the concept. The importance of this equation cannot be overemphasized, as it characterizes neutral particles (in this case photons) undergoing collisions as characterized by the scattering phase function in a 1D slab medium. More precisely, particles enter a homogeneous slab medium with the particle intensity distribution to be numerically determined. We find applications in light scattering for graphical rendering as well as deep penetration photon transport in a scattering medium as considered here. Noting the algebraic nature of the solution, numerous numerical attempts at an efficient algorithm have appeared in the literature-- many involving numerical linear algebra. Most notable are the Discrete Ordinates Method [DOM] of Stamnes and the Analytical Discrete Ordinates (ADO) method of Siewert as well as the Laplace Transform (LTSN) method of Vilhena. The methods are all centered on the determination of eigenvalues (or zeros of a polynomial in the case of the LTSN method) of a linear system enabling the solution to be represented as a sum of exponential eigenvectors. Because of the unstable nature of the solution, unless one takes care, such a representation leads to numerical catastrophe. Here, we derive an alternative form of solution to overcome this difficulty for application to deep penetration.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner

Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the large-scale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster.

42 ENGINEERING↗
DOE OSTI2017

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditioned $\ell^1$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Reduced‐cost sparsity‐exploiting algorithm for solving coupled‐cluster equations

We present an algorithm for reducing the computational work involved in coupled‐cluster (CC) calculations by sparsifying the amplitude correction within a CC amplitude update procedure. We provide a theoretical justification for this approach, which is based on the convergence theory of inexact Newton iterations. We demonstrate by numerical examples that, in the simplest case of the CCD equations, we can sparsify the amplitude correction by setting, on average, roughly 90% nonzero elements to zeros without a major effect on the convergence of the inexact Newton iterations.

Brabec, Jiri↗
DOE OSTI2023

Real-time control of connected vehicles in signalized corridors using pseudospectral convex optimization

Recent advances in Connected and Automated Vehicle (CAV) technologies have opened up new opportunities to enable safe, efficient, and sustainable transportation systems. However, developing reliable and rapid speed control algorithms in highly dynamic environments with complex inter-vehicle interactions and nonlinear vehicle dynamics is still a daunting task. In this paper, we develop a novel speed control method for CAVs to produce optimal speed profiles that minimize the fuel consumption and avoid idling at signalized intersections. To this end, an optimal control problem is formulated using the information of the upcoming traffic signal to adapt vehicles' speeds to avoid frequent stop-and-go driving patterns. Here, by applying the pseudospectral discretization method and the sequential convex programming method, the computational efficiency is greatly improved, enabling potential real-time on-vehicle applications. In addition, the algorithm is implemented under a model predictive control framework to ensure online control with instant response for collision avoidance and robust vehicle coordination. The proposed algorithm is verified through numerical simulations of three different traffic scenarios. The convergence and accuracy of the proposed approach are demonstrated by comparing with a popular nonlinear solver. Furthermore, the benefit of the proposed method in both traffic mobility and fuel efficiency is validated using the speed profile determined from a traffic following model in a simulation software as the baseline.

42 ENGINEERING↗
DOE OSTI2014

AHF: Array-Based Half-Facet Data Structure for Mixed-Dimensional and Non-Manifold Meshes

We present an Array-based Half-Facet mesh data structure, or AHF, for efficient mesh query and modification operations. The AHF extends the compact array-based half-edge and half-face data structures (T.J. Alumbaugh and X. Jiao, Compact array-based mesh data structures, IMR, 2005) to support mixed-dimensional and non-manifold meshes. The design goals of our data structure include generality to support such meshes, efficiency of neighborhood queries and mesh modification, compactness of memory footprint, and facilitation of interoperability of mesh-based application codes. To accomplish these goals, our data structure uses sibling half-facets as a core abstraction, coupled with other explicit and implicit representations of entities. A unique feature of our data structure is a comprehensive implementation in MATLAB, which allows rapid prototyping, debugging, testing, and deployment of meshing algorithms and other mesh-based numerical methods. We have also developed C++ implementation built on top of MOAB (T.J. Tautges, R. Meyers, and K. Merkley, MOAB: A Mesh-Oriented Database, Sandia National Laboratories, 2004). We present some comparisons of the memory requirements and computational costs, and also demonstrate its effectiveness with a few sample applications.

Dyedov, Volodymyr↗
DOE OSTI2011

Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.

97 MATHEMATICS AND COMPUTING↗