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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 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Reduction of discretization error for ray tracing of MOC through a correction on collision probabilities

A new correction model for ray tracing of the method of characteristics is proposed in order to reduce discretization error. As the ray tracing parameters such as azimuthal angle division, polar angle division and ray separation are considered in this study. In the method of characteristics, region average scalar fluxes can be implicitly expressed by collision probabilities, although these collision probabilities are not directly treated in the ordinary calculation scheme. From this viewpoint, difference between a coarse ray tracing condition and a detailed one can be interpreted as the difference in the estimation of collision probabilities. In other words, the discretization error for ray tracing can be recognized as a consequence of inaccurate collision probabilities caused by coarse ray tracing. This discussion suggests that accurate region average scalar flux can be obtained through an appropriate correction on collision probabilities. In this paper, a correction model on collision probabilities is theoretically derived based on the neutron balance equation, and its validity is confirmed through typical single assembly calculations. The effectiveness of the present correction method is also discussed in this paper. It is confirmed that discretization error for ray tracing can be significantly reduced by the present correction method in a multi-assembly calculation, though the correction factor is estimated in single assembly geometry. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Nonperturbative analysis of field theories quantized on the light cone (Final Scientific Report for ER41087)

The primary focus of the work was the development of methods for the nonperturbative solution of quantum chromodynamics (QCD) in a form that yields wave functions for the eigenstates, from which hadronic properties can be computed. The principal approach was to use a light-front Hamiltonian formulation. In light-front coordinates, t+z/c plays the role of time, with t the ordinary time, z a space direction, and c the speed of light. This leads to a relativistic formulation that retains useful characteristics of nonrelativistic treatments. A bound state of many constituents can be represented by wave functions that define probabilities for each possible arrangement of internal momenta. These functions satisfy integral equations that can be approximated numerically to yield a matrix representation. The matrix problem can be solved by iterative methods. The approximate wave functions can then be used to compute properties of the bound state. Methods have been developed for model theories and gauge theories, including quantum electrodynamics and theories that are supersymmetric. The work has required the development of new numerical algorithms and computer codes for singular integral equations and eigenvalue problems. A key aspect of the work is the construction of practical procedures for nonperturbative regularization and renormalization. Two methods of regularization have been studied. One is the addition of heavy Pauli--Villars (PV) particles to the Lagrangian, with their metrics and couplings tuned to provide the necessary cancellations in the regularization. The other method of regularization is the addition of supersymmetric partners, to extend a theory to a supersymmetric form. The supersymmetric theories were solved by the supersymmetric discrete light-cone quantization (SDLCQ) method. The most significant accomplishments of the project were the SDLCQ calculation of direct evidence for a Maldacena duality conjecture, construction of a practical light-front quantization for QED in an arbitrary covariant gauge, and invention of the light-front coupled-cluster method, designed to eliminate the need for Fock-space truncations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2000

Simulation studies of vestibular macular afferent-discharge patterns using a new, quasi-3-D finite volume method

A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.

NASA Center ARC↗
DOE OSTI2014

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2017

Electromagnetic Scattering by Spheroidal Volumes of Discrete Random Medium

We use the superposition T-matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing non-sphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.

Electromagnetic scattering; Multi-particle groups;↗
NASA NTRS2003

Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results

The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.

Gogos, George↗
DOE OSTI2019

Ceramic nuclear fuel fracture modeling with the extended finite element method

Ceramic fuel pellets used in nuclear light water reactors experience significant fracture due to the high thermal gradients experienced under normal operating conditions. This has important effects on the performance of the fuel system. Because of this, a realistic, physically based fracture modeling capability is essential to predict fuel behavior in a wide variety of normal and off-normal conditions. The extended finite element method (X-FEM) is a powerful method to represent arbitrary propagating discrete cracks in finite element models, and has many characteristics that make it attractive for nuclear fuel performance analysis. This paper describes the implementation of X-FEM in a multiphysics fuel performance code and presents applications of that capability. These applications include several thermal mechanics fracture benchmark problems, which demonstrate the accuracy of this approach. It also includes application of this capability to study nuclear fuel fracture, both on stationary and propagating cracks. The study on stationary cracks shows the effects that varying the number of radial cracks and the length of those cracks have on the energy release rate. Here, the propagating crack case demonstrates random initiation and subsequent propagation of interacting thermally induced cracks during an initial ramp to full power with fresh fuel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1983

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques and a problem adaptive computational algorithm are presented for predicting the nonlinear steady state temperature distribution in structures and solids. In the proposed techniques, the structure is discretized by using the finite element method. The vector of nodal temperatures is then expressed as a linear combination of a small number of global temperature modes (or basis vectors), and the Bubnov Galerkin technique is used to compute the amplitudes of the global modes. The global temperature modes (or basis vectors) are chosen to include the various order derivatives of the nodal temperature vector with respect to preselected path parameter(s). The potential of the proposed reduction methods for solution of large scale, nonlinear thermal problems is discussed and the effectiveness of the methods is demonstrated by means of numerical examples, including steady state conduction, convection, and radiation modes of heat transfer.

Noor, A. K.↗
DOE OSTI2013

Spatially Varying Embedded Stochastic Galerkin Methods for Steady-State PDEs

Existing discretizations for stochastic PDEs, based on a tensor product between the deter ministic basis and the stochastic basis, treat the required resolution of uncertainty as uniform across the physical domain. However, solutions to many PDEs of interest exhibit spatially localized features that may result in uncertainty being severely over or under-resolved by existing discretizations. In this report, we explore the mechanics and accuracy of using a spatially varying stochastic expansion. This is achieved through an adaptive refinement algorithm where simple error estimates are used to independently drive refinement of the stochastic basis at each point in the physical domain. Results are presented comparing the accuracy of the adaptive techinque to the accuracy achieved using uniform refinement.

Cyr, Eric C.↗
NASA NTRS1987

Variational approach to probabilistic finite elements

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗
NASA NTRS1991

Variational approach to probabilistic finite elements

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗
NASA NTRS2016

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Diosady, Laslo T.↗
DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes

We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h{sup 2}) convergence of the scalar flux on orthogonal, random, and multi-level meshes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Evaluating Methods for Measuring Grid Frequency in Low-Inertia Power Systems: Preprint

Accurate measurement of grid frequency is a critical component of reliable grid control. Traditionally, methods such as phase locked loops (PLLs) and discrete Fourier transforms (DFTs) have been used in inverters and phasor measurement units (PMUs) to measure frequency. However, as the percentage of inverter-based resources (IBRs) such as solar and wind has increased, these conventional frequency measurement methods are proving unable to guarantee reliable control in some cases. One challenge is measuring frequency during transient events, where there is a disruption in the steady state sinusoidal voltage. During these events, the underlying frequency of the grid may barely change, but measurement methods report a large spike in frequency due to the disrupted waveform. New methods must balance between suppressing spikes in frequency during faults, and providing fast, accurate, measurements in all other grid operation conditions, especially during events with high rate-of-change-of frequency (ROCOF), which are more prevalent in high-IBR power systems. This paper first surveys frequency measurement methods that have been proposed to reduce measurement errors during transient events. Then, both conventional and more novel frequency measurement methods are tested against an IEEE standard and industry recommendations, and their performance is evaluated for events simulated in PSCAD. Results quantify the trade-offs in performance during different grid conditions and lead to suggestions for the most appropriate frequency and ROCOF measurement methods for low inertia grids.

frequency↗
DOE OSTI2014

WE-A-17A-04: Development of An Ultra-Fast Monte Carlo Dose Engine for High Dose Rate Brachytherapy

Purpose: Current clinical brachytherapy dose calculations are based on AAPM TG43 guidelines, which approximate the patient geometry as a large water phantom. This ignores heterogeneities and tends to overestimate skin dose. Although Monte Carlo (MC) dose calculations have been recognized as the most accurate method, its associated long computational time is a major bottleneck for routine clinical applications. This work aims to develop a GPU-based ultra-fast MC dose engine (gBMC) for HDR brachytherapy to provide clinical users with accurate sub-minute dose calculations. Methods: Standard photon transport with discrete events including: Compton scattering, Rayleigh scattering and Photoelectric effect, was implemented. Secondary electrons were transported under the continuous slowing down approximation. To reduce the GPU thread divergence, photons and electrons were separately transported. Transport of photons was grouped according to energy. The source model in gBMC can be either a phase-space file generated using Geant4 or a parameterized source model. This dose engine was validated against TG43 in a water phantom and against Geant4 calculations in heterogeneous patient geometries. Results: A phase space file was generated for the Varian VS2000 Ir-192 source. In a water phantom, the calculated radial dose function was within 0.6% of the TG43 calculations for radial distances from 1 cm to 20 cm. The anisotropy functions were within 1% for radial distances from 1 cm to 20 cm except for polar angles larger than 173°. Local point-dose differences were within 2%. In a Mammosite breast cancer case with 22 dwell locations, gBMC and Geant4 isodose lines compared well. The computation time was about 28 seconds using the phase-space file source and 20 seconds using the parameterized source to simulate 1 billion particles, yielding less than 1% statistical uncertainty. Conclusion: The gBMC dose engine makes it possible to use fast and accurate MC dose calculations for clinical work.

60 APPLIED LIFE SCIENCES↗