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At least 343 records · Page 19

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DOE OSTI2014

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm

The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell's equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper derives and solves the numerical dispersion relation for the PSATD algorithm and compares the results with corresponding behavior of the more conventional pseudo-spectral time-domain (PSTD) and finite difference time-domain (FDTD) algorithms. In general, PSATD offers superior stability properties over a reasonable range of time steps. More importantly, one version of the PSATD algorithm, when combined with digital filtering, is almost completely free of the numerical Cherenkov instability for time steps (scaled to the speed of light) comparable to or smaller than the axial cell size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxation terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Ensemble-type numerical uncertainty information from single model integrations

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of the influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs

In this work, we study the semi-classical limit of the Schrödinger equation with random inputs, and show that the semi-classical Schrödinger equation produces O(ε) oscillations in the random variable space. With the Gaussian wave packet transform, the original Schrödinger equation is mapped to an ordinary differential equation (ODE) system for the wave packet parameters coupled with a partial differential equation (PDE) for the quantity w in rescaled variables. Further, we show that the w equation does not produce ε dependent oscillations, and thus it is more amenable for numerical simulations. We propose multi-level sampling strategy in implementing the Gaussian wave packet transform, where in the most costly part, i.e. simulating the w equation, it is sufficient to use ε independent samples. We also provide extensive numerical tests as well as meaningful numerical experiments to justify the properties of the numerical algorithm, and hopefully shed light on possible future directions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Total experimental uncertainty in hydrodynamic testing of a semisubmersible wind turbine, considering numerical propagation of systematic uncertainty

Quantifying the uncertainty in experimental results is a vital step in properly validating numerical simulation tools for designing floating wind turbines; without a good understanding of the experimental uncertainties, it is impossible to confirm if numerical simulation tools can capture the physics with acceptable accuracy. Recent validation studies suggest that the wave-induced, low-frequency surge and pitch motions of semisubmersible-type floating wind turbines are consistently underpredicted by numerical simulations, but it has not been possible to state whether or not this underprediction is within the level of experimental error. Here, previously assessed systematic uncertainty components in hydrodynamic tests of the OC5-DeepCwind semisubmersible are propagated to response metrics of interest using numerical simulation tools, and combined with the system's random uncertainty to obtain the total experimental uncertainty. The uncertainty in the low-frequency response metrics is found to be most sensitive to the system properties (e.g., mooring stiffness and center of gravity), and also the wave elevation. The results of the present study suggest that the underprediction of the low-frequency response behavior observed in previous validation studies is larger than the experimental uncertainty.

17 WIND ENERGY↗

DOE OSTI2024

Wave-powered water pump for upwelling in aquaculture: Numerical model and ocean test

Wave-powered upwelling can increase the productivity and survivability of several aquaculture species. This enhancement is due to transporting cold, nutrient-rich ocean water, typically found lower in the water column, to the surface. Macroalgaes, like kelp, exhibit increased growth from these altered conditions. The University of New Hampshire’s (UNH) wave-powered water pump (wave pump) is a point absorber wave energy converter (WEC) that uses ocean waves to create relative motion between a spar buoy and a concentric float which drives an internal pump. A numerical model of the wave pump was developed using WEC-Sim to predict device performance in the ocean. Wave pump performance was evaluated during a five day ocean test near Appledore Island in Maine in March 2023, where volumetric flow rate, relative distance between spar and float, and wave conditions were measured. These data were then used for numerical model validation. The ocean deployment recorded the device’s performance in a variety of sea states, with average significant wave heights up to 0.7 m. The ocean test data were compared to the WEC-Sim numerical model of the device with favorable results. Average values of device stroke period, stroke height, and flow rate agreed between the ocean test and model data to within approximately 16 to 22%. Furthermore, the validated numerical model provides a valuable tool for improving the design and developing a commercial-scale, wave-powered water pump for use in aquaculture.

16 TIDAL AND WAVE POWER↗

DOE OSTI2017

Numerical Analysis of Experiments on Thermally Induced Dissociation of Methane Hydrates in Porous Media

Numerical simulation is essential for the prediction and evaluation of hydrocarbon reservoir performance. Numerical simulators developed for the description of the behavior of hydrates under production and the corresponding flow of fluids and heat accounting for all known processes are powerful, but they need validation through comparison to field or experimental data in order to instill confidence in their predictions. In this study, we analyze by means of numerical simulation the results of an experiment of methane hydrate dissociation by thermal stimulation in unconsolidated porous media heated through the vessel walls. The physics captured by the model include multicomponent heat and mass transfer, multiphase flow through porous media, and the phase behavior of the CH 4 + H 2 O system involved in methane hydrate formation and dissociation. The set of governing equations consists of the mass and energy conservation equations coupled with constitutive relationships, i.e., the dissolution of gas in H 2 O, relative permeability and capillary pressure models, composite thermal conductivity models, and methane hydrate phase equilibria. The model geometry describes accurately the hydrate reactor used in a recent experimental study investigating methane hydrate dissociation behavior [Chong et. al. Appl. Energy 2016, 177, 409-421]. The cumulative gas production is estimated and validated against three tests of experimental data involving different boundary temperatures, showing a good agreement between observations and numerical predictions. The predicted evolution of the spatial distributions of different phases over time shows that hydrate dissociation progresses inward from the reactor boundary to the center, methane gas accumulates to the top of the reactor because of buoyancy, and water migrates down to the bottom of the reactor because of gravity. A sharp hydrate dissociation front is predicted, and the estimated location of hydrate dissociation front suggests a linear relationship with the square root of time. A sensitivity analysis on the thermal conductivity of sand under fully saturated conditions is conducted to elucidate its effect on the gas production behavior. In addition, the energy efficiency ratio computed from the simulation of this boundary-wall heating technique varies from 14.0 to 16.2. Deviations between observations and predictions of the evolution of the temperature profile are attributed to initial heterogeneous distribution of the hydrate phase in the hydrate reactor.

42 ENGINEERING↗

DOE OSTI2014

Theoretical and numerical predictions of hypervelocity impact-generated plasma

The hypervelocity impact generated plasmas (HVIGP) in thermodynamic non-equilibrium state were theoretically analyzed, and a physical model was presented to explore the relationship between plasma ionization degree and internal energy of the system by a group of equations including a chemical reaction equilibrium equation, a chemical reaction rate equation, and an energy conservation equation. A series of AUTODYN 3D (a widely used software in dynamic numerical simulations and developed by Century Dynamic Inc.) numerical simulations of the impacts of hypervelocity Al projectile on its targets at different incident angles were performed. The internal energy and the material density obtained from the numerical simulations were then used to calculate the ionization degree and the electron temperature. Based on a self-developed 2D smooth particle hydrodynamic (SPH) code and the theoretical model, the plasmas generated by 6 hypervelocity impacts were directly simulated and their total charges were calculated. The numerical results are in good agreements with the experimental results as well as the empirical formulas, demonstrating that the theoretical model is justified by the AUTODYN 3D and self-developed 2D SPH simulations and applicable to predict HVIGPs. The study is of significance for astrophysical and cosmonautic researches and safety.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Numerical thermalization in particle-in-cell simulations with Monte-Carlo collisions

Numerical thermalization in collisional one-dimensional (1D) electrostatic (ES) particle-in-cell (PIC) simulations was investigated. Two collision models, the pitch-angle scattering of electrons by the stationary ion background and large-angle collisions between the electrons and the neutral background, were included in the PIC simulation using Monte-Carlo methods. The numerical results show that the thermalization times in both models were considerably reduced by the additional Monte-Carlo collisions as demonstrated by comparisons with Turner's previous simulation results based on a head-on collision model [M. M. Turner, Phys. Plasmas 13, 033506 (2006)]. However, the breakdown of Dawson's scaling law in the collisional 1D ES PIC simulation is more complicated than that was observed by Turner, and the revised scaling law of the numerical thermalization time with numerical parameters are derived on the basis of the simulation results obtained in this study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Numerical simulations of impulsively generated Alfvén waves in solar magnetic arcades

We perform numerical simulations of impulsively generated Alfvén waves in an isolated solar arcade, which is gravitationally stratified and magnetically confined. We study numerically the propagation of Alfvén waves along the magnetic structure that extends from the lower chromosphere, where the waves are generated, to the solar corona, and analyze the influence of the arcade size and the width of the initial pulses on the wave propagation and reflection. Our model of the solar atmosphere is constructed by adopting the temperature distribution based on the semi-empirical VAL-C model and specifying the curved magnetic field lines that constitute the asymmetric magnetic arcade. The propagation and reflection of Alfvén waves in this arcade is described by 2.5-dimensional magnetohydrodynamic equations that are numerically solved by the FLASH code. Our numerical simulations reveal that the Alfvén wave amplitude decreases as a result of a partial reflection of Alfvén waves in the solar transition region, and that the waves that are not reflected leak through the transition region and reach the solar corona. We also find the decrement of the attenuation time of Alfvén waves for wider initial pulses. Moreover, our results show that the propagation of Alfvén waves in the arcade is affected by the spatial dependence of the Alfvén speed, which leads to phase mixing that is stronger for more curved and larger magnetic arcades. We discuss the processes that affect the Alfvén wave propagation in an asymmetric solar arcade and conclude that besides phase mixing in the magnetic field configuration, the plasma properties of the arcade, the size of the initial pulse, and the structure of the solar transition region all play a vital role in the Alfvén wave propagation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS

We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit N → ∞, h → 0, and N{sub nb} → ∞, where N is the total number of particles, h is the smoothing length, and N{sub nb} is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions N → ∞ and h → 0 are sufficient to achieve convergence, while holding N{sub nb} fixed. We demonstrate that if N{sub nb} is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as N → ∞ and h → 0. Formal numerical convergence in SPH is possible only if N{sub nb} is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for N{sub nb} by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find N{sub nb} ∝N {sup 0.5}. This means that if SPH is to be used as a numerically convergent method, the required computational cost does not scale with particle number as O(N), but rather as O(N {sup 1} {sup +} {sup δ}), where δ ≈ 0.5, with a weak dependence on the form of the smoothing kernel.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Numerical experiments on the detailed energy conversion and spectrum studies in a corona current sheet

In this paper, we study the energy conversion and spectra in a corona current sheet (CS) by 2.5 dimensional MHD numerical simulations. Numerical results show that many Petschek-like fine structures with slow-mode shocks mediated by plasmoid instabilities develop during the magnetic reconnection process. The termination shocks can also be formed above the primary magnetic island and at the head of secondary islands. These shocks play important roles in generating thermal energy in a corona CS. For a numerical simulation with initial conditions close to the solar corona environment, the ratio of the generated thermal energy to the total dissipated magnetic energy is around 1/5 before secondary islands appear. After secondary islands appear, the generated thermal energy starts to increase sharply and this ratio can reach a value of about 3/5. In an environment with a relatively lower plasma density and plasma β, the plasma can be heated to a much higher temperature. After secondary islands appear, the one-dimensional energy spectra along the CS do not behave as a simple power law and the spectrum index increases with the wave number. The average spectrum index for the magnetic energy spectrum along the CS is about 1.8. The two-dimensional spectra intuitively show that part of the high energy is cascaded to large kx and ky space after secondary islands appear. The plasmoid distribution function calculated from numerical simulations behaves as a power law closer to f(ψ)∼ψ{sup −1} in the intermediate ψ regime. By using η{sub eff}=v{sub inflow}⋅L, the effective magnetic diffusivity is estimated to be about 10{sup 11} ∼ 10{sup 12} m{sup 2} s{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Fast computation of synthetic seismograms within a medium containing remote localized perturbations: a numerical solution to the scattering problem

We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modelling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the subvolume containing the perturbations or scatterers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modelled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhof–Helmholtz integrals that naturally adapt to the numerical scheme employed for modelling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered ‘exact’ as the total numerical error is comparable to that of the method employed for modelling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localized sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarized in a dedicated section.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Resolution requirements for numerical modeling of neutrino quantum kinetics

Neutrino quantum kinetics is a rapidly evolving field in computational astrophysics, with a primary focus on collective neutrino oscillations in core-collapse supernovae and postmerger phases of binary neutron star mergers. In recent years, there has been considerable debate concerning resolution dependence in numerical simulations. In this paper, we conduct a comprehensive resolution study in both angular- and spatial directions by using two independent schemes of quantum kinetic neutrino transport: finite volume and pseudospectral methods. We complement our discussion by linear stability analysis including inhomogeneous modes. Our result suggests that decreasing spatial resolutions underestimates the growth of flavor instability, and then leads to wrong asymptotic states of flavor conversions, which potentially has a critical impact on astrophysical consequences. We further delve into numerical results of low resolution simulations, that reveals the underlying mechanism responsible for numerical artifacts caused by insufficient resolutions. Finally, this study settles the debate on requirements of resolutions and serves as a guideline for numerical modeling of quantum kinetic neutrino transport.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Numerical heating in particle-in-cell simulations with Monte Carlo binary collisions

The binary Monte Carlo (MC) collision algorithm is a standard and robust method to include binary Coulomb collision effects in particle-in-cell (PIC) simulations of plasmas. Here we show that the coupling between PIC and MC algorithms can give rise to (nonphysical) numerical heating of the system that significantly exceeds that observed when these algorithms operate independently. We argue that this deleterious effect results from an inconsistency between the particle motion associated with MC collisions and the work performed by the collective electromagnetic field on the PIC grid. This inconsistency manifests as the (artificial) stochastic production of electromagnetic energy, which ultimately heats the plasma particles. Here, the MC-induced numerical heating can significantly impact the evolution of the simulated system for long simulation times (≳10 3 collision periods, for typical numerical parameters). We describe the source of the MC-induced numerical heating analytically and discuss strategies to minimize it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Numerical and Visual Representations of Uncertainty Lead to Different Patterns of Decision Making

Although visualizations are a useful tool for helping people to understand information, they can also have unintended effects on human cognition. This is especially true for uncertain information, which is difficult for people to understand. Prior work has found that different methods of visualizing uncertain information can produce different patterns of decision making from users. However, uncertainty can also be represented via text or numerical information, and few studies have systematically compared these types of representations to visualizations of uncertainty. We present two experiments that compared visual representations of risk (icon arrays) to numerical representations (natural frequencies) in a wildfire evacuation task. Like prior studies, we found that different types of visual cues led to different patterns of decision making. In addition, our comparison of visual and numerical representations of risk found that people were more likely to evacuate when they saw visualizations than when they saw numerical representations. These experiments reinforce the idea that design choices are not neutral: seemingly minor differences in how information is represented can have important impacts on human risk perception and decision making.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part II: The Effect of Roughness on the Performance of a High-Pressure Turbine Blade

Abstract Turbine blades generally present surface roughness introduced in the manufacturing process or caused by in-service degradation, which can have a significant impact on aero-thermal performance. A better understanding of the fundamental physical mechanisms arising from the interaction between the roughness and the turbine flow at engine-relevant conditions can provide insights for the design of blades with improved efficiency and longer operational life. To this end, a high-fidelity numerical framework combining a well-validated solver for direct numerical simulation and a second-order accurate immersed boundary method is employed to predict roughness-induced aero-thermal effects on an LS89 high-pressure turbine (HPT) blade at engine-relevant conditions. Different amplitudes and distributions of surface roughness are investigated and a reference smooth-blade simulation under the same flow conditions is conducted for comparison. Roughness of increasing amplitude progressively shifts the blade suction side boundary layer transition upstream, producing larger values of the turbulent kinetic energy and higher total wake losses. The on-surface data-capturing capabilities of the numerical framework provide direct measurements of the heat flux and the skin friction coefficient, hence offering quantitative information between the surface topology and engineering-relevant performance parameters. This work may provide a benchmark for future numerical studies of turbomachinery flows with roughness.

Engineering↗