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DOE OSTI2014

A two-parameter continuation method for computing numerical solutions of spin-1 Bose–Einstein condensates

We describe a novel two-parameter continuation method combined with a spectral-collocation method (SCM) for computing the ground state and excited-state solutions of spin-1 Bose–Einstein condensates (BEC), where the second kind Chebyshev polynomials are used as the basis functions for the trial function space. To compute the ground state solution of spin-1 BEC, we implement the single parameter continuation algorithm with the chemical potential μ as the continuation parameter, and trace the first solution branch of the Gross–Pitaevskii equations (GPEs). When the curve-tracing is close enough to the target point, where the normalization condition of the wave function is going to be satisfied, we add the magnetic potential λ as the second continuation parameter with the magnetization M as the additional constraint condition. Then we implement the two-parameter continuation algorithm until the target point is reached, and the ground state solution of the GPEs is obtained. The excited state solutions of the GPEs can be treated in a similar way. Some numerical experiments on {sup 23}Na and {sup 87}Rb are reported. The numerical results on the spin-1 BEC are the same as those reported in [10]. Further numerical experiments on excited-state solutions of spin-1 BEC suffice to show the robustness and efficiency of the proposed two-parameter continuation algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Hydrodynamic flows on curved surfaces: Spectral numerical methods for radial manifold shapes

We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of symmetry for radial manifold shapes, we develop spectral Galerkin methods based on hyperinterpolation with Lebedev quadratures for L 2 -projection to spherical harmonics. We demonstrate our methods by investigating hydrodynamic responses as the surface geometry is varied. Relative to the case of a sphere, we find significant changes can occur in the observed hydrodynamic flow responses as exhibited by quantitative and topological transitions in the structure of the flow. We present numerical results based on the Rayleigh-Dissipation principle to gain further insights into these flow responses. We explore the roles played by the geometry especially concerning the positive and negative Gaussian curvature of the interface. We offer general approaches for taking geometric effects into account for investigations of hydrodynamic phenomena within curved fluid interfaces.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Time-step dependent force interpolation scheme for suppressing numerical Cherenkov instability in relativistic particle-in-cell simulations

The WT scheme, a piecewise polynomial force interpolation scheme with time-step dependency, is proposed in this paper for relativistic particle-in-cell (PIC) simulations. The WT scheme removes the lowest order numerical Cherenkov instability (NCI) growth rate for arbitrary time steps allowed by the Courant condition. While NCI from higher order resonances is still present, the numerical tests show that for smaller time steps, the numerical instability grows much slower than using the optimal time step found in previous studies. The WT scheme is efficient for improving the quality and flexibility of relativistic PIC simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Machine learning based algorithms for uncertainty quantification in numerical weather prediction models

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the corresponding physical parameters during model configuration can significantly impact the accuracy of model forecasts. There is no combination of physical schemes that works best for all times, at all locations, and under all conditions. It is therefore of considerable interest to understand the interplay between the choice of physics and the accuracy of the resulting forecasts under different conditions. This paper demonstrates the use of machine learning techniques to study the uncertainty in numerical weather prediction models due to the interaction of multiple physical processes. The first problem addressed herein is the estimation of systematic model errors in output quantities of interest at future times, and the use of this information to improve the model forecasts. The second problem considered is the identification of those specific physical processes that contribute most to the forecast uncertainty in the quantity of interest under specified meteorological conditions. In order to address these questions we employ two machine learning approaches, random forests and artificial neural networks. The discrepancies between model results and observations at past times are used to learn the relationships between the choice of physical processes and the resulting forecast errors. Numerical experiments are carried out with the Weather Research and Forecasting (WRF) model. The output quantity of interest is the model precipitation, a variable that is both extremely important and very challenging to forecast. The physical processes under consideration include various micro-physics schemes, cumulus parameterizations, short wave, and long wave radiation schemes. The experiments demonstrate the strong potential of machine learning approaches to aid the study of model errors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Impact of mixed grain size sediment input on braided river Morphodynamics: Insights from experimental and numerical modeling

The rate of sediment supply has significant impacts on river morphology, making it crucial to understand the geomorphic changes and grain size distribution dynamics in rivers. However, the effects of varying grain size sediment input on morphological changes in braided channels remain poorly understood. This study is the first to investigate the bar development and sediment sorting processes in braided channels with non-uniform sediment inputs using both numerical and experimental approaches. We applied a two-dimensional numerical model, Nays2DH to confirm and generalize experimental results. The model reproduced key experiment results, including 1) stream elevation changes, and 2) grain size distribution. Using this validated model, we explored the morphological changes and sorting process in a braided river with sediment inputs. The numerical experiments demonstrate that sediment input controls the elevation of the stream bed and the grain size distribution. Notably, both the elevation and grain-size distribution become relatively stable in downstream of the channel. Additionally, the simulation results suggest that an increased sediment supply leads to greater channel complexity, with bed surface armoring decreasing.

Nays2DH↗

DOE OSTI2016

Study of the force coefficients on plates using an open source numerical wave tank

An open source numerical wave tank based on the OpenFOAM® software was setup and tested to solve the Navier-Stokes equations. This work focused on submerged plates because of their simple geometry, their importance as a design component (e.g., heave plates), and the broad availability of published experimental results. Two-dimensional plates in an oscillatory flow, as well as three-dimensional circular disks and square plates undergoing forced oscillations were simulated in conditions where the nonlinearity of hydrodynamic viscous drag and inertia forces can be probed easily. The effect of plate thickness as well as the ability of the numerical simulations to predict wave radiation damping at shallow plate submergence were also considered. Overall, force coefficient predictions were very satisfactory when compared to experimental data, and generally exhibited less scatter. Here, the influence of both Keulegan-Carpenter number and frequency parameter on the hydrodynamic force could be assessed as well from these numerical simulations as from past laboratory experiments.

13 HYDRO ENERGY↗

DOE OSTI2024

Numerical challenges for energy conservation in N -body simulations of collapsing self-interacting dark matter halos

Dark matter (DM) halos can be subject to gravothermal collapse if the DM is not collisionless, but engaged in strong self-interactions instead. When the scattering is able to efficiently transfer heat from the centre to the outskirts, the central region of the halo collapses and reaches densities much higher than those for collisionless DM. This phenomenon is potentially observable in studies of strong lensing. Current theoretical efforts are motivated by observations of surprisingly dense substructures. However, a comparison with observations requires accurate predictions. One method to obtain such predictions is to use N-body simulations. Collapsed halos are extreme systems that pose severe challenges when applying state-of-the-art codes to model self-interacting dark matter (SIDM). In this work, we investigate the root of such problems, with a focus on energy non-conservation. Moreover, we discuss possible strategies to avoid them. We ran N-body simulations, both with and without SIDM, of an isolated DM-only halo and we adjusted the numerical parameters to check the accuracy of the simulation. We find that not only the numerical scheme for SIDM can lead to energy non-conservation, but also the modelling of gravitational interaction and the time integration are problematic. The main issues we find are: (a) particles changing their time step in a non-time-reversible manner; (b) the asymmetry in the tree-based gravitational force evaluation; and (c) SIDM velocity kicks breaking the time symmetry. Tuning the parameters of the simulation to achieve a high level of accuracy allows us to conserve energy not only at early stages of the evolution, but also later on. However, the cost of the simulations becomes prohibitively large as a result. Some of the problems that make the simulations of the gravothermal collapse phase inaccurate can be overcome by choosing appropriate numerical schemes. However, other issues still pose a challenge. Our findings motivate further works on addressing the challenges in simulating strong DM self-interactions.

dark matter↗

DOE OSTI2013

Thermodiffusion in concentrated ferrofluids: A review and current experimental and numerical results on non-magnetic thermodiffusion

Ferrofluids are colloidal suspensions consisting of magnetic nanoparticles dispersed in a carrier liquid. Their thermodiffusive behaviour is rather strong compared to molecular binary mixtures, leading to a Soret coefficient (S{sub T}) of 0.16 K{sup −1}. Former experiments with dilute magnetic fluids have been done with thermogravitational columns or horizontal thermodiffusion cells by different research groups. Considering the horizontal thermodiffusion cell, a former analytical approach has been used to solve the phenomenological diffusion equation in one dimension assuming a constant concentration gradient over the cell's height. The current experimental work is based on the horizontal separation cell and emphasises the comparison of the concentration development in different concentrated magnetic fluids and at different temperature gradients. The ferrofluid investigated is the kerosene-based EMG905 (Ferrotec) to be compared with the APG513A (Ferrotec), both containing magnetite nanoparticles. The experiments prove that the separation process linearly depends on the temperature gradient and that a constant concentration gradient develops in the setup due to the separation. Analytical one dimensional and numerical three dimensional approaches to solve the diffusion equation are derived to be compared with the solution used so far for dilute fluids to see if formerly made assumptions also hold for higher concentrated fluids. Both, the analytical and numerical solutions, either in a phenomenological or a thermodynamic description, are able to reproduce the separation signal gained from the experiments. The Soret coefficient can then be determined to 0.184 K{sup −1} in the analytical case and 0.29 K{sup −1} in the numerical case. Former theoretical approaches for dilute magnetic fluids underestimate the strength of the separation in the case of a concentrated ferrofluid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Numerical study of effect of secondary electron emission on discharge characteristics in low pressure capacitive RF argon discharge

Based on the drift and diffusion approximation theory, a 1D fluid model on capacitively coupled RF argon glow discharge at low pressure is established to study the effect of secondary electron emission (SEE) on the discharge characteristics. The model is numerically solved by using a finite difference method and the numerical results are obtained. The numerical results indicate that when the SEE coefficient is larger, the plasma density is higher and the time of reaching steady state is longer. It is also found that the cycle-averaged electric field, electric potential, and electron temperature change a little as the SEE coefficient is increased. Moreover, the discharge characteristics in some nonequilibrium discharge processes with different SEE coefficients have been compared. The analysis shows that when the SEE coefficient is varied from 0.01 to 0.3, the cycle-averaged electron net power absorption, electron heating rate, thermal convective term, electron energy dissipation, and ionization all have different degrees of growth. While the electron energy dissipation and ionization are quite special, there appear two peaks near each sheath region in the discharge with a relatively larger SEE coefficient. In this case, the discharge is certainly operated in a hybrid α-γ-mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Experimental and numerical analysis of pre-compressed masonry walls in two-way-bending with second order effects

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a combined experimental and numerical homogenizedapproach. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine. In parallel, a wide experimental campaign is conducted on walls in two way bending, with the double aim of both validating the numerical model and investigating the behavior of walls that may not be reduced to simple cantilevers or simply supported beams. Panels investigated are dry-joint in scale square walls simply supported at the base and on a vertical edge, exhibiting the classical Rondelet’s mechanism. The results obtained are compared with those provided by the numerical model.

42 ENGINEERING↗

DOE OSTI2014

Numerical design of SiC bulk crystal growth for electronic applications

Presented study concerns numerical simulation of Physical Vapor Transport (PVT) growth of bulk Silicon Carbide (SiC) crystals. Silicon Carbide is a wide band gap semiconductor, with numerous applications due to its unique properties. Wider application of SiC is limited by high price and insufficient quality of the product. Those problems can be overcame by optimizing SiC production methods. Experimental optimization of SiC production is expensive because it is time consuming and requires large amounts of energy. Numerical modeling allows to learn more about conditions inside the reactor and helps to optimize the process at much lower cost. In this study several simulations of processes with different reactor geometries were presented along with discussion of reactor geometry influence on obtained monocrystal shape and size.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

On one numerical scheme of the solution of a three-dimensional problem of diffraction of an electromagnetic wave on thin ideally conductive screens

In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.