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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 55 records · Page 3

Paraniso 1.0: 3-D Full Waveform Seismic Simulation in General Anisotropic Media

Many geologic materials and minerals are seismically anisotropic, with the most general anisotropic material having up to 21 independent elastic coefficients. This report outlines the development of a 3-D, generally anisotropic, linear elastic full waveform finite-difference solver. First, a mathematical description of the solution equations will be described. The finite-difference implementation of these equations will then be shown. Finally, a comparison of results from this new solver to other solutions will be provided as verification that the new algorithm can accurately replicate these solutions.

58 GEOSCIENCES↗

Finite-Difference Simulation for Infrasound Generated by Finite-Extent Ground Motions

Underground explosions can produce infrasound in the atmosphere, and the wavefield characteristics are often governed by the ground surface motions. Finite-difference methods are popular for infrasound simulation as their generality and robustness allow for complex atmospheric structures and surface topography. A simple point-source approximation is often used because infrasound wavelengths tend to be large relative to the source dimensions. However, this assumption may not be able to capture the complexity of explosion-induced ground motions if the surface area is not compact, and appropriate source models must be incorporated into the finite-difference simulations for accurate infrasound prediction. In this study, we develop a point source representation of the complex ground motions for infrasound sources. Instead of a single point source, we use a series of point sources distributed over the source area. These distributed point sources can be equivalent to air volume changes produced by the ground motions in the atmosphere. Further, we apply the distributed point-source method to a series of buried chemical explosions conducted during the Source Physics Experiment Phase I. Epicentral ground-motion measurements during the experiments provide a way to calculate accurate distributed point sources. We validate and evaluate the accuracy of distributed point source approach for infrasound simulations by direct comparison with acoustic observations in the field experiment.

58 GEOSCIENCES↗

Interaction between two conducting spheres in weakly ionized collisional plasma

Charging of two conducting spheres in a weakly ionized collisional plasma flow is considered. The spheres are arranged along the flow, and the plasma is assumed to consist of two ion species with the charges equal in magnitude but opposite in sign. The problem is analyzed with allowance for the external electric field, charging of the spheres due to the sedimentation of plasma ions on them, the fields of the sphere charges, the space charge field, and the processes of recombination and molecular diffusion. The interaction between the spheres and plasma is studied by numerically solving a time-dependent problem in a bispherical coordinate system by the finite difference method. The steady-state values of the sphere charges and the distributions of the space charge and ion densities in the ambient plasma are found as functions of the plasma parameters and the distance between the spheres. The electrostatic forces acting on the spheres are determined, and the effects of the external field, the space charge fields, and the fields of the sphere charges are comparatively analyzed. It is shown that, for the considered plasma parameters, the main electrostatic effect in the interaction between two spheres is their mutual approach in the external field due to the difference in their charges (one sphere catches up with the other). Due to the friction force with the neutral gas, this mutual approach is much slower than all other processes in the system. For widely spaced spheres, the results coincide with the solution obtained previously for a solitary sphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An implicit logarithmic finite-difference technique for two dimensional coupled viscous Burgers’ equation

This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

97 MATHEMATICS AND COMPUTING↗

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗

Acoustic Codes in 2D Spherical Coordinate

Finite-difference methods are widely used to simulate infrasound propagation in the atmosphere. Flexibility of finite-difference scheme allows implementation of highly heterogeneous media for sound propagation as well as complex source models for sound generation. While full 3-D finite-difference methods have been utilized for local infrasound propagation with pronounced topography, 2-D modeling approach has been preferred for regional and global propagation as full 3-D methods generally require enormous computational resources. Infrasound propagation is often simulated with a second-order finite difference scheme. This lowest-order finite-difference scheme is robust and straightforward to implement complex boundary conditions, but the solution includes large error with numerical dispersion and dissipation. This large numerical error may make the second-order finite-difference not optimal for long range infrasound propagation modeling as the numerical dispersion degrades the accuracy of the solution unacceptably. Here, we developed a high-order finite-difference solver for long-range infrasound simulation. The high-order scheme is particularly popular for linear wave modeling in aeroacoustics owing to its low-dispersive and low-dissipative behavior. We develop and evaluate a high-order finite difference scheme in 2-D axisymmetric coordinates. The axisymmetry allows to approximate 3-D spherical sound propagation and amplitude attenuation by a 2-D method. AC2Dr is developed to simulate infrasound propagation in realistic atmosphere, but can be used for linear acoustic waves in general materials with background flow. AC2Dr in an axisymmetric coordinates allows for spherical radiation of acoustic waves from compact sources.

Sjogreen, Bjorn↗

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.

58 GEOSCIENCES↗

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods

We develop a general algorithm for the analysis the spectral stability of generalized multistage Runge–Kutta methods of various orders of accuracy as applied to the numerical integration with respect to time of an initial-boundary-value problem for the second-order parabolic equation. The expression for the function of spectral stability is obtained in two alternative forms: on the basis of matrix relations and in the determinant form. We study specific realizations of various generalized explicit Runge–Kutta methods and their spectral stability. It is shown that all explicit generalized Runge–Kutta methods possess the property of conditional spectral stability and the property of conditional monotonicity of the numerical solution in time whose violation leads to the appearance of false oscillations of the approximate solution. The stability function for these methods is polynomial. It is shown that the application of two-stage generalized explicit Runge–Kutta methods leads to the appearance of predictor-corrector-type schemes. In the case of nonstationary one-dimensional heat-conduction problem, on the basis of a one-stage generalized Runge–Kutta method, we obtain the classical two-layer conditionally stable explicit finite-difference scheme on a four-point template. It is demonstrated that the five-stage generalized Runge–Kutta–Merson method is characterized by the weakest condition of spectral stability as compared with all investigated explicit generalized Runge–Kutta methods.

42 ENGINEERING↗

Faraday rotation study of plasma bubbles in GeV wakefield accelerators

We visualize plasma bubbles driven by 0.67 PW laser pulses in a plasma of density ne≈5×1017cm−3 by imaging Faraday rotation patterns imprinted on linearly polarized probe pulses of wavelength λpr=1.05 μm and duration τpr=2 or 1 ps that cross the bubble's path at right angles. When the bubble captures and accelerates tens to hundreds of pC of electron charges, we observe two parallel streaks of length cτpr straddling the drive pulse propagation axis, separated by ∼45 μm, in which probe polarization rotates by 0.3° to more than 5° in opposite directions. Accompanying simulations show that they result from Faraday rotation within portions of dense bubble side walls that are pervaded by the azimuthal magnetic field of accelerating electrons during the probe transit across the bubble. Analysis of the width of the streaks shows that quasi-monoenergetic high-energy electrons and trailing lower energy electrons inside the bubble contribute distinguishable portions of the observed signals, and relativistic flow of sheath electrons suppresses Faraday rotation from the rear of the bubble. The results demonstrate favorable scaling of Faraday rotation diagnostics to 40× lower plasma density than previously demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multicolor generation using silicon nanodisk absorber

A multicolored matrix that spans the visible range was demonstrated by using silicon nanodisk arrays. A nanostructured silicon substrate, which featured periodic silicon nanodisk arrays of various diameters, inter-nanodisk distances, and heights, was fabricated using electron-beam lithography and reactive ion etching. These silicon nanodisks were able to support HE{sub 1m} leaky modes, which depended on the diameter of the nanodisks, resulting in wavelength-dependent reflection spectra. The resonant wavelength redshifted linearly with the increasing nanodisk diameter. The output color lay in the visible range and was observed to be tunable when varying the diameter, interdistance, and height. The results of finite-difference time-domain simulations exhibited close agreement with the observed optical properties of the periodic silicon nanodisk arrays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Photonic crystal ring resonator based optical filters for photonic integrated circuits

In this paper, a two Dimensional (2D) Photonic Crystal Ring Resonator (PCRR) based optical Filters namely Add Drop Filter, Bandpass Filter, and Bandstop Filter are designed for Photonic Integrated Circuits (PICs). The normalized output response of the filters is obtained using 2D Finite Difference Time Domain (FDTD) method and the band diagram of periodic and non-periodic structure is attained by Plane Wave Expansion (PWE) method. The size of the device is minimized from a scale of few tens of millimeters to the order of micrometers. The overall size of the filters is around 11.4 μm × 11.4 μm which is highly suitable of photonic integrated circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Design and analysis of photonic crystal micro-cavity based optical sensor platform

In this paper, the design of a two-dimensional photonic crystal micro-cavity based integrated-optic sensor platform is proposed. The behaviour of designed cavity is analyzed using two-dimensional Finite Difference Time Domain (FDTD) method. The structure is designed by deliberately inserting some defects in a photonic crystal waveguide structure. Proposed structure shows a quality factor (Q) of about 1e5 and the average sensitivity of 500nm/RIU in the wavelength range of 1450 – 1580 nm. Sensing technique is based on the detection of shift in upper-edge cut-off wavelength for a reference signal strength of –10 dB in accordance with the change in refractive index of analyte.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Monotonicity conditions in the nodal mimetic finite difference method for diffusion problems on quadrilateral meshes

A set of sufficient and necessary conditions for the local stiffness matrix of the nodal mimetic finite difference method on quadrilaterals is derived under which such matrix is a singular M-matrix. These conditions are directly related to the shape of the quadrilaterals and to the value of the off-diagonal elements and they are illustrated by the new concept, here introduced, of monotonicity region. When such conditions are satisfied, the global matrix for the Poisson problem with Dirichlet boundary conditions is a singular M-matrix. After setting the boundary condition, yields a monotone matrix operator and we prove that the final discretization possesses a Discrete Maximum Principle.

97 MATHEMATICS AND COMPUTING↗

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗

Visible light broadband perfect absorbers

The visible light broadband perfect absorbers based on the silver (Ag) nano elliptical disks and holes array are studied using finite difference time domain simulations. The semiconducting indium silicon dioxide thin film is introduced as the space layer in this sandwiched structure. Utilizing the asymmetrical geometry of the structures, polarization sensitivity for transverse electric wave (TE)/transverse magnetic wave (TM) and left circular polarization wave (LCP)/right circular polarization wave (RCP) of the broadband absorption are gained. The absorbers with Ag nano disks and holes array show several peaks absorbance of 100% by numerical simulation. These simple and flexible perfect absorbers are particularly desirable for various potential applications including the solar energy absorber.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Surface harmonics method for two-dimensional time-dependent neutron transport problems of square-lattice nuclear reactors

Time-dependent equations of the Surface Harmonics Method (SHM) have been derived from the time-dependent neutron transport equation with explicit representation of delayed neutrons for solving the two-dimensional time-dependent problems. These equations have been realized in the SUHAM-TD code. The TWIGL benchmark problem has been used for verification of the SUHAM-TD code. The results of the study showed that computational costs required to achieve necessary accuracy of the solution can be an order of magnitude less than with the use of the conventional finite difference method (FDM). (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗