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At least 289 records · Page 16

Efficient numerical algorithm for multi-level ionization of high-atomic-number gases

An efficient numerical algorithm for laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the system of differential equations describing ionization evolution. Using analytical solutions resolves the multiscale issue of ionization due to different characteristic time scales of ionization processes and the main code time step. Algorithm efficiency and memory requirements are significantly improved by using a locally reduced system of differential equations. The algorithm also assigns proper orbital quantum numbers and their projections to ionization states. The algorithm is verified and validated using experimental data.

Cheng, A. (ORCID:000000021945282X)↗

Sierra/SolidMechanics 4.56 Verification Tests Manual

Presented in this document is a small portion of the tests that exist in the Sierra / SolidMechanics (Sierra / SM) verication test suite. Most of these tests are run nightly with the Sierra / SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra / SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This document can be used to conrm that a given code capability is veried or referenced as a compilation of example problems. Additional example problems are provided in the Sierra / SM Example Problems Manual. Note, many other verication tests exist in the Sierra / SM test suite, but have not yet been included in this manual.

97 MATHEMATICS AND COMPUTING↗

Sierra/SolidMechanics 5.0 Verification Tests Manual

Presented in this document is a small portion of the tests that exist in the Sierra/SolidMechanics (Sierra/SM) verification test suite. Most of these tests are run nightly with the Sierra / SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra / SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems. Additional example problems are provided in the Sierra/SM Example Problems Manual. Note, many other verification tests exist in the Sierra/SM test suite, but have not yet been included in this manual.

97 MATHEMATICS AND COMPUTING↗

Sierra/SolidMechanics 5.6 Verification Tests Manual

Presented in this document is a small portion of the tests that exist in the Sierra / SolidMechanics (Sierra / SM) verfication test suite. Most of these tests are run nightly with the Sierra / SM code suite, and the results of the test are checked versus the correct analytical result. For each of the tests presented in this document, the test setup, a description of the analytic solution, and comparison of the Sierra / SM code results to the analytic solution is provided. Mesh convergence is also checked on a nightly basis for several of these tests. This document can be used to confirm that a given code capability is verfied or referenced as a compilation of example problems. Additional example problems are provided in the Sierra / SM Example Problems Manual. Note, many other verfication tests exist in the Sierra / SM test suite, but have not yet been included in this manual.

97 MATHEMATICS AND COMPUTING↗

Transient and steady-state velocity of domain walls for a complete range of drive fields

Approximate analytic solutions for transient and steady-state 180 deg domain wall motion in bulk magnetic material are obtained from the dynamic torque equations with a Gilbert damping term. The results for the Walker region in which the transient solution approaches the familiar Walker steady-state solution are presented in a slightly new form for completeness. An analytic solution corresponding to larger drive fields predicts an oscillatory motion with an average value which decreases with drive field for reasonable values of the damping parameter. These results agree with those obtained by a computer solution of the torque equation and those obtained with the assumption of a very large anisotropy field.

Bourne, H. C., Jr.↗

Transient and steady-state velocity of domain walls for a complete range of drive fields

Approximate analytic solutions for transient and steady-state 180 deg domain-wall motion in bulk magnetic material are obtained from the dynamic torque equations with a Gilbert damping term. The results for the Walker region in which the transient solution approaches the familiar Walker steady-state solution are presented in a slightly new form for completeness. An analytic solution corresponding to larger drive fields predicts an oscillatory motion with an average value of the velocity which decreases with drive field for reasonable values of the damping parameter. These results agree with those obtained by others from a computer solution of the torque equation and those obtained by others with the assumption of a very large anisotropy field.

Bourne, H. C., Jr.↗

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Weinman, J. A.↗

Studies of Fundamental Particle Dynamics in Microgravity

This work summarizes theoretical and experimental concepts used to design the flight experiment mission for SHIVA - Spaceflight Holography Investigation in a Virtual Apparatus. SHIVA is a NASA project that exploits a unique, holography-based, diagnostics tool to understand the behavior of small particles subjected to transient accelerations. The flight experiments are designed for testing model equations, measuring g, g-jitter, and other microgravity phenomena. Data collection will also include experiments lying outside of the realm of existing theory. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity. Recent results include interacting particles, particle-wall interactions, bubbles, and Reynolds numbers larger than unity. The Space Station provides an ideal environment for SHIVA. Limited ground experiments have already confirmed some aspects of the theory. In general the space environment is required for the overall experiment, especially for cases containing very heavy particles, very light particles, bubbles, collections of particles and for characterization of the space environment and its effect on particle experiments. Lightweight particles and bubbles typically rise too fast in a gravitational field and heavy particles sink too fast. In a microgravity environment, heavy and light particles can be studied side-by-side for long periods of time.

Rangel, Roger↗

SHIVA-(Spaceflight Holography in a Virtual Apparatus)

SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus) will expand our understanding of the fundamental physics of particle movement in fluids by exploiting the power of holography in a spaceflight experiment'. In addition, the study will exploit the movement of particles in fluids to observe and quantify microgravity phenomena that are extremely important in materials sciences with applications both in space and on earth. The regime under scrutiny is the low Reynolds number, Stokes regime or creeping flow, which covers particles and bubbles moving at very low velocity. The equations describing this important regime have been under development and investigation for over 100 years and yet a complete analytical solution of the general equation had remained elusive yielding only approximations and numerical solutions. In the course of the ongoing NASA NRA, the first analytical solution of the general equation was produced by members of the investigator team using the mathematics of fractional derivatives. This opened the way to an even more insightful and important investigation of the phenomena in microgravity.

Trolinger, James D.↗

Modeling of Compressible Flow with Friction and Heat Transfer Using the Generalized Fluid System Simulation Program (GFSSP)

The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.

Bandyopadhyay, Alak↗

Combined structures-controls optimization of lattice trusses

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Balakrishnan, A. V.↗

First saturation correction in high energy proton-nucleus collisions. Part I. Time evolution of classical Yang-Mills fields beyond leading order

In high energy proton-nucleus collisions, the single- and double-inclusive soft gluon productions at the leading order have been calculated and phenomenologically studied in various approaches for many years. These studies do not take into account the saturation and multiple rescatterings in the field of the proton. The first saturation correction to these leading order results (the terms that are enhanced by the combination \( {\alpha}_s^2{\mu}^2 \) , where μ 2 is the proton’s color charge squared per unit transverse area) has not been completely derived despite recent attempts using a diagrammatic approach. This paper is the first in a series of papers towards analytically completing the first saturation correction to physical observables in high energy proton-nucleus collisions. Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime using the Color Glass Condensate effective theory and compute physical observables constructed from classical gluon fields. In the current paper, the Yang-Mills equations are solved perturbatively in the field of the dilute object (the proton). Next-to-leading order and next-to-next-to-leading order analytic solutions are explicitly constructed. A systematic way to obtain all higher order analytic solutions is outlined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A process to verify numerical models for seismic fluid-structure interaction in advanced reactor vessels

Seismic design and qualification of a liquid-filled advanced nuclear reactor will have to account for fluid-structure interaction (FSI). Interaction between the tank, internal components, and contained liquid will rely on analysis of numerical models that must be verified and validated. Here this study demonstrates a verification process for models of a base-supported cylindrical tank by comparing numerical predictions and analytical solutions. The numerical models are consistent with the assumptions made to derive analytical solutions, namely, either a rigid or a linear elastic tank, ideal fluid, and small-amplitude, unidirectional, horizontal inputs. One software platform is used to illustrate the process. Seismic FSI analysis is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Reported responses are those used for design, including hydrodynamic pressures on the tank wall, shear forces and moments at the tank base, and wave heights of the contained liquid. The accuracy of the numerical results is discussed. The numerical models are verified for calculating the pressures on the tank wall and reactions at its base. Accurate simulation of wave action is challenging for both solvers. Recommendations for modeling, code development, and steps for verification are provided. Although focused on reactor vessels and one software platform, the verification process described herein is broadly applicable to liquid-filled vessels and other finite element codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification Testing For Solid-Element Material Models 11-19 in DYNA3D/ParaDyn

This technical report documents the creation and implementation of verification tests for solid-element material models 11 through 19 available in DYNA3D/ParaDyn. The verification tests covered all aspects of each material model, except for the Weibull distribution functionality in material models 15 and 19. General test cases were created to verify the elastic and plastic behavior of the material models. Other additional tests were developed to examine the intricacies of each material model. Each test involved the use a kinematic load case and specification of material parameters necessary to activate corresponding features of the material model. The load cases prescribed the full time history of the kinematic motion for the solid elements, and these loads are independent of the material model or element formulation. When possible, closed form solutions were then derived for each verification test in a continuum setting. The DYNA3D simulations for each test were carried out over a unit time interval, t ϵ [0, 1], and the as implemented DYNA3D response was compared to the closed form solutions evaluated at discrete points in time. A relative error measure was determined for each test to justify the proper implementation of the material model. The relative errors comparing the DYNA3D solution to the analytical solution were, in general, on the order of machine precision except where noted. This signifies the proper implementation of solid-element material models 11-19. In the development of these verification tests, six bugs were found and fixed in the source code. Additionally, this work generated eighteen DYNA3D input decks and answer extraction scripts in the DYNA3D/ParaDyn Software Quality Assurance test suite, which are comprised of a total of 285 solid-element tests. Testing for each material model utilizes two input decks and answer extraction scripts, where one focuses on the linear elastic response and the other examines the inelastic and remaining functionalities of the material model. In total, this work added 285 individual verification test problems in the DYNA3D/ParaDyn test suite.

42 ENGINEERING↗

Propulsive re-entry aerodynamics Interim report, 1 Jun. 1967 - 1 Jun. 1968

This report discusses the progress accomplished during the first year of a two-year contract to study Propulsive Re-Entry Aerodynamics. Analytical methods were developed during the first year to predict the flow field in the immediate vicinity of a planetary entry system composed of an aeroshell with a single retrorocket which exhausts into a subsonic or supersonic counterflowing planetary atmosphere. In the second year a digital computer program will be developed for the analytical solutions, and the analytical model will be tested by performing an experimental test program and comparing the experimental results with the analytical predictions. The analytical investigation considers the flow field due to a single supersonic retrorocket exhausting from an aeroshell into oncoming subsonic, transonic, or supersonic streams in the large thrusting coefficient regime, 0.5 < C(sub T) = T/q(sub ∞) A(sub m) < 15, which is the range of thrusting coefficients encountered during the terminal landing phase for planetary landing on Mars or Venus. Analyses are provided for all the geometrical features of the flow field such as the location of the terminal shock, jet boundary, and the profile for the interface between the jet and atmospheric gases. In addition, analyses are developed which describe the growth of the mixing layers along the interface and at the edge of the jet boundary and dead-air region and the reattachment of the shear layer to the aeroshell or the recompression of the shear layer in wake type flow. A comprehensive discussion of the experimental wind tunnel test program to be accomplished in Phase II is presented.

Philip O Jarvinen↗

Finite analytic numerical solution of two-dimensional channel flow over a backward-facing step

Laminar channel flow over a backward-facing step is investigated. The finite analytic (FA) method is used to obtain the numerical solution. The FA solutions predict the recirculation zone lengths and the recirculated mass flow rates for Reynolds numbers, Re, of 25, 50, 73, 125, 191 and 229 which correlate well with experimental measurements. The general flow patterns of the recirculation region flows for the Reynolds numbers considered in this study are similar to each other.

Ho, K.-S.↗

A three-dimensional laser ray-tracing methodology for radiation-hydrodynamics simulations

We report on a methodology for performing laser ray-tracing in three spatial dimensions for radiation-hydrodynamics simulation codes. Our method, which is an extension of that developed in Haines et al., Comput. Fluids 201, 104478 (2020), utilizes an automatically generated separate mesh for the laser ray-tracing from the radiation-hydrodynamics mesh. This enables the laser mesh to be tailored to minimize ray noise with significantly fewer rays than would be required when the ray-tracing is performed on the radiation-hydrodynamics mesh, primarily by allowing the use of high-aspect-ratio cells that are not suitable for hydrodynamics solvers. For a planar target, we show that our method provides a ≈ 100× reduction in computational expense to achieve a fixed level of ray noise relative to ray-tracing directly on the radiation-hydrodynamics mesh. The relatively low ray requirement also enables efficient computation of cross-beam energy transfer. Each cell in the logically cubic laser mesh is a non-convex dodecahedron with triangular sides, and numerical integration of the ray trajectories and inverse bremsstrahlung is performed by mapping each cell to the unit cube. We will describe our methodology in detail as well as its implementation in the xRAGE radiation-hydrodynamics code, discuss performance, and present the results from applying the methodology to test problems with analytic solutions for laser ray-tracing through a quadratic density gradient with an analytic solution as well as for a laser-driven heat front. In 3D radiation-hydrodynamics simulations of laser-driven experiments performed on the National Ignition Facility, laser ray-tracing with our methodology uses less than 1% of total computational time while introducing acceptably low levels of ray noise.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Large-scale separation and hysteresis in cascades

An approach using a two-dimensional thin aerofoil, allied with the theory of viscous bluff-body separation, is used to study the initial cross-over from massive separation to an attached flow in a single-row unstaggered cascade. Analytic solutions are developed for the limit of small cascade-spacing. From the analytic solutions several interesting features of the cascade are examined, including multiple-solution branches and multiple regions of hysteresis. In addition, numerical results are presented for several selected aerofoils. Some of the aerofoils are found to contain markedly enlarged regions of hysteresis for certain critical cascade spacings.

Rothmayer, A. P.↗