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DOE OSTI2016

Topological self-dual configurations in a Maxwell–Higgs model with a CPT-odd and Lorentz-violating nonminimal coupling

We have studied the existence of topological self-dual configurations in a nonminimal CPT-odd and Lorentz-violating (LV) Maxwell–Higgs model, where the LV interaction is introduced by modifying the minimal covariant derivative. The Bogomol’nyi–Prasad–Sommerfield formalism has been implemented, revealing that the scalar self-interaction implying self-dual equations contains a derivative coupling. The CPT-odd self-dual equations describe electrically neutral configurations with finite total energy proportional to the total magnetic flux, which differ from the charged solutions of other CPT-odd and LV models previously studied. In particular, we have investigated the axially symmetrical self-dual vortex solutions altered by the LV parameter. For large distances, the profiles possess general behavior similar to the vortices of Abrikosov–Nielsen–Olesen. However, within the vortex core, the profiles of the magnetic field and energy can differ substantially from ones of the Maxwell–Higgs model depending if the LV parameter is negative or positive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

Abstract. Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1975

A fast semidirect method for computing transonic aerodynamic flows

A fast, semidirect, iterative computational method, previously introduced for finite-difference solution of subsonic and slightly supercritical flow over airfoils, is extended both to apply to strongly supercritical conditions and to include full second-order accuracy in computing inviscid flows over airfoils. The nonlinear small-disturbance equations are solved iteratively by a direct, linear, elliptic solver. General, fully conservative, type-dependent difference equations are formulated, including parabolic- and shock-point transition operators that provide consistency with the integral conservation laws. These equations specialize to either first-order or to fully second-order-accurate equations. Various free parameters are evaluated for rapid convergence of the first-order scheme. Resulting pressure distributions and computing times are compared with the improved Murman-Cole line-relaxation method.

Martin, E. D.↗

NASA NTRS1983

Scattering from a V-shaped groove in the resonance domain

Radiation scattered from a V-shaped groove in the resonance domain is measured and compared with predictions from a rigorous theory. The calculated scattering is found to accurately predict the number of peaks and the general shape of the observed scattering. Small variations in groove shape are found to alter peak heights noticeably and peak positions slightly. The finite beam size causes unavoidable discrepancies between calculated and measured scattering. The theory of Maystre provides a very good tool for determining the scattering capabilities of different shapes without having to measure them.

White, G. S.↗

NASA NTRS1983

An analytical investigation of shape control of large space structures by applied temperatures

An analytical procedure for the static shape control of flexible space structures subjected to thermal distortions is developed which is based on prescribing temperatures in control elements having much higher coefficients of thermal expansion than the main structure. The temperatures at the control elements are defined so as to minimize the overall thermal distortion of the structure from its ideal shape, and a matrix equation is obtained which can be solved for the set of optimum control temperatures. A formulation of the procedure for continuous structures governed by differential equations and a formulation for discrete (finite element modeled) structures governed by matrix equations are presented. The equations from the continuous formulation are employed for the shape control of a simple beam distorted by nonuniform heating, and the discrete formulation is applied in a general purpose finite-element structural analysis computer program for the shape control of a 750 m radiometer antenna reflector dish subjected to orbital heating. A reduction in thermal distortion by a factor of nearly 50 was obtained with the use of only seven control elements. Results for four different sets of control locations for the antenna are presented in which reductions in distortion of up to a factor of four were obtained.

Haftka, R. T.↗

NASA NTRS1988

Investigation of supersonic chemically reacting and radiating channel flow

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Mani, Mortaza↗

NASA NTRS1994

Analyzing Seals With Two-Phase Flows

SEAL computer program analyzes steady-state performance of face seal with two-phase leakage flow. Calculates general trends of performance under both low- and high-leakage conditions and, by extrapolation, behavior in intermediate region. Parameters investigated include subcooling, coning of seal faces, speeds of rotation, conductivities of seal materials, and widths of seal faces. Program incorporates idealized mathematical models, and based on finite-difference approach. Written in FORTRAN 77.

Lau, S.↗

NASA NTRS2005

Coupled fvGCM-GCE Modeling System, 3D Cloud-Resolving Model and Cloud Library

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional singlecolumn models in simulating various types of clouds and cloud systems from Merent geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloudscale model (termed a super-parameterization or multiscale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameteridon NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. A seed fund is available at NASA Goddard to build a MMF based on the 2D Goddard cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM). A prototype MMF in being developed and production nms will be conducted at the beginning of 2005. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes, (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), (3) A cloud library generated by Goddard MMF, and 3D GCE model, and (4) A brief discussion on the GCE model on developing a global cloud simulator.

Tao, Wei-Kuo↗

NASA NTRS2006

Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

Svard, Magnus↗

DOE OSTI2023

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels

Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.

Karwa, Vishesh↗

DOE OSTI2016

A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimate for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Theory of the phonon side-jump contribution in anomalous Hall effect

The role of electron-phonon scattering in finite-temperature anomalous Hall effect is still poorly understood. In this work we present a Boltzmann theory for the side-jump contribution from electron-phonon scattering, which is derived from the microscopic quantum mechanical theory. Furthermore, we show that the resulting phonon side-jump conductivity generally approaches different limiting values in the high and low temperature limits, and hence can exhibit strong temperature dependence in the intermediate temperature regime. Our theory is amenable to ab initio treatment, which makes quantitative comparison between theoretical and experimental results possible.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1974

Subsonic and supersonic indicial aerodynamics and aerodynamic transfer function for complex configurations

A general theory for indicial-potential-compressible aerodynamics around complex configurations is presented. The motion is assumed to consist of constant subsonic or supersonic speed (steady state) and small perturbations around the steady state. Using the finite-element method to discretize the space problem, a set of differential-difference equations in time relating the potential to its normal derivative on the surface of the body was obtained. The aerodynamics transfer function was derived by using standard method of operational calculus.

Morino, L.↗

NASA NTRS1976

Incremental analysis of large elastic deformation of a rotating cylinder

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

Buchanan, G. R.↗

NASA NTRS1986

Regularity estimates up to the boundary for elliptic systems of difference equations

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations.

Strikwerda, J. C.↗

NASA NTRS1987

Navier-Stokes computations of prolate spheroids at angle of attack

Three-dimensional viscous flow calculations are made for a 6:1 prolate spheroid at conditions for which detailed experimental data are available. The computations are made with two finite-volume algorithms for the compressible Navier-Stokes equations, one using central differencing for the convective and pressure terms and the other using an upwind-biased flux-difference-splitting approach. The effects of grid density and artificial dissipation on the accuracy of the numerical results are included. Generally good agreement of the computations with the experimental results is obtained over a range of Reynolds numbers and angles-of-attack, up to 30 deg, although the results at lower Reynolds numbers are sensitive to the assumed transition location.

Vatsa, V. N.↗

NASA NTRS1992

A turbulence model for iced airfoils and its validation

A turbulence model based on the extension of the algebraic eddy viscosity formulation of Cebeci and Smith developed for two dimensional flows over smooth and rough surfaces is described for iced airfoils and validated for computed ice shapes obtained for a range of total temperatures varying from 28 to -15 F. The validation is made with an interactive boundary layer method which uses a panel method to compute the inviscid flow and an inverse finite difference boundary layer method to compute the viscous flow. The interaction between inviscid and viscous flows is established by the use of the Hilbert integral. The calculated drag coefficients compare well with recent experimental data taken at the NASA-Lewis Icing Research Tunnel (IRT) and show that, in general, the drag increase due to ice accretion can be predicted well and efficiently.

Shin, Jaiwon↗

NASA NTRS1992

A generalized approach to the thermal analysis of the Long Duration Exposure Facility's flight experiments

The generalized method used in the thermal analysis of the LDEF flight experiments is presented. The approach consists of developing a mathematical lumped parameter node representation of the experiment; defining the source and sink temperature boundary conditions; calculating the albedo, infrared, and solar orbital heating fluxes; and solving with a finite difference technique. The temperature predictions can be made either on a per orbit basis or for any length of mission time using a daily averaged calculated composite flux. The thermal analysis of the Ultra Heavy Cosmic Ray Experiment (UHCRE-A0178) is presented as an example of this approach.

Sampair, Thomas R.↗