Quasi-isotropic approximation of geometric optics
Modified geometric optics method for solution of Maxwell equations
Kravtsov, Yu. A.↗
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Evaluating lightning hazards to building environments using explicit numerical solutions of Maxwell's equations
The objective here is to describe the lightning hazards to buildings and their internal environments using advanced formulations of Maxwell's Equations. The method described is the Three Dimensional Finite Difference Time Domain Solution. It can be used to solve for the lightning interaction with such structures in three dimensions with the inclusion of a considerable amount of detail. Special techniques were developed for including wire, plumbing, and rebar into the model. Some buildings have provisions for lightning protection in the form of air terminals connected to a ground counterpoise system. It is shown that fields and currents within these structures can be significantly high during a lightning strike. Time lapse video presentations were made showing the electric and magnetic field distributions on selected cross sections of the buildings during a simulated lightning strike.
Collier, Richard S.↗
Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft
Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.
power↗
Vectorization of a particle simulation method for hypersonic rarefied flow
An efficient particle simulation technique for hypersonic rarefied flows is presented at an algorithmic and implementation level. The implementation is for a vector computer architecture, specifically the Cray-2. The method models an ideal diatomic Maxwell molecule with three translational and two rotational degrees of freedom. Algorithms are designed specifically for compatibility with fine grain parallelism by reducing the number of data dependencies in the computation. By insisting on this compatibility, the method is capable of performing simulation on a much larger scale than previously possible. A two-dimensional simulation of supersonic flow over a wedge is carried out for the near-continuum limit where the gas is in equilibrium and the ideal solution can be used as a check on the accuracy of the gas model employed in the method. Also, a three-dimensional, Mach 8, rarefied flow about a finite-span flat plate at a 45 degree angle of attack was simulated. It utilized over 10 to the 7th particles carried through 400 discrete time steps in less than one hour of Cray-2 CPU time. This problem was chosen to exhibit the capability of the method in handling a large number of particles and a true three-dimensional geometry.
Mcdonald, Jeffrey D.↗
Investigation of mass transfer between two parallel walls at different temperatures by a moment method
One-dimensional flow between two fixed parallel walls composed of the same substance but at different temperatures and spaced a distance 1 apart is considered. The hot plate is the evaporating surface (source) and the cold plate is the condensing surface (sink). The vapor between the two plates is assumed to be a monatomic gas consisting of Maxwell molecules. Lee's moment method is used to obtain a set of six nonlinear equations. Both the nonlinear equations and a linearized approximation to them are solved.
Sloat, T. N.↗
Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1M Unknowns
Matrix methods for solving integral equations via direct solve LU factorization are presently limited to weeks to months of very expensive supercomputer time for problems sizes of several hundred thousand unknowns. This report presents matrix LU factor solutions for electromagnetic scattering problems for problem sizes to one million unknowns with thousands of right hand sides that run in mere days on PC level hardware. This EM solution is accomplished by utilizing the numerical low rank nature of spatially blocked unknowns using the Adaptive Cross Approximation for compressing the rank deficient blocks of the system Z matrix, the L and U factors, the right hand side forcing function and the final current solution. This compressed matrix solution is applied to a frequency domain EM solution of Maxwell's equations using standard Method of Moments approach. Compressed matrix storage and operations count leads to orders of magnitude reduction in memory and run time.
Shaeffer, John↗
Comprehensive Thematic T-Matrix Reference Database: A 2014-2015 Update
The T-matrix method is one of the most versatile and efficient direct computer solvers of the macroscopic Maxwell equations and is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper is the seventh update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2013. It also lists a number of earlier publications overlooked previously.
electromagnetic scattering↗
An Implicit Characteristic Based Method for Electromagnetics
An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.
Beggs, John H.↗
An Approximate Dissipation Function for Large Strain Rubber Thermo-Mechanical Analyses
Mechanically induced viscoelastic dissipation is difficult to compute. When the constitutive model is defined by history integrals, the formula for dissipation is a double convolution integral. Since double convolution integrals are difficult to approximate, coupled thermo-mechanical analyses of highly viscous rubber-like materials cannot be made with most commercial finite element software. In this study, we present a method to approximate the dissipation for history integral constitutive models that represent Maxwell-like materials without approximating the double convolution integral. The method requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. Numerical data is provided to demonstrate the limitations of this approximate method for determining dissipation. Rubber cylinders with imbedded steel disks and with an imbedded steel ball are dynamically loaded, and the nonuniform heating within the cylinders is computed.
Johnson, Arthur R.↗
A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations
A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.
Liu, Yen↗
The origin of spurious solutions in computational electromagnetics
The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.
Jiang, Bo-Nan↗
SOLAR COLLECTOR DEVELOPMENT
State-of-the-art of solar collectors which concentrate low-level solar energy to a usable density for the particular energy-conversion method
SOLAR COLLECTOR↗
Preliminary Investigation of the 'freeze-casting' Method for Forming Refractory Powders
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Maxwell, W A↗
Multi-Component Diffusion with Application To Computational Aerothermodynamics
The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.
Sutton, Kenneth↗
Analysis of microstrip dipoles and slots transversely coupled to a microstrip line using the FDTD method
Printed dipole elements and their complement, linear slots, are elementary radiators that have found use in low-profile antenna arrays. Low-profile antenna arrays, in addition to their small size and low weight characteristics, offer the potential advantage of low-cost, high-volume production with easy integration with active integrated circuit components. The design of such arrays requires that the radiation and impedance characteristics of the radiating elements be known. The FDTD (Finite-Difference Time-Domain) method is a general, straight-forward implementation of Maxwell's equations and offers a relatively simple way of analyzing both printed dipole and slot elements. Investigated in this work is the application of the FDTD method to the analysis of printed dipole and slot elements transversely coupled to an infinite transmission line in a multilayered configuration. Such dipole and slot elements may be used in dipole and slot series-fed-type linear arrays, where element offsets and interelement line lengths are used to obtain the desired amplitude distribution and beam direction, respectively. The design of such arrays is achieved using transmission line theory with equivalent circuit models for the radiating elements. In an equivalent circuit model, the dipole represents a shunt impedance to the transmission line, where the impedance is a function of dipole offset, length, and width. Similarly, the slot represents a series impedance to the transmission line. The FDTD method is applied to single dipole and slot elements transversely coupled to an infinite microstrip line using a fixed rectangular grid with Mur's second order absorbing boundary conditions. Frequency-dependent circuit and scattering parameters are obtained by saving desired time-domain quantities and using the Fourier transform. A Gaussian pulse excitation is applied to the microstrip transmission line, where the resulting reflected signal due to the presence of the radiating element is used to determine the equivalent element impedance.
Tulintseff, A. N.↗
Reflection Coefficients on Surfaces of Different Periodic Structure
Diffraction properties of lossy periodic gratings with the metal base were investigated by solving Maxwell's equations numerically using the differential method. Two periodic surfaces were employed in the simulation: triangle structure and tilting triangle structure. Based on the numerical solution and in conjunction with the algorithm of Adams-Moulton, we computed reflection coefficients of plane waves with different wavelengths and different incident angles. The dielectric properties were also explored using various dielectric constants. The results show that the reflection coefficients of both TE and TM waves are quite sensitive to the incident angles of the plane waves when the metal sheet exists, which is in good agreement with the experimental data.
Niu, Pengfei↗
Information theory lateral density distribution for Earth inferred from global gravity field
Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.
Rubincam, D. P.↗
Finite difference time domain modeling of steady state scattering from jet engines with moving turbine blades
The approach chosen to model steady state scattering from jet engines with moving turbine blades is based upon the Finite Difference Time Domain (FDTD) method. The FDTD method is a numerical electromagnetic program based upon the direct solution in the time domain of Maxwell's time dependent curl equations throughout a volume. One of the strengths of this method is the ability to model objects with complicated shape and/or material composition. General time domain functions may be used as source excitations. For example, a plane wave excitation may be specified as a pulse containing many frequencies and at any incidence angle to the scatterer. A best fit to the scatterer is accomplished using cubical cells in the standard cartesian implementation of the FDTD method. The material composition of the scatterer is determined by specifying its electrical properties at each cell on the scatterer. Thus, the FDTD method is a suitable choice for problems with complex geometries evaluated at multiple frequencies. It is assumed that the reader is familiar with the FDTD method.
Ryan, Deirdre A.↗