Application of FDTD Method to Periodic Structures
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Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations
The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.
Canuto, C.↗
Preconditioned minimal residual methods for Chebyshev spectral calculations
The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.
Canuto, C.↗
A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces
Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.
Lenardic, A.↗
On the Coupling of CDISC Design Method with FPX Rotor Code
A rotor section aerodynamics design package is developed by coupling Constrained Direct Iterative Surface Curvature (CDISC) design method with the FPX rotor code. The coupling between the CDISC design and the FPX flow analysis is fully automated. The CDISC design method employs a predictor-corrector procedure iteratively to determine a surface geometry which produces a target pressure distribution, where the target pressure distributions is either pre-defined or automatically generated through flow and geometry constraints. The FPX code is an eXtended Full-Potential rotor Computational Fluid Dynamics (CFD) code, which solves the three-dimensional unsteady full-potential equation in a strong conservative form using an implicit approximate factorization finite-difference scheme with entropy and viscosity corrections. Application of the CDISC design method coupled with the FPX rotor code is made for rotor blades in hovering motions. Several design examples are presented to demonstrate the capability of the new package in rotor section design.
Hu, Hong↗
Discrete approximation methods for parameter identification in delay systems
Approximation schemes for parameter identification problems in which the governing state equation is a linear functional differential equation of retarded type are constructed. The basis of the schemes is the replacement of the parameter identification problem having an infinite dimensional state equation by a sequence of approximating parameter identification problems in which the states are given by finite dimensional discrete difference equations. The difference equations are constructed using linear semigroup theory and rational function approximations to the exponential. Sufficient conditions are given for the convergence of solutions to the approximating problems, which can be obtained using conventional methods, to solutions to the original parameter identification problem. Finite difference and spline based schemes using Paderational function approximations to the exponential are constructed, and shown to satisfy the sufficient conditions for convergence. A discussion and analysis of numerical results obtained through the application of the schemes to several examples is included.
Rosen, I. G.↗
Error evaluation for difference approximations to ordinary differential equations
Method involves relationships between errors introduced by using finite sampling rates and parameters describing specific numerical method used. Procedurre is used in design and analysi of digital filters and simulators.
Hammond, J. L., Jr.↗
Integrated numerical methods for hypersonic aircraft cooling systems analysis
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
Petley, Dennis H.↗
The finite ground plane effect on the microstrip antenna radiation patterns
The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.
Huang, J.↗
Unsteady aerodynamics in time and frequency domains for finite time arbitrary motion of rotary wings in hover and forward flight
Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.
Dinyavari, M. A. H.↗
On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations
The method of pseudocompressibility is being tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite-difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibility for solving the pressure field, coupled with an implicit, approximate-factorization scheme. This coupling is known as the pseudocompressibility method. The pseudocompressibility method introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. However, these waves limit the time-accuracy of the computations. The effects of these waves are analyzed and criteria are set for choosing the pseudocompressibility parameters that govern the pressure wave speed. Test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.
Rogers, S. E.↗
Detecting Structural Failures Via Acoustic Impulse Responses
Advanced method of acoustic pulse reflectivity testing developed for use in determining sizes and locations of failures within structures. Used to detect breaks in electrical transmission lines, detect faults in optical fibers, and determine mechanical properties of materials. In method, structure vibrationally excited with acoustic pulse (a "ping") at one location and acoustic response measured at same or different location. Measured acoustic response digitized, then processed by finite-impulse-response (FIR) filtering algorithm unique to method and based on acoustic-wave-propagation and -reflection properties of structure. Offers several advantages: does not require training, does not require prior knowledge of mathematical model of acoustic response of structure, enables detection and localization of multiple failures, and yields data on extent of damage at each location.
Bayard, David S.↗
Fracture Mechanics of Thin, Cracked Plates Under Tension, Bending and Out-of-Plane Shear Loading
Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed.
Zehnder, Alan T.↗
Characterization of Meta-Materials Using Computational Electromagnetic Methods
An efficient and powerful computational method is presented to synthesize a meta-material to specified electromagnetic properties. Using the periodicity of meta-materials, the Finite Element Methodology (FEM) is developed to estimate the reflection and transmission through the meta-material structure for a normal plane wave incidence. For efficient computations of the reflection and transmission over a wide band frequency range through a meta-material a Finite Difference Time Domain (FDTD) approach is also developed. Using the Nicholson-Ross method and the Genetic Algorithms, a robust procedure to extract electromagnetic properties of meta-material from the knowledge of its reflection and transmission coefficients is described. Few numerical examples are also presented to validate the present approach.
Deshpande, Manohar↗
Engineering calculations of three-dimensional inviscid hypersonic flow fields
An approximate solution technique has been developed for three-dimensional, inviscid, hypersonic flows. The method uses Maslen's explicit pressure equation and the assumption of approximate stream surfaces in the shock layer. This approximation represents a simplification of Maslen's asymmetric method. The solution procedure involves iteratively changing the shock shape in the subsonic-transonic region until the correct body shape is obtained. Beyond this region, the shock surface is determined by using a marching procedure. Results are presented herein for a paraboloid and elliptic cone at angle of attack. Calculated surface pressure distributions, shock shapes, and property profiles are compared with experimental data and finite-difference solutions of the Euler equations. Comparisons of the results of the present method with experimental data and detailed predictions are very good. Since the present method provides a very rapid computational procedure, it can be used for parametric or preliminary design applications. One useful application would be to incorporate a heating procedure for aerothermal studies.
Riley, Christopher J.↗
Thermal Test Suite for Code Maintenance and Validation of Diablo
This document describes a series of test problems that ensure that the Thermal capabilities of Diablo are working correctly. Diablo utilizes the Finite Element Method to discretize the problem in space and a trapezoidal rule finite difference scheme to discretize the problem in time. This suite will test the codes capabilities to handle various boundary conditions, source terms, and initial conditions. It will also test the coupling between thermal and solid effects, and the use of various linear and nonlinear solvers.
42 ENGINEERING↗
Experimental Study of the 3 He and Neutron Spin Structure at Low Q 2 and The Upgrade of the JLab Polarized 3 He Target
In the scattering process off a nuclear or nucleon target, the Gerasimov-Drell-Hearn (GDH) sum rule for real photons (Q 2 =0 where Q 2 ≡ -q 2 with q the photon's 4-momentum) relates static properties of the target particle's ground state to dynamic properties of all its excited states. On the other side of the Q 2 spectrum, the Bjorken sum rule holds in the Bjorken limit Q 2 → ∞. Bjorken sum rule relates the final structure functions of the proton and neutron to the nucleon axial coupling constant in weak decay. These two sum rules belong to domains where calculations are achievable but use different degrees of freedom: hadronic degrees of freedom at low Q 2 versus partonic degrees of freedom at intermediate Q 2 . Meanwhile, different methods have been used to connect the two sum rules at finite Q 2 values: Chiral Perturbation Theory is used to expand the GDH sum rule while Operator Product Expansion is used to expand the Bjorken sum rule. In recent decades, improvements in polarized beam and polarized target techniques have made it possible to test theoretical predictions in the intermediate Q 2 region. During the Jefferson Lab (JLab) Hall A E97110 experiment, a precise measurement of polarized cross sections was performed at 0.02 < Q 2 < 0.3 GeV 2 using a polarized 3 He target as an effective polarized neutron target. The measured data allowed us to test predictions of Chiral Perturbation Theory at very low Q 2 . Furthermore, an extrapolation to the real photon point Q 2 =0 tests the GDH sum rule on the neutron. In order to reach the small angles necessary for the low Q 2 range, a new septum magnet was installed in Hall A for this experiment. Unfortunately, the magnet was mis-wired during initial running. There were therefore two periods for this experiment: the first period had the defective magnet due to mis-wiring; while in the second period, the magnet had been fixed and was working properly. The cross sections and the asymmetries for the first period must be extracted using a difficult and unusual method employing focal plane variables in the spectrometer. In the work described in this thesis, the target-plane and focal-plane method will be established first and confirmed by elastic scattering cross section measurements from carbon foil and 3 He targets. Cross sections and asymmetries of inelastic scattering were then extracted using the same method, which constitute the main physics results of this thesis. Preliminary results on ITT , the integral of the polarized cross section, were also extracted and are presented in this thesis. In addition to the data analysis of E97110, this thesis includes instrumentation work performed on the polarized 3 He target at JLab. For the 12 GeV program of JLab, the polarized 3 He target is being upgraded to satisfy new experimental requirements. The new target is a convection-based cell with two transfer tubes rather than a single transfer tube as in the former 6 GeV design. The first stage of the target upgrade aims to produce a 40 cm long, 10 amg target that can withstand 30 μA of electron beam current with an in-beam polarization of 55%, doubling the figure-of-merit from the 6 GeV time. Several studies were conducted at the Test Lab of JLab on the new convection cell. Work and improvement done on the Pulse Nuclear Magnetic Resonance (NMR) polarimetry and its test results will be presented. As this thesis is written, the target is being installed in Hall C of JLab in preparation for a 6-month long running from November 2019 to May 2020.
Ton, Nguyen↗