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A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.
A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.
The independent modal space control (IMSC) method is described and compared with the coupled controls method. Although the coupled controls require fewer actuators, the IMSC provides: larger choice of control techniques, including nonlinear control; lower computational effort; lower computer storage requirement; lower control energy; provable robustness; and actuator location flexibility.
The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.
A vertically-coupled whispering gallery mode (WGM) resonator optical waveguide, a method of reducing a group velocity of light, and a method of making a waveguide are provided. The vertically-coupled WGM waveguide comprises a cylindrical rod portion having a round cross-section and an outer surface. First and second ring-shaped resonators are formed on the outer surface of the cylindrical rod portion and are spaced from each other along a longitudinal direction of the cylindrical rod. The first and second ringshaped resonators are capable of being coupled to each other by way an evanescent field formed in an interior of the cylindrical rod portion.
A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.
The utility of several approximate scattering methods for predicting collision induced spectral pressure broadening has been tested by comparison with accurate close coupling results. In particular, broadening of the pure rotational spectra of HD, HCl, CO, and HCN - all perturbed by low energy collisions with He atoms - has been computed using the effective potential formalism of Rabitz, the decoupled l-dominant approximation of DePristo and Alexander, and the j(2)-conserving coupled states method of McGuire and Kouri. For this last method, pressure broadening cross sections have been obtained with the new, correct expression recently derived by Goldflam and Kouri as well as with an earlier formalism based on an incorrect labeling of the scattering matrices. These methods were found to be generally diasppointing for predicting pressure broadening with the exception of the new, correctly formulated j(2)-conserving coupled states method which was found to agree quantitatively (better than 5%) with close coupling values for all cases studied.
Time-domain and frequency-domain methods for coupling substructures with general linear damping are discussed. A time-domain method is presented which employs a state variable representation of each substructure. Also presented is a method which employs frequency-domain coupling together with DFT and FFT transformations to obtain transient response solutions.
Exposure estimates inside space vehicles, surface habitats, and high altitude aircraft exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETCHEDS and FLUKA, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion (A<4) transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.
A hybrid method for light scattering by an arbitrary particle using the scattering-order formulation of the coupled dipole method is described. An arbitrary particle is divided into two or more segments, and the field scattered by the particle is obtained from the fields scattered by each segment together with the field due to interactions among segments. An exact or approximate theory is used to calculate the scattered field from each segment, and interactions are included using the scattering-order formulation of the coupled dipole method. Calculations show that for certain particles, this hybrid approach can require fewer computations and give more accurate results than the scattering-order method.
Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.
The Ca3 and Ca4 metallic clusters have been investigated using state-of-the-art ab initio quantum mechanical methods. Large atomic natural orbital basis sets have been used in conjunction with the singles and doubles coupled-cluster (CCSD) method, a coupled-cluster method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), and the multireference configuration interaction (MRCI) method. The equilibrium geometries, binding energies and harmonic vibrational frequencies have been determined with each of the methods so that the accuracy of the coupled-cluster methods may be assessed. Since the CCSD(T) method reproduces the MRCI results very well, cubic and quartic force fields of Ca3 and Ca4 have been determined using this approach and used to evaluate the fundamental vibrational frequencies. The infrared intensities of both the e' mode of Ca3 and the t2 mode of Ca4 are found to be small. The results obtained in this study are compared and contrasted with those from our earlier studies on small Be and Mg clusters.
Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one- dimensional convection-diffusion-reaction (CDR) equations. Accuracy, stability, conservation, and dense-output are first considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, (N = 2), additive Runge-Kutta (ARK(sub 2)) methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms of the partitioned method are of equal order to those of the elemental methods. Derived ARK(sub 2) methods have vanishing stability functions for very large values of the stiff scaled eigenvalue, z['] yields -infinity, and retain high stability efficiency in the absence of stiffness, z['] yield 0. Extrapolation-type stage- value predictors are provided based on dense-output formulae. Optimized methods minimize both leading order ARK(sub 2) error terms and Butcher coefficient magnitudes as well as maximize conservation properties. Numerical tests of the new schemes on a CDR problem show negligible stiffness leakage and near classical order convergence rates. However, tests on three simple singular-perturbation problems reveal generally predictable order reduction. Error control is best managed with a PID-controller. While results for the fifth-order method are disappointing, both the new third- and fourth-order methods are at least as efficient as existing ARK(sub 2) methods.
The H + CO --> HCO reaction has been characterized with correlation consistent basis sets at five levels of theory in order to benchmark the sensitivities of the barrier height and reaction ergicity to the one-electron and n-electron expansions of the electronic wave function. Single and multireference methods are compared and contrasted. The coupled cluster method RCCSD(T) was found to be in very good agreement with Davidson-corrected internally-contracted multireference configuration interaction (MRCI+Q). Second-order Moller-Plesset perturbation theory (MP2) was also employed. The estimated complete basis set (CBS) limits for the barrier height (in kcal/mol) for the five methods, including harmonic zero-point energy corrections, are MP2, 4.66; RCCSD, 4.78; RCCSD(T), 4.15; MRCI, 5.10; and MRCI+Q, 4.07. Similarly, the estimated CBS limits for the ergicity of the reaction are: MP2, -17.99; RCCSD, -13.34; RCCSD(T), -13.79; MRCI, -11.46; and MRCI+Q, -13.70. Additional basis set explorations for the RCCSD(T) method demonstrate that aug-cc-pVTZ sets, even with some functions removed, are sufficient to reproduce the CBS limits to within 0.1-0.3 kcal/mol.
Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.
A method of assembling an energy harvesting system is provided. The method includes coupling at least one energy storage device in flow communication with at least one apparatus that is configured to generate thermal energy and to transfer the thermal energy into at least one fluid stream. The energy storage device is configured to store the fluid stream. Moreover, the method includes coupling at least one fluid transfer device downstream from the energy storage device. The fluid transfer device receives the fluid stream from the energy storage device. A bladeless turbine is coupled in flow communication with the fluid transfer device, wherein the bladeless turbine receives the fluid stream to generate power.
This work presents a general framework for model reduction of non-equilibrium energy transfer and dissociation processes. The multi-group maximum-entropy method is coupled with the quasi-classical trajectory method to directly construct a reduced order model for chemical non-equilibrium. Kinetic data is calculated by applying detailed balance at a microscopic level, overcoming the limitation of calculating recombination kinetic data. This approach enables the construction of a reduced order model for kinetics which bypasses the need to compute state-to-state kinetic data. This physics based reduced order model ensures that an equilibrium distribution is reached given infinite time, while allowing for non-equilibrium distributions during the relaxation and dissociation processes. A proof-of-concept test case demonstrates the applicability of this model by comparison with state-to-state kinetic data for the N2(Chi (sup 1) Sigma ((sub g), (sup plus sign)) minus N ((exp 4) S (sub u)) system with excellent agreement.
A coupled zonal method has been developed for modeling flows about aircraft with highly integrated advanced nozzle installations in which the exhaust plume interacts with the aircraft flow field to enhance performance. A cost effective flow analysis is achieved by dividing the flow domain into zones and coupling the zonal solutions. PAN AIR is used to model the flow in the inviscid zone which surrounds the aircraft. The plume zone flow field is solved with a PNS code. The flow in the optional internal nozzle zone is modeled using a full Navier-Stokes code. An automated iterative procedure couples the inviscid and plume zones by passing updated boundary conditions between the zones. The coupled analysis provides converged solutions for the overall flow field. The method is demonstrated for a highly integrated nonaxisymmetric vectored nozzle installed on a swept-wing aircraft.