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Results for “generalized finite differences”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Optical NOR logic gate design on square lattice photonic crystal platform

We numerically demonstrate a new configuration of all-optical NOR logic gate with square lattice photonic crystal (PhC) waveguide using finite difference time domain (FDTD) method. The logic operations are based on interference effect of optical waves. We have determined the operating frequency range by calculating the band structure for a perfectly periodic PhC using plane wave expansion (PWE) method. Response time of this logic gate is 1.98 ps and it can be operated with speed about 513 GB/s. The proposed device consists of four linear waveguides and a square ring resonator waveguides on PhC platform.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Breather management in the derivative nonlinear Schrödinger equation with variable coefficients

We investigate breather solutions of the generalized derivative nonlinear Schrödinger (DNLS) equation with variable coefficients, which is used in the description of femtosecond optical pulses in inhomogeneous media. The solutions are constructed by means of the similarity transformation, which reduces a particular form of the generalized DNLS equation into the standard one, with constant coefficients. Examples of bright and dark breathers of different orders, that ride on finite backgrounds and may be related to rogue waves, are presented. - Highlights: • Exact solutions of a generalized derivative NLS equation are obtained. • The solutions are produced by means of a transformation to the usual integrable equation. • The validity of the solutions is verified by comparing them to numerical counterparts. • Stability of the solutions is checked by means of direct simulations. • The model applies to the propagation of ultrashort pulses in optical media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Free surface modeling in OWC chamber with parabolic side walls using 3D BEM

In this paper, BEM was used for free surface modeling in OWC chamber and out of it. Linear kinematic and dynamic boundary conditions were used for free surface out of OWC chamber and nonlinear forms were used for free surface in the chamber. These boundary conditions were discretized by finite differences method. Also, some thermodynamics relations were applied for trapped air behavior modeling in OWC chamber. Wave specifications in Chabahar region were used in modeling because these waves have an acceptable power for electricity generation. The results show a good agreement with results of other researches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Mimetic Finite Differences and Algebraic Multilevel Methods for Reservoir Performance Predictions: CRADA Final Report

The need to better predict and control reservoir performance is driving the development of increasingly sophisticated reservoir models that use unstructured general polyhedral grids to capture highly detailed stratigraphy. However, both discretization methods and scalable iterative solution algorithms for these situations are an active area of research. In this work we compared the performance of a new Mimetic Finite Difference (MFD) method with two new Mixed Finite Element methods, and LANL and the CRADA Participant investigated the performance of Los Alamos National Laboratory’s algebraic multigrid code on realistic flow problems. Furthermore, uncertainty quantification requires rapid evaluations of reservoir models. To do this, fine-scale reservoir models need to be coarsened and yet important fine-scale features and processes that have a significant impact on flows need to be preserved. To this end, we investigated the use of multi-resolution methods, such as the Multilevel Multiscale Mimetic (M3) method, to coarsen reservoir models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Low-power, ultrafast, and dynamic all-optical tunable plasmonic analog to electromagnetically induced transparency in two resonators side-coupled with a waveguide system

We theoretically and numerically investigate a low-power, ultrafast, and dynamic all-optical tunable plasmonic analog to electromagnetically induced transparency (EIT) in two nanodisk resonators side-coupled to a metal-insulator-metal plasmonic waveguide system. The optical Kerr effect is enhanced by the slow light effect of the plasmonic EIT-like effect and the plasmonic waveguide based on graphene-Ag composite material structures with giant effective Kerr nonlinear coefficient. The optical Kerr effect modulation method is applied to improve tuning rate with response time of subpicoseconds or even femtoseconds. With dynamically tuning the propagation phase of the plasmonic waveguide, π-phase shift of the transmission spectrum in the plasmonic EIT-like system is achieved under excitation of a pump light with an intensity as low as 5.85 MW/cm{sup 2}. The group delay is controlled between 0.09 and 0.4 ps. All observed schemes are analyzed rigorously through finite-difference time-domain simulations and coupled-mode formalism. Results show a new direction toward the low power consumption and ultrafast responses of integration plasmonic photonic devices and all-optical dynamical storage of light devices in optical communication and quantum information processing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Accurate gradient approximation for complex interface problems in 3D by an improved coupling interface method

Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Development of a layered two-dimensional approach for modelling fuel rod behaviour

Historically, light water reactor (LWR) fuel performance codes have been developed using layered one-dimensional (1D) or two-dimensional (2D) axisymmetric approaches. In a layered 1D analysis the fuel rod is divided into a number of axial layers, each of which is represented using a 1D axisymmetric model with generalized plane strain assumptions. These simulations are typically solved using a finite difference technique. A limited set of data such as fission gas behaviour, has an effect on all layers. The 2D axisymmetric approach improves the axial fidelity of the simulation by employing a finite element representation of the fuel rod geometry, and more readily allows for phenomena such as axial heat transfer to be represented. Depending upon the fuel rod analysis being investigated the assumptions made in layered 1D or 2D axisymmetric approaches can result in important physics not being adequately captured. Therefore, the Bison fuel performance code has been developed over the last 10 years to provide flexibility in modelling of fuel behaviour. The code is capable of investigating fuel behaviour in 1D, layered 1D, 2D, 2D-axisymmetric, and 3D geometric representations depending upon the fidelity required for a particular analysis. Recently, a new layered 2D approach has been developed and implemented. This approach utilizes a similar technique to layered 1D except the thermo-mechanical analysis in each layer is solved on layered disks that can have azimuthally varying boundary conditions. These azimuthally varying conditions are important for a variety of fuel rod applications including discrete fuel fracture and rod behaviour during Loss of Coolant Accidents (LOCA). This paper describes the development of the layered 2D approach and the types of analyses for which it is applicable. Results are presented that illustrate the improvement in model predictions provided by this approach over layered 1D and 2D-axisymmetric approaches for the LOCA rod behaviour.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Nonlinear radiative heat transfer and Hall effects on a viscous fluid in a semi-porous curved channel

In this paper, effects of Hall currents and nonlinear radiative heat transfer in a viscous fluid passing through a semi-porous curved channel coiled in a circle of radius R are analyzed. A curvilinear coordinate system is used to develop the mathematical model of the considered problem in the form partial differential equations. Similarity solutions of the governing boundary value problems are obtained numerically using shooting method. The results are also validated with the well-known finite difference technique known as the Keller-Box method. The analysis of the involved pertinent parameters on the velocity and temperature distributions is presented through graphs and tables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Optimal Control of a Degenerate PDE for Surface Shape

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape in this paper. Specifically, we consider an objective (tracking) functional for surface shape with the prescribed mean curvature equation in graph form as a state constraint. The control variable is the prescribed curvature. We prove existence of an optimal control, and using improved regularity estimates, we show sufficient differentiability to make sense of the first order optimality conditions. This allows us to rigorously compute the gradient of the objective functional for both the continuous and discrete (finite element) formulations of the problem. Numerical results are shown to illustrate the minimizers and optimal controls on different domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

High-fidelity numerical solution of the time-dependent Dirac equation

A stable high-order accurate finite difference method for the time-dependent Dirac equation is derived. Grid-convergence studies in 1-D and 3-D corroborate the analysis. The method is applied to time-resolved quantum tunneling where a comparison with the solution to the time-dependent Schrödinger equation in 1-D illustrates the differences between the two equations. In contrast to the conventional tunneling probability decay predicted by the Schrödinger equation, the Dirac equation exhibits Klein tunneling. Solving the time-dependent Dirac equation with a step potential in 3-D reveals that particle spin affects the tunneling process. The observed spin-dependent reflection allows for a new type of spin-selective measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

We consider specific realizations of different implicit generalized Runge–Kutta methods as applied to the numerical integration with respect to time of initial-boundary-value problems for the second-order parabolic equations and investigate their spectral stability. It is shown that all implicit generalized Runge–Kutta methods are unconditionally spectrally stable but some of them have the conditional property of monotonicity of the numerical solution with respect to time. The functions of spectral stability of the implicit generalized Runge–Kutta methods are rational. We compare the analytic solution of the nonstationary one-dimensional problem of heat conduction with the numerical solutions of this problem obtained by different implicit generalized Runge–Kutta methods. It is shown that, in this case, the application of the one-stage Radau methods with subsequent discretization of the problem with respect to the space variable leads to the classical forward finite difference scheme (Laasonen scheme), whereas the use of the one-stage Gauss–Legendre method leads to a six-point symmetric scheme (Crank–Nicolson scheme). It is shown that diagonally implicit generalized Nørsett and Burrage methods are realized in almost the same way as the one-stage Radau and Gauss–Legendre methods but their accuracy in the time step is 10–1000 times higher. On the basis of comparison of the numerical and analytic solutions, we conclude that, in order to get practically suitable numerical solutions without any restrictions on the time step, it is reasonable to use one- and three-stage generalized Radau methods or two- and four-stage Lobatto IIIC methods. All other explicit and implicit generalized Runge–Kutta methods require certain restrictions imposed on the time step.

42 ENGINEERING↗
DOE OSTI2017

Theoretical Analysis of Photoelectron Spectra of Pure and Mixed Metal Clusters: Disentangling Size, Structure, and Composition Effects

A theoretical/computational description and analysis of the spectra of electron binding energies of Al 12 - , Al 13 - and Al 12 Ni- clusters, which differ in size and/or composition by a single atom yet possess strikingly different measured photoelectron spectra, is presented. It is shown that the measured spectra can not only be reproduced computationally with quantitative fidelity – this is achieved through a combination of state-of-the-art density functional theory with a highly accurate scheme for conversion of the Kohn-Sham eigenenergies into electron binding energies – but also explained in terms of the effects of size, structure/symmetry and composition. Furthermore, a new methodology is developed and applied that provides for disentanglement and differential assignment of the separate roles played by size, structure/symmetry and composition in defining the observed differences in the measured spectra. The methodology is general and applicable to any finite system, homogeneous or heterogeneous. Finally, we project that in combination with advances in synthesis techniques this methodology will become an indispensable computation-based aid in the design of controlled synthesis protocols for manufacture of nanosystems and nanodevices with precisely desired electronic and other characteristics.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A numerical hybrid model for outdoor sound propagation in complex urban environments

Noise mapping in large and dense urban areas is computationally challenging, if not impossible, with the use of conventional numerical techniques. Recently, promising results have shown the potential of energy-based models to compete with conventional numerical techniques. In this study, a hybrid full-wave/diffusion propagation model is proposed to address some of the flaws of the traditional diffusion model. The full-wave model is used for predicting sound propagation (i) near the source, where interactions between waves are important, and (ii) outside the cluttered environment, where free-field-like conditions apply. Finally, the diffusion model is used in regions where diffusion conditions are met.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗