Finite element-finite difference thermal/structural analysis of large space truss structures
NASA Technical Reports Server (NTRS)
Warren, Andrew H.; Arelt, Joseph E.; Eskew, William F.; Rogers, Karen M.
1992-01-01
A technique of automated and efficient thermal-structural processing of truss structures that interfaces the finite element and finite difference method was developed. The thermal-structural analysis tasks include development of the thermal and structural math models, thermal analysis, development of an interface and data transfer between the models, and finally an evaluation of the thermal stresses and displacements in the structure. Consequently, the objective of the developed technique was to minimize the model development time, in order to assure an automatic transfer of data between the thermal and structural models as well as to minimize the computer resources needed for the analysis itself. The method and techniques described are illustrated on the thermal/structural analysis of the Space Station Freedom main truss.
NASA Astrophysics Data System (ADS)
von Sydow, Lina
2013-10-01
The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.
NASA Astrophysics Data System (ADS)
Jia, Jinhong; Wang, Hong
2015-07-01
Numerical methods for space-fractional diffusion equations often generate dense or even full stiffness matrices. Traditionally, these methods were solved via Gaussian type direct solvers, which requires O (N3) of computational work per time step and O (N2) of memory to store where N is the number of spatial grid points in the discretization. In this paper we develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite difference methods (both steady-state and time-dependent) space-fractional diffusion equations with fractional derivative boundary conditions in one space dimension. The method requires O (N) of memory and O (Nlog N) of operations per iteration. Due to the application of effective preconditioners, significantly reduced numbers of iterations were achieved that further reduces the computational cost of the fast method. Numerical results are presented to show the utility of the method.
Single-cone real-space finite difference scheme for the time-dependent Dirac equation
NASA Astrophysics Data System (ADS)
Hammer, René; Pötz, Walter; Arnold, Anton
2014-05-01
A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to optimal linear scaling behavior for the computational effort per space-time grid-point. It allows for an easy and efficient parallelization. A functional for a norm on the grid is identified. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation is shown and exact stability conditions are derived. Finally, a single-cone scheme for the two-component (2+1)D Dirac equation, its properties, and a simulation of scattering at a Klein step are presented.
ATLAS: A real-space finite-difference implementation of orbital-free density functional theory
NASA Astrophysics Data System (ADS)
Mi, Wenhui; Shao, Xuecheng; Su, Chuanxun; Zhou, Yuanyuan; Zhang, Shoutao; Li, Quan; Wang, Hui; Zhang, Lijun; Miao, Maosheng; Wang, Yanchao; Ma, Yanming
2016-03-01
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference (FD) method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler-Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al3Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations.
Real-space finite difference scheme for the von Neumann equation with the Dirac Hamiltonian
NASA Astrophysics Data System (ADS)
Schreilechner, Magdalena; Pötz, Walter
2016-07-01
A finite difference scheme for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian is presented. It is based on a sequential left-right (ket-bra) application of a staggered space-time scheme for the pure-state Dirac equation and offers a numerical treatment of the general mixed-state dynamics of an isolated quantum system within the von Neumann equation. Thereby this direct scheme inherits all the favorable features of the finite-difference scheme for the pure-state Dirac equation, such as the single-cone energy-momentum dispersion, convergence conditions, and scaling behavior. A conserved functional is identified. Moreover this scheme is shown to conserve both Hermiticity and positivity. Numerical tests comprise a numerical analysis of stability, as well as the simulation of a mixed-state time-evolution of Gaussian wave functions, illustrating Zitterbewegung and transverse current oscillations. Imaginary-potential absorbing boundary conditions and parameters which pertain to topological insulator surface states were used in the numerical simulations.
NASA Astrophysics Data System (ADS)
Raynaud, M.; Bransier, J.
A space-marching finite difference algorithm is developed for solving the one-dimensional inverse heat conduction problem. The method is easy to apply, stable, and as accurate as the most efficient existing methods. An experimental set-up made of a rectangular parallelepiped polymerized around a woof of thermocouples has been designed especially to validate the method. The thermal conductivity of the test specimen was previously determined with the same set-up, and the specific heat is estimated during the experiments. The estimated surface heat flux is in very good agreement with the heat flux measured by a foil heat flux gage, regardless of the sensor locations. These results show that the method remains effective in spite of the cumulated effects of the errors due to the data acquisition system, to the location and calibration of the sensors, and to the simultaneous estimation of the specific heat.
Accurate Finite Difference Algorithms
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1996-01-01
Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.
An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension
Bolstad, John H.
1982-06-01
Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.
Ebadian, Behnaz; Farzin, Mahmoud; Talebi, Saeid; Khodaeian, Niloufar
2012-01-01
Background: Available restorative space and bar height is an important factor in stress distribution of implant-supported overdentures. The purpose of this study was to evaluate the effect of different vertical restorative spaces and different bar heights on the stress distribution around implants by 3D finite element analysis. Materials and Methods: 3D finite element models were developed from mandibular overdentures with two implants in the interforaminal region. In these models, four different bar heights from gingival crest (0.5, 1, 1.5, 2 mm) with 15 mm occlusal plane height and three different occlusal plane heights from gingival crest (9, 12, 15 mm) with 2 mm bar height were analyzed. A vertical unilateral and a bilateral load of 150 N were applied to the central occlusal fossa of the first molar and the stress of bone around implant was analyzed by finite element analysis. Results: By increasing vertical restorative space, the maximum stress values around implants were found to be decreased in unilateral loading models but slightly increased in bilateral loading cases. By increasing bar height from gingival crest, the maximum stress values around implants were found to be increased in unilateral loading models but slightly decreased in bilateral loading cases. In unilateral loading models, maximum stress was found in a model with 9 mm occlusal plane height and 1.5 mm bar height (6.254 MPa), but in bilateral loading cases, maximum stress was found in a model with 15 mm occlusal plane height and 0.5 mm bar height (3.482 MPa). Conclusion: The reduction of bar height and increase in the thickness of acrylic resin base in implant-supported overdentures are biomechanically favorable and may result in less stress in periimplant bone. PMID:23559952
NASA Astrophysics Data System (ADS)
Liu, Yang; Sen, Mrinal K.
2011-09-01
Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations. Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of
NASA Astrophysics Data System (ADS)
Cole, James B.
2014-09-01
The finite difference time domain (FDTD) algorithm is a popular tool for photonics design and simulations, but it also can yield deep insights into the fundamental nature of light and - more speculatively - into the discretization and connectivity and geometry of space-time. The CFL stability limit in FDTD can be interpreted as a limit on the speed of light. It depends not only on the dimensionality of space-time, but also on its connectivity. Thus the speed of light not only tells us something about the dimensionality of space-time but also about its connectivity. The computational molecule in conventional 2-D FDTD is (х +/- h,y)-(x,+/- y h)-(x-y), where h= triangle x = triangle y . It yields the CFL stability limit ctriangle/h<= t/h 1 √2 . Including diagonal nodes (x+/- h, y +/- h) in the computational molecule changes the connectivity of the space and changes the CFL limit. The FDTD model also predicts precursor signals (which physically exist). The Green's function of the FDTD model, which differs from that of the wave equation, may tell us something about underlying periodicities in space-time. It may be possible to experimentally observe effects of space-time discretization and connectivity in optics experiments.
NASA Technical Reports Server (NTRS)
Collier, Richard S.
1997-01-01
This report describes finite difference computer calculations for the Space Shuttle Launch Pad which predict lightning induced electric currents and electric and magnetic fields caused by a lightning strike to the Lightning Protection System caternary wire. Description of possible lightning threats to Shuttle Payload components together with specifications for protection of these components, result from the calculation of lightning induced electric and magnetic fields inside and outside the during a lightning event. These fields also induce currents and voltages on cables and circuits which may be connected to, or a part of, shuttle payload components. These currents and voltages are also calculated. These threat levels are intended as a guide for designers of payload equipment to specify any shielding and/or lightning protection mitigation which may be required for payload components which are in the process of preparation or being transferred into the Shuttle Orbiter.
Nonstandard finite difference schemes
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.
1995-01-01
The major research activities of this proposal center on the construction and analysis of nonstandard finite-difference schemes for ordinary and partial differential equations. In particular, we investigate schemes that either have zero truncation errors (exact schemes) or possess other significant features of importance for numerical integration. Our eventual goal is to bring these methods to bear on problems that arise in the modeling of various physical, engineering, and technological systems. At present, these efforts are extended in the direction of understanding the exact nature of these nonstandard procedures and extending their use to more complicated model equations. Our presentation will give a listing (obtained to date) of the nonstandard rules, their application to a number of linear and nonlinear, ordinary and partial differential equations. In certain cases, numerical results will be presented.
Numerical computation of transonic flows by finite-element and finite-difference methods
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
NASA Astrophysics Data System (ADS)
Tan, Sirui; Huang, Lianjie
2014-11-01
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.
Tan, Sirui; Huang, Lianjie
2014-11-01
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.
Mimetic finite difference method
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
NASA Technical Reports Server (NTRS)
Sohn, Kiho D.; Ip, Shek-Se P.
1988-01-01
Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.
NASA Astrophysics Data System (ADS)
Koltenbah, Benjamin E. C.; Parazzoli, Claudio G.; Greegor, Robert B.; Dowell, David H.
2002-07-01
Recent interest in advanced laser light sources has stimulated development of accelerator systems of intermediate beam energy, 100-200 MeV, and high charge, 1-10 nC, for high power FEL applications and high energy, 1-2 GeV, high charge, SASE-FEL applications. The current generation of beam transport codes which were developed for high-energy, low-charge beams with low self-fields are inadequate to address this energy and charge regime, and better computational tools are required to accurately calculate self-fields. To that end, we have developed a new version of PARMELA, named PARMELA_B and written in Fortran 95, which includes a coherent synchrotron radiation (CSR) routine and an improved, generalized space charge (SC) routine. An electron bunch is simulated by a collection of macro-particles, which traverses a series of beam line elements. At each time step through the calculation, the momentum of each particle is updated due to the presence of external and self-fields. The self-fields are due to CSR and SC. For the CSR calculations, the macro-particles are further combined into macro-particle-bins that follow the central trajectory of the bend. The energy change through the time step is calculated from expressions derived from the Liénard-Wiechart formulae, and from this energy change the particle's momentum is updated. For the SC calculations, we maintain the same rest-frame-electrostatic approach of the original PARMELA; however, we employ a finite difference Poisson equation solver instead of the symmetrical ring algorithm of the original code. In this way, we relax the symmetry assumptions in the original code. This method is based upon standard numerical procedures and conserves momentum to first order. The SC computational grid is adaptive and conforms to the size of the pulse as it evolves through the calculation. We provide descriptions of these two algorithms, validation comparisons with other CSR and SC methods, and a limited comparison with
Finite Topological Spaces as a Pedagogical Tool
ERIC Educational Resources Information Center
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
Exponential Finite-Difference Technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.
1989-01-01
Report discusses use of explicit exponential finite-difference technique to solve various diffusion-type partial differential equations. Study extends technique to transient-heat-transfer problems in one dimensional cylindrical coordinates and two and three dimensional Cartesian coordinates and to some nonlinear problems in one or two Cartesian coordinates.
On the wavelet optimized finite difference method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1994-01-01
When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.
1996-01-01
A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.
Adaptive finite difference for seismic wavefield modelling in acoustic media.
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang's optimised finite difference scheme. PMID:27491333
Adaptive finite difference for seismic wavefield modelling in acoustic media
NASA Astrophysics Data System (ADS)
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-08-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme.
Adaptive finite difference for seismic wavefield modelling in acoustic media
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme. PMID:27491333
Finite element and finite difference methods in electromagnetic scattering
NASA Astrophysics Data System (ADS)
Morgan, Michael A.
Finite-difference and finite-element methods for the computational analysis of EM scattering phenomena are examined in chapters contributed by leading experts. Topics addressed include an FEM for composite scatterers, coupled finite- and boundary-element methods for EM scattering, absorbing boundary conditions for the direct solution PDEs arising in EM scattering problems, application of the control-region approximation to two-dimensional EM scattering, coupled potentials for EM fields in inhomogeneous media, the method of conforming boundary elements for transient electromagnetics, and the finite-difference time-domain method for numerical modeling of EM wave interactions with arbitrary structures. Extensive diagrams and graphs of typical results are provided.
NASA Astrophysics Data System (ADS)
Tan, Sirui; Huang, Lianjie
2014-05-01
For modelling large-scale 3-D scalar-wave propagation, the finite-difference (FD) method with high-order accuracy in space but second-order accuracy in time is widely used because of its relatively low requirements of computer memory. We develop a novel staggered-grid (SG) FD method with high-order accuracy not only in space, but also in time, for solving 2- and 3-D scalar-wave equations. We determine the coefficients of the FD operator in the joint time-space domain to achieve high-order accuracy in time while preserving high-order accuracy in space. Our new FD scheme is based on a stencil that contains a few more grid points than the standard stencil. It is 2M-th-order accurate in space and fourth-order accurate in time when using 2M grid points along each axis and wavefields at one time step as the standard SGFD method. We validate the accuracy and efficiency of our new FD scheme using dispersion analysis and numerical modelling of scalar-wave propagation in 2- and 3-D complex models with a wide range of velocity contrasts. For media with a velocity contrast up to five, our new FD scheme is approximately two times more computationally efficient than the standard SGFD scheme with almost the same computer-memory requirement as the latter. Further numerical experiments demonstrate that our new FD scheme loses its advantages over the standard SGFD scheme if the velocity contrast is 10. However, for most large-scale geophysical applications, the velocity contrasts often range approximately from 1 to 3. Our new method is thus particularly useful for large-scale 3-D scalar-wave modelling and full-waveform inversion.
Finite-difference computations of rotor loads
NASA Technical Reports Server (NTRS)
Caradonna, F. X.; Tung, C.
1985-01-01
This paper demonstrates the current and future potential of finite-difference methods for solving real rotor problems which now rely largely on empiricism. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advance-ratio flight. Comparisons are made with experimental pressure data.
Finite-difference computations of rotor loads
NASA Technical Reports Server (NTRS)
Caradonna, F. X.; Tung, C.
1985-01-01
The current and future potential of finite difference methods for solving real rotor problems which now rely largely on empiricism are demonstrated. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advanced-ratio flight. Comparisons are made with experimental pressure data.
Stochastic finite-difference time-domain
NASA Astrophysics Data System (ADS)
Smith, Steven Michael
2011-12-01
This dissertation presents the derivation of an approximate method to determine the mean and the variance of electro-magnetic fields in the body using the Finite-Difference Time-Domain (FDTD) method. Unlike Monte Carlo analysis, which requires repeated FDTD simulations, this method directly computes the variance of the fields at every point in space at every sample of time in the simulation. This Stochastic FDTD simulation (S-FDTD) has at its root a new wave called the Variance wave, which is computed in the time domain along with the mean properties of the model space in the FDTD simulation. The Variance wave depends on the electro-magnetic fields, the reflections and transmission though the different dielectrics, and the variances of the electrical properties of the surrounding materials. Like the electro-magnetic fields, the Variance wave begins at zero (there is no variance before the source is turned on) and is computed in the time domain until all fields reach steady state. This process is performed in a fraction of the time of a Monte Carlo simulation and yields the first two statistical parameters (mean and variance). The mean of the field is computed using the traditional FDTD equations. Variance is computed by approximating the correlation coefficients between the constituitive properties and the use of the S-FDTD equations. The impetus for this work was the simulation time it takes to perform 3D Specific Absorption Rate (SAR) FDTD analysis of the human head model for cell phone power absorption in the human head due to the proximity of a cell phone being used. In many instances, Monte Carlo analysis is not performed due to the lengthy simulation times required. With the development of S-FDTD, these statistical analyses could be performed providing valuable statistical information with this information being provided in a small fraction of the time it would take to perform a Monte Carlo analysis.
Finite-difference modelling of wavefield constituents
NASA Astrophysics Data System (ADS)
Robertsson, Johan O. A.; van Manen, Dirk-Jan; Schmelzbach, Cedric; Van Renterghem, Cederic; Amundsen, Lasse
2015-11-01
The finite-difference method is among the most popular methods for modelling seismic wave propagation. Although the method has enjoyed huge success for its ability to produce full wavefield seismograms in complex models, it has one major limitation which is of critical importance for many modelling applications; to naturally output up- and downgoing and P- and S-wave constituents of synthesized seismograms. In this paper, we show how such wavefield constituents can be isolated in finite-difference-computed synthetics in complex models with high numerical precision by means of a simple algorithm. The description focuses on up- and downgoing and P- and S-wave separation of data generated using an isotropic elastic finite-difference modelling method. However, the same principles can also be applied to acoustic, electromagnetic and other wave equations.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
NASA Technical Reports Server (NTRS)
Roberts, G. O.; Fowlis, W. W.; Miller, T. L.
1984-01-01
Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.
Dispersion-relation-preserving finite difference schemes for computational acoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1993-01-01
Time-marching dispersion-relation-preserving (DRP) schemes can be constructed by optimizing the finite difference approximations of the space and time derivatives in wave number and frequency space. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. Close agreement with the exact solutions is obtained.
Finite-Difference Algorithms For Computing Sound Waves
NASA Technical Reports Server (NTRS)
Davis, Sanford
1993-01-01
Governing equations considered as matrix system. Method variant of method described in "Scheme for Finite-Difference Computations of Waves" (ARC-12970). Present method begins with matrix-vector formulation of fundamental equations, involving first-order partial derivatives of primitive variables with respect to space and time. Particular matrix formulation places time and spatial coordinates on equal footing, so governing equations considered as matrix system and treated as unit. Spatial and temporal discretizations not treated separately as in other finite-difference methods, instead treated together by linking spatial-grid interval and time step via common scale factor related to speed of sound.
Verifying continuous-variable entanglement in finite spaces
Sperling, J.; Vogel, W.
2009-05-15
Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite-dimensional subspaces. Entanglement can be fully characterized as a finite-dimensional property, even though in general the truncation of the Hilbert space may cause fake nonclassicality. A generalization for multipartite quantum states is also given.
Compact finite difference method for American option pricing
NASA Astrophysics Data System (ADS)
Zhao, Jichao; Davison, Matt; Corless, Robert M.
2007-09-01
A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h[greater-or-equal, slanted]0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.
Finite-difference migration to zero offset
Li, Jianchao
1992-07-01
Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.
Finite-difference migration to zero offset
Li, Jianchao.
1992-01-01
Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.
Simulating Space Capsule Water Landing with Explicit Finite Element Method
NASA Technical Reports Server (NTRS)
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Spectral differences in real-space electronic structure calculations
NASA Astrophysics Data System (ADS)
Jordan, D. K.; Mazziotti, D. A.
2004-01-01
Real-space grids for electronic structure calculations are efficient because the potential is diagonal while the second derivative in the kinetic energy may be sparsely evaluated with finite differences or finite elements. In applications to vibrational problems in chemical physics a family of methods known as spectral differences has improved finite differences by several orders of magnitude. In this paper the use of spectral differences for electronic structure is studied. Spectral differences are implemented in two electronic structure programs PARSEC and HARES which currently employ finite differences. Applications to silicon clusters and lattices indicate that spectral differences achieve the same accuracy as finite differences with less computational work.
Finite difference discretisation of a model for biological nerve conduction
NASA Astrophysics Data System (ADS)
Aderogba, A. A.; Chapwanya, M.; Jejeniwa, O. A.
2016-06-01
A nonstandard finite difference method is proposed for the discretisation of the semilinear FitzHugh-Nagumo reaction diffusion equation. The equation has been useful in describing, for example, population models, biological models, heat and mass transfer models, and many other applications. The proposed approach involves splitting the equation into the space independent and the time independent sub equation. Numerical simulations for the full equation are presented.
Software suite for finite difference method models.
Arola, T; Hannula, M; Narra, N; Malmivuo, J; Hyttinen, J
2006-01-01
We have developed a software suite for finite difference method (FDM) model construction, visualization and quasi-static simulation to be used in bioelectric field modeling. The aim of the software is to provide a full path from medical image data to simulation of bioelectric phenomena and results visualization. It is written in Java and can be run on various platforms while still supporting all features included. The software can be distributed across a network utilizing dedicated servers for calculation intensive tasks. Supported visualization modes are both two- and three-dimensional modes. PMID:17946057
The Complex-Step-Finite-Difference method
NASA Astrophysics Data System (ADS)
Abreu, Rafael; Stich, Daniel; Morales, Jose
2015-07-01
We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.
NASA Astrophysics Data System (ADS)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
Efficient discretization in finite difference method
NASA Astrophysics Data System (ADS)
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
TUNED FINITE-DIFFERENCE DIFFUSION OPERATORS
Maron, Jason; Low, Mordecai-Mark Mac E-mail: mordecai@amnh.org
2009-05-15
Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as viscosity or resistivity. If the goal is stability only, the diffusion must act at the grid scale, but should affect structure at larger scales as little as possible. For physical diffusivities the diffusion scale depends on the problem, and diffusion may act at larger scales as well. Diffusivity can undesirably limit the computational time step in both cases. We construct tuned finite-difference diffusion operators that minimally limit the time step while acting as desired near the diffusion scale. Such operators reach peak values at the diffusion scale rather than at the grid scale, but behave as standard operators at larger scales. These operators will be useful for simulations with high magnetic diffusivity or kinematic viscosity such as in the simulation of astrophysical dynamos with magnetic Prandtl number far from unity, or for numerical stabilization using hyperdiffusivity.
Calculation of sensitivity derivatives in thermal problems by finite differences
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Malkus, D. S.
1981-01-01
The optimum design of a structure subject to temperature constraints is considered. When mathematical optimization techniques are used, derivatives of the temperature constraints with respect to the design variables are usually required. In the case of large aerospace structures, such as the Space Shuttle, the computation of these derivatives can become prohibitively expensive. Analytical methods and a finite difference approach have been considered in studies conducted to improve the efficiency of the calculation of the derivatives. The present investigation explores two possibilities for enhancing the effectiveness of the finite difference approach. One procedure involves the simultaneous solution of temperatures and derivatives. The second procedure makes use of the optimum selection of the magnitude of the perturbations of the design variables to achieve maximum accuracy.
Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Amirali, I.; Amiraliyev, G. M.; Cakir, M.; Cimen, E.
2014-01-01
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392
Explicit finite difference methods for the delay pseudoparabolic equations.
Amirali, I; Amiraliyev, G M; Cakir, M; Cimen, E
2014-01-01
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
NASA Astrophysics Data System (ADS)
Fisher, Travis C.; Carpenter, Mark H.
2013-11-01
Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.
Finite element analysis of a deployable space structure
NASA Technical Reports Server (NTRS)
Hutton, D. V.
1982-01-01
To assess the dynamic characteristics of a deployable space truss, a finite element model of the Scientific Applications Space Platform (SASP) truss has been formulated. The model incorporates all additional degrees of freedom associated with the pin-jointed members. Comparison of results with SPAR models of the truss show that the joints of the deployable truss significantly affect the vibrational modes of the structure only if the truss is relatively short.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Geometrical Series and Phase Space in a Finite Oscillatory Motion
ERIC Educational Resources Information Center
Mareco, H. R. Olmedo
2006-01-01
This article discusses some interesting physical properties of oscillatory motion of a particle on two joined inclined planes. The geometrical series demonstrates that the particle will oscillate during a finite time. Another detail is the converging path to the origin of the phase space. Due to its simplicity, this motion may be used as a…
Quantum mechanics in finite-dimensional Hilbert space
NASA Astrophysics Data System (ADS)
de la Torre, A. C.; Goyeneche, D.
2003-01-01
The quantum mechanical formalism for the position and momentum of a particle on a one-dimensional lattice is developed. Some mathematical features characteristic of finite-dimensional Hilbert spaces are compared with the infinite-dimensional case. The construction of an unbiased basis for state determination is discussed.
Comparison of finite-difference and analytic microwave calculation methods
Friedlander, F.I.; Jackson, H.W.; Barmatz, M.; Wagner, P.
1996-12-31
Normal modes and power absorption distributions in microwave cavities containing lossy dielectric samples were calculated for problems of interest in materials processing. The calculations were performed both using a commercially available finite-difference electromagnetic solver and by numerical evaluation of exact analytic expressions. Results obtained by the two methods applied to identical physical situations were compared. The studies validate the accuracy of the finite-difference electromagnetic solver. Relative advantages of the analytic and finite-difference methods are discussed.
Finite element models of the space shuttle main engine
NASA Technical Reports Server (NTRS)
Muller, G. R.
1980-01-01
Finite element models were developed as input to dynamic simulations of the high pressure fuel turbopump (HPFTP), the high pressure oxidizer turbopump (HPOTP), and the space shuttle main engine (SSME). Descriptions are provided for the five basic finite element models: HPFTP rotor, HPFTP case, HPOTP rotor, HPOTP case, and SSME (excluding turbopumps). Modal results are presented for the HPFTP rotor, HPFTP case, HPOTP rotor, coupled HPFTP rotor and case, HPOTP case, coupled HPOTP rotor and case, SSME (excluding turbopumps), and SSME (including turbopumps). Results for the SSME (including turbopumps) model are compared to data from a SSME HPOTP modal survey.
One-node coarse-mesh finite difference algorithm for fine-mesh finite difference operator
Shin, H.C.; Kim, Y.H.; Kim, Y.B.
1999-07-01
This paper is concerned with speeding up the convergence of the fine-mesh finite difference (FMFD) method for the neutron diffusion problem. The basic idea of the new algorithm originates from the two-node coarse-mesh finite difference (CMFD) schemes for nodal methods, where the low-order CMFD operator is iteratively corrected through a global-local iteration so that the final solution of the CMFD problem is equivalent to the high-order nodal solution. Unlike conventional CMFD methods, the new CMFD algorithm is based on one-node local problems, and the high-order solution over the local problem is determined by using the FMFD operator. Nonlinear coupling of CMFD and FMFD operators was previously studied by Aragones and Ahnert. But, in their work, the coarse-mesh operator is corrected by the so-called flux discontinuity factors, and the local problem is defined differently in the sense of boundary conditions and the core dissection scheme.
Finite-element reentry heat-transfer analysis of space shuttle Orbiter
NASA Technical Reports Server (NTRS)
Ko, William L.; Quinn, Robert D.; Gong, Leslie
1986-01-01
A structural performance and resizing (SPAR) finite-element thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR finite-element solutions agreed reasonably well with those obtained from the conventional finite-difference method.
Finite difference time domain analysis of chirped dielectric gratings
NASA Technical Reports Server (NTRS)
Hochmuth, Diane H.; Johnson, Eric G.
1993-01-01
The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.
Space-time formulation for finite element modeling of superconductors
Ashworth, Stephen P; Grilli, Francesco; Sirois, Frederic; Laforest, Marc
2008-01-01
In this paper we present a new model for computing the current density and field distributions in superconductors by means of a periodic space-time formulation for finite elements (FE). By considering a space dimension as time, we can use a static model to solve a time dependent problem. This allows overcoming one of the major problems of FE modeling of superconductors: the length of simulations, even for relatively simple cases. We present our first results and compare them to those obtained with a 'standard' time-dependent method and with analytical solutions.
Finite difference modeling of Biot's poroelastic equations atseismic frequencies
Masson, Y.J.; Pride, S.R.; Nihei, K.T.
2006-02-24
Across the seismic band of frequencies (loosely defined as<10 kHz), a seismic wave propagating through a porous material willcreate flow in the pore space that is laminar; that is, in thislow-frequency "seismic limit," the development of viscous boundary layersin the pores need not be modeled. An explicit time steppingstaggered-grid finite difference scheme is presented for solving Biot'sequations of poroelasticity in this low-frequency limit. A key part ofthis work is the establishment of rigorous stability conditions. It isdemonstrated that over a wide range of porous material properties typicalof sedimentary rock and despite the presenceof fluid pressure diffusion(Biot slow waves), the usual Courant condition governs the stability asif the problem involved purely elastic waves. The accuracy of the methodis demonstrated by comparing to exact analytical solutions for both fastcompressional waves and slow waves. Additional numerical modelingexamples are also presented.
An optimized finite-difference scheme for wave propagation problems
NASA Technical Reports Server (NTRS)
Zingg, D. W.; Lomax, H.; Jurgens, H.
1993-01-01
Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.
Application of a new finite difference algorithm for computational aeroacoustics
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1995-01-01
Acoustic problems have become extremely important in recent years because of research efforts such as the High Speed Civil Transport program. Computational aeroacoustics (CAA) requires a faithful representation of wave propagation over long distances, and needs algorithms that are accurate and boundary conditions that are unobtrusive. This paper applies a new finite difference method and boundary algorithm to the Linearized Euler Equations (LEE). The results demonstrate the ability of a new fourth order propagation algorithm to accurately simulate the genuinely multidimensional wave dynamics of acoustic propagation in two space dimensions with the LEE. The results also show the ability of a new outflow boundary condition and fourth order algorithm to pass the evolving solution from the computational domain with no perceptible degradation of the solution remaining within the domain.
NASA Technical Reports Server (NTRS)
Leonard, B. P.
1992-01-01
Judging by errors in the computational-fluid-dynamics literature in recent years, it is not generally well understood that (above first-order) there are significant differences in spatial truncation error between formulations of convection involving a finite-difference approximation of the first derivative, on the one hand, and a finite-volume model of flux differences across a control-volume cell, on the other. The difference between the two formulations involves a second-order truncation-error term (proportional to the third-derivative of the convected variable). Hence, for example, a third (or higher) order finite-difference approximation for the first-derivative convection term is only second-order accurate when written in conservative control-volume form as a finite-volume formulation, and vice versa.
Computer-Oriented Calculus Courses Using Finite Differences.
ERIC Educational Resources Information Center
Gordon, Sheldon P.
The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…
Hybrid finite element-finite difference method for thermal analysis of blood vessels.
Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B
2000-01-01
A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems. PMID:10949130
Coupled finite-difference/finite-element approach for wing-body aeroelasticity
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
1992-01-01
Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
Conservative properties of finite difference schemes for incompressible flow
NASA Technical Reports Server (NTRS)
Morinishi, Youhei
1995-01-01
The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.
Techniques for correcting approximate finite difference solutions. [considering transonic flow
NASA Technical Reports Server (NTRS)
Nixon, D.
1978-01-01
A method of correcting finite-difference solutions for the effect of truncation error or the use of an approximate basic equation is presented. Applications to transonic flow problems are described and examples are given.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Finite-difference solutions of the 3-D eikonal equation
Fei, Tong; Fehler, M.C.; Hildebrand, S.T.
1995-12-31
Prestack Kirchhoff depth migration requires the computation of traveltimes from surface source and receiver locations to subsurface image locations. In 3-D problems, computational efficiency becomes important. Finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference method for computing the first arrival traveltime by solving the eikonal equation has been developed in Cartesian coordinates. The method, which is unconditionally stable and computationally efficient, can handle instabilities due to caustics and provide information about head waves. The comparison of finite-difference solutions of the acoustic wave equation with the traveltime solutions from the eikonal equation in various structure models demonstrate that the method developed here can provide correct first arrival traveltime information even in areas of complex velocity structure.
Numerical techniques in linear duct acoustics. [finite difference and finite element analyses
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1980-01-01
Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.
Practical aspects of prestack depth migration with finite differences
Ober, C.C.; Oldfield, R.A.; Womble, D.E.; Romero, L.A.; Burch, C.C.
1997-07-01
Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatial parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.
Fei, T.; Larner, K.
1995-11-01
Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitrary variations in velocity and density and can handle turning waves as well. However, conventional finite-difference methods for solving the acoustic- or elastic-wave equation suffer from numerical dispersion when too few samples per wavelength are used. The flux-corrected transport (FCT) algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite-difference wavefield continuation. The flux-correction procedure endeavors to incorporate diffusion into the wavefield continuation process only where needed to suppress the numerical dispersion. Incorporating the flux-correction procedure in conventional finite-difference modeling or reverse-time migration can provide finite-difference solutions with no numerical dispersion even for impulsive sources. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use for finite-difference approximations of increasing order. Through demonstrations of modeling and migration on both synthetic and field data, the authors show the benefits of the FCT algorithm, as well as its inability to fully recover resolution lost when the spatial sampling becomes too coarse.
Decomposition of Fuzzy Soft Sets with Finite Value Spaces
Jun, Young Bae
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter. PMID:24558342
Decomposition of fuzzy soft sets with finite value spaces.
Feng, Feng; Fujita, Hamido; Jun, Young Bae; Khan, Madad
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter. PMID:24558342
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Optimizations on Designing High-Resolution Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Liu, Yen; Koomullil, George; Kwak, Dochan (Technical Monitor)
1994-01-01
We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.
Improved finite-difference vibration analysis of pretwisted, tapered beams
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1984-01-01
An improved finite difference procedure based upon second order central differences is developed. Several difficulties encountered in earlier works with fictitious stations that arise in using second order central differences, are eliminated by developing certain recursive relations. The need for forward or backward differences at the beam boundaries or other similar procedures is eliminated in the present theory. By using this improved theory, the vibration characteristics of pretwisted and tapered blades are calculated. Results of the second order theory are compared with published theoretical and experimental results and are found to be in good agreement. The present method generally produces close lower bound solutions and shows fast convergence. Thus, extrapolation procedures that are customary with first order finite-difference methods are unnecessary. Furthermore, the computational time and effort needed for this improved method are almost the same as required for the conventional first order finite-difference approach.
NASA Astrophysics Data System (ADS)
MacKinnon, Robert J.; Carey, Graham F.
2003-01-01
A new class of positivity-preserving, flux-limited finite-difference and Petrov-Galerkin (PG) finite-element methods are devised for reactive transport problems.The methods are similar to classical TVD flux-limited schemes with the main difference being that the flux-limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite-element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity-preserving property. Analysis of the latter scheme shows that positivity-preserving solutions of the resulting difference equations can only be guaranteed if the flux-limited scheme is both implicit and satisfies an additional lower-bound condition on time-step size. We show that this condition also applies to standard Galerkin linear finite-element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time-step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction.
Finite-difference schemes for anisotropic diffusion
Es, Bram van; Koren, Barry; Blank, Hugo J. de
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
Thermal finite-element analysis of space shuttle main engine turbine blade
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Tong, Michael T.; Kaufman, Albert
1987-01-01
Finite-element, transient heat transfer analyses were performed for the first-stage blades of the space shuttle main engine (SSME) high-pressure fuel turbopump. The analyses were based on test engine data provided by Rocketdyne. Heat transfer coefficients were predicted by performing a boundary-layer analysis at steady-state conditions with the STAN5 boundary-layer code. Two different peak-temperature overshoots were evaluated for the startup transient. Cutoff transient conditions were also analyzed. A reduced gas temperature profile based on actual thermocouple data was also considered. Transient heat transfer analyses were conducted with the MARC finite-element computer code.
Thermal finite-element analysis of space shuttle main engine turbine blade
Abdul-Aziz, A.; Tong, M.T.; Kaufman, A.
1987-10-01
Finite-element, transient heat transfer analyses were performed for the first-stage blades of the space shuttle main engine (SSME) high-pressure fuel turbopump. The analyses were based on test engine data provided by Rocketdyne. Heat transfer coefficients were predicted by performing a boundary-layer analysis at steady-state conditions with the STAN5 boundary-layer code. Two different peak-temperature overshoots were evaluated for the startup transient. Cutoff transient conditions were also analyzed. A reduced gas temperature profile based on actual thermocouple data was also considered. Transient heat transfer analyses were conducted with the MARC finite-element computer code.
Nonlinear triggered lightning models for use in finite difference calculations
NASA Technical Reports Server (NTRS)
Rudolph, Terence; Perala, Rodney A.; Ng, Poh H.
1989-01-01
Two nonlinear triggered lightning models have been developed for use in finite difference calculations. Both are based on three species of air chemistry physics and couple nonlinearly calculated air conductivity to Maxwell's equations. The first model is suitable for use in three-dimensional modeling and has been applied to the analysis of triggered lightning on the NASA F106B Thunderstorm Research Aircraft. The model calculates number densities of positive ions, negative ions, and electrons as a function of time and space through continuity equations, including convective derivative terms. The set of equations is closed by using experimentally determined mobilities, and the mobilities are also used to determine the air conductivity. Results from the model's application to the F106B are shown. The second model is two-dimensional and incorporates an enhanced air chemistry formulation. Momentum conservation equations replace the mobility assumption of the first model. Energy conservation equations for neutrals, heavy ions, and electrons are also used. Energy transfer into molecular vibrational modes is accounted for. The purpose for the enhanced model is to include the effects of temperature into the air breakdown, a necessary step if the model is to simulate more than the very earliest stages of breakdown. Therefore, the model also incorporates a temperature-dependent electron avalanche rate. Results from the model's application to breakdown around a conducting ellipsoid placed in an electric field are shown.
Incoherent systems and coverings in finite dimensional Banach spaces
Temlyakov, V N
2014-05-31
We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles.
All-electron Kohn–Sham density functional theory on hierarchic finite element spaces
Schauer, Volker; Linder, Christian
2013-10-01
In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.
A comparison of the finite difference and finite element methods for heat transfer calculations
NASA Technical Reports Server (NTRS)
Emery, A. F.; Mortazavi, H. R.
1982-01-01
The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.
Finite difference modeling of rotor flows including wake effects
NASA Technical Reports Server (NTRS)
Caradonna, F. X.; Desopper, A.; Tung, C.
1982-01-01
Rotary wing finite difference methods are investigated. The main concern is the specification of boundary conditions to properly account for the effect of the wake on the blade. Examples are given of an approach where wake effects are introduced by specifying an equivalent angle of attack. An alternate approach is also given where discrete vortices are introduced into the finite difference grid. The resulting computations of hovering and high advance ratio cases compare well with experiment. Some consideration is also given to the modeling of low to moderate advance ratio flows.
NASA Technical Reports Server (NTRS)
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
Selecting step sizes in sensitivity analysis by finite differences
NASA Technical Reports Server (NTRS)
Iott, J.; Haftka, R. T.; Adelman, H. M.
1985-01-01
This paper deals with methods for obtaining near-optimum step sizes for finite difference approximations to first derivatives with particular application to sensitivity analysis. A technique denoted the finite difference (FD) algorithm, previously described in the literature and applicable to one derivative at a time, is extended to the calculation of several simultaneously. Both the original and extended FD algorithms are applied to sensitivity analysis for a data-fitting problem in which derivatives of the coefficients of an interpolation polynomial are calculated with respect to uncertainties in the data. The methods are also applied to sensitivity analysis of the structural response of a finite-element-modeled swept wing. In a previous study, this sensitivity analysis of the swept wing required a time-consuming trial-and-error effort to obtain a suitable step size, but it proved to be a routine application for the extended FD algorithm herein.
Ruess, Jakob
2015-12-28
Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space. PMID:26723647
NASA Astrophysics Data System (ADS)
Ruess, Jakob
2015-12-01
Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space.
NASA Astrophysics Data System (ADS)
Ying, Jinyong; Xie, Dexuan
2015-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.
Modelling the core convection using finite element and finite difference methods
NASA Astrophysics Data System (ADS)
Chan, K. H.; Li, Ligang; Liao, Xinhao
2006-08-01
Applications of both parallel finite element and finite difference methods to thermal convection in a rotating spherical shell modelling the fluid dynamics of the Earth's outer core are presented. The numerical schemes are verified by reproducing the convection benchmark test by Christensen et al. [Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wilcht, J., Zhang, K., 2001. A numerical dynamo benchmark. Phys. Earth Planet. Interiors 128, 25-34.]. Both global average and local characteristics agree satisfactorily with the benchmark solution. With the element-by-element (EBE) parallelization technique, the finite element code demonstrates nearly optimal linear scalability in computational speed. The finite difference code is also efficient and scalable by utilizing a parallel library Aztec [Tuminaro, R.S., Heroux, M., Hutchinson, S.A., Shadid, J.N., 1999. Official AZTEC User's Guide: Version 2.1.].
Comparison of finite difference and finite element solutions to the variably saturated flow equation
NASA Astrophysics Data System (ADS)
Simpson, M. J.; Clement, T. P.
2003-01-01
Numerical solutions to the equation governing variably saturated flow are usually obtained using either the finite difference (FD) method or the finite element (FE) method. A detailed comparison of these methods shows that the main difference between them is in how the numerical schemes spatially average the variation of material properties. Further differences are also observed in the way that flux boundaries are represented in FE and FD methods. A modified finite element (MFE) algorithm is used to explore the significance of these differences. The MFE algorithm enables a direct comparison with a typical FD solution scheme, and explicitly demonstrates the differences between FE and FD methods. The MFE algorithm provides an improved approximation to the partial differential equation over the usual FD approach while being computationally simpler to implement than the standard FE solution. One of the main limitations of the MFE algorithm is that the algorithm was developed by imposing several restrictions upon the more general FE solution; however, the MFE is shown to be preferable over the usual FE and FD solutions for some of the test problems considered in this study. The comparison results show that the FE (or MFE) solution can avoid the erroneous results encountered in the FD solution for coarsely discretized problems. The improvement in the FE solution is attributed to the broader hydraulic conductivity averaging and differences in the representation of flux type boundaries.
Using the Finite Difference Calculus to Sum Powers of Integers.
ERIC Educational Resources Information Center
Zia, Lee
1991-01-01
Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…
Scheme For Finite-Difference Computations Of Waves
NASA Technical Reports Server (NTRS)
Davis, Sanford
1992-01-01
Compact algorithms generating and solving finite-difference approximations of partial differential equations for propagation of waves obtained by new method. Based on concept of discrete dispersion relation. Used in wave propagation to relate frequency to wavelength and is key measure of wave fidelity.
Direct Finite-Difference Simulations Of Turbulent Flow
NASA Technical Reports Server (NTRS)
Rai, Man Mohan; Moin, Parviz
1991-01-01
Report discusses use of upwind-biased finite-difference numerical-integration scheme to simulate evolution of small disturbances and fully developed turbulence in three-dimensional flow of viscous, incompressible fluid in channel. Involves use of computational grid sufficiently fine to resolve motion of fluid at all relevant length scales.
Finite difference methods for the solution of unsteady potential flows
NASA Technical Reports Server (NTRS)
Caradonna, F. X.
1982-01-01
Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver. PMID:26034665
Reducing finite lattice spacing errors for staggered fermions
NASA Astrophysics Data System (ADS)
Luo, Yubing
1998-12-01
In this thesis we study on-shell-improved lattice QCD with staggered fermions using Symanzik's improvement program. We present a complete and detailed discussion of the finite lattice spacing corrections to staggered fermion matrix elements. Expanding upon arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order a terms in the on-shell-improved action. We propose a general program to improve fermion operators to remove all O(a) corrections from their matrix elements, and demonstrate this program for the examples of matrix elements of fermion bilinears and BK. We find the former does have O(a) corrections while the latter does not. Also, we give an explicit form of lattice currents which are accurate to order a2 at the tree-level. Furthermore, we find that there are as many as 15 independent lattice operators of dimension-6 (including both gauge and fermion operators) which must be added to the unimproved action to form an O(a2)-improved action. Among them, the total number of dimension-6 gauge operators and fermion bilinears is 5. The other ten terms are four- fermion operators. At the tree level and tadpole-improved tree level, all ten four-fermion operators are absent.
Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations
NASA Astrophysics Data System (ADS)
Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.
The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.
Finite-difference lattice-Boltzmann methods for binary fluids.
Xu, Aiguo
2005-06-01
We investigate two-fluid Bhatnagar-Gross-Krook (BGK) kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric systems it contributes models C, D, and E which are especially useful when the total masses and/or local temperatures of the two components are greatly different. The kinetic models are discretized based on an octagonal discrete velocity model. The discrete-velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations. The combination of a discrete-velocity kinetic model and an appropriate finite-difference scheme composes a finite-difference lattice Boltzmann method. The validity of the formulated methods is verified by investigating (i) uniform relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion behavior. PMID:16089910
Time dependent wave envelope finite difference analysis of sound propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1984-01-01
A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.
Experimentally constructing finite difference algorithms in numerical relativity
NASA Astrophysics Data System (ADS)
Anderson, Matthew; Neilsen, David; Matzner, Richard
2002-04-01
Computational studies of gravitational waves require numerical algorithms with long-term stability (necessary for convergence). However, constructing stable finite difference algorithms (FDA) for the ADM formulation of the Einstein equations, especially in multiple dimensions, has proven difficult. Most FDA's are constructed using rules of thumb gained from experience with simple model equations. To search for FDA's with improved stability, we adopt a brute-force approach, where we systematically test thousands of numerical schemes. We sort the spatial derivatives of the Einstein equations into groups, and parameterize each group by finite difference type (centered or upwind) and order. Furthermore, terms proportional to the constraints are added to the evolution equations with additional parameters. A spherically symmetric, excised Schwarzschild black hole (one dimension) and linearized waves in multiple dimensions are used as model systems to evaluate the different numerical schemes.
NASA Technical Reports Server (NTRS)
Steger, J. L.; Caradonna, F. X.
1980-01-01
An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.
Fei, Tong; Larner, K.
1993-11-01
Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitary variations in velocity and density, and can handle turning waves well. However, conventional finite-difference methods for solving the acousticwave equation suffer from numerical dispersion when too few samples per wavelength are used. Here, we present two flux-corrected transport (FCT) algorithms, one based the second-order equation and the other based on first-order wave equations derived from the second-order one. Combining the FCT technique with conventional finite-difference modeling or reverse-time wave extrapolation can ensure finite-difference solutions without numerical dispersion even for shock waves and impulsive sources. Computed two-dimensional migration images show accurate positioning of reflectors with greater than 90-degree dip. Moreover, application to real data shows no indication of numerical dispersion. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use of approximations of increasing order.
Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer
NASA Astrophysics Data System (ADS)
Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian
2015-10-01
Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.
Finite difference seismic modeling of axial magma chambers
Swift, S.A.; Dougherty, M.E.; Stephen, R.A. )
1990-11-01
The authors tested the feasibility of using finite difference methods to model seismic propagation at {approximately}10 Hx through a two-dimensional representation of an axial magma chamber with a thin, liquid lid. This technique produces time series of displacement or pressure at seafloor receivers to mimic a seismic refraction experiment and snapshots of P and S energy propagation. The results indicate that the implementation is stable for models with sharp velocity contrasts and complex geometries. The authors observe a high-energy, downward-traveling shear phase, observable only with borehole receivers, that would be useful in studying the nature and shape of magma chambers. The ability of finite difference methods to model high-order wave phenomena makes this method ideal for testing velocity models of spreading axes and for planning near-axis drilling of the East Pacific Rise in order to optimize the benefits from shear wave imaging of sub-axis structure.
Semianalytical computation of path lines for finite-difference models
Pollock, D.W.
1988-01-01
A semianalytical particle tracking method was developed for use with velocities generated from block-centered finite-difference ground-water flow models. Based on the assumption that each directional velocity component varies linearly within a grid cell in its own coordinate directions, the method allows an analytical expression to be obtained describing the flow path within an individual grid cell. Given the intitial position of a particle anywhere in a cell, the coordinates of any other point along its path line within the cell, and the time of travel between them, can be computed directly. For steady-state systems, the exit point for a particle entering a cell at any arbitrary location can be computed in a single step. By following the particle as it moves from cell to cell, this method can be used to trace the path of a particle through any multidimensional flow field generated from a block-centered finite-difference flow model. -Author
Optimized Finite-Difference Coefficients for Hydroacoustic Modeling
NASA Astrophysics Data System (ADS)
Preston, L. A.
2014-12-01
Responsible utilization of marine renewable energy sources through the use of current energy converter (CEC) and wave energy converter (WEC) devices requires an understanding of the noise generation and propagation from these systems in the marine environment. Acoustic noise produced by rotating turbines, for example, could adversely affect marine animals and human-related marine activities if not properly understood and mitigated. We are utilizing a 3-D finite-difference acoustic simulation code developed at Sandia that can accurately propagate noise in the complex bathymetry in the near-shore to open ocean environment. As part of our efforts to improve computation efficiency in the large, high-resolution domains required in this project, we investigate the effects of using optimized finite-difference coefficients on the accuracy of the simulations. We compare accuracy and runtime of various finite-difference coefficients optimized via criteria such as maximum numerical phase speed error, maximum numerical group speed error, and L-1 and L-2 norms of weighted numerical group and phase speed errors over a given spectral bandwidth. We find that those coefficients optimized for L-1 and L-2 norms are superior in accuracy to those based on maximal error and can produce runtimes of 10% of the baseline case, which uses Taylor Series finite-difference coefficients at the Courant time step limit. We will present comparisons of the results for the various cases evaluated as well as recommendations for utilization of the cases studied. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Calculating rotordynamic coefficients of seals by finite-difference techniques
NASA Technical Reports Server (NTRS)
Dietzen, F. J.; Nordmann, R.
1987-01-01
For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.
Finite difference time domain grid generation from AMC helicopter models
NASA Technical Reports Server (NTRS)
Cravey, Robin L.
1992-01-01
A simple technique is presented which forms a cubic grid model of a helicopter from an Aircraft Modeling Code (AMC) input file. The AMC input file defines the helicopter fuselage as a series of polygonal cross sections. The cubic grid model is used as an input to a Finite Difference Time Domain (FDTD) code to obtain predictions of antenna performance on a generic helicopter model. The predictions compare reasonably well with measured data.
Finite difference time domain calculations of antenna mutual coupling
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Kunz, Karl S.
1991-01-01
The Finite Difference Time Domain (FDTD) technique was applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been exclusively applied to antennas. Here, calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained during the method of moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.
Finite difference time domain calculations of antenna mutual coupling
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Kunz, Karl S.
1991-01-01
The Finite Difference Time Domain (FDTD) technique has been applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been extensively applied to antennas. In this short paper calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained using the Method of Moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.
Finite difference methods for the solution of unsteady potential flows
NASA Technical Reports Server (NTRS)
Caradonna, F. X.
1985-01-01
A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.
Finite difference schemes for long-time integration
NASA Technical Reports Server (NTRS)
Haras, Zigo; Taasan, Shlomo
1993-01-01
Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.
High Order Finite Difference Methods for Multiscale Complex Compressible Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.
2002-01-01
The classical way of analyzing finite difference schemes for hyperbolic problems is to investigate as many as possible of the following points: (1) Linear stability for constant coefficients; (2) Linear stability for variable coefficients; (3) Non-linear stability; and (4) Stability at discontinuities. We will build a new numerical method, which satisfies all types of stability, by dealing with each of the points above step by step.
NASA Technical Reports Server (NTRS)
Mccoy, M. J.
1980-01-01
Various finite difference techniques used to solve Laplace's equation are compared. Curvilinear coordinate systems are used on two dimensional regions with irregular boundaries, specifically, regions around circles and airfoils. Truncation errors are analyzed for three different finite difference methods. The false boundary method and two point and three point extrapolation schemes, used when having the Neumann boundary condition are considered and the effects of spacing and nonorthogonality in the coordinate systems are studied.
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
Finite difference program for calculating hydride bed wall temperature profiles
Klein, J.E.
1992-10-29
A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis.
Fuzzy logic to improve efficiency of finite element and finite difference schemes
Garcia, M.D.; Heger, A.S.
1994-05-01
This paper explores possible applications of logic in the areas of finite element and finite difference methods applied to engineering design problems. The application of fuzzy logic to both front-end selection of computational options and within the numerical computation itself are proposed. Further, possible methods of overcoming these limitations through the application of methods are explored. Decision strategy is a fundamental limitation in performing finite element calculations, such as selecting the optimum coarseness of the grid, numerical integration algorithm, element type, implicit versus explicit schemes, and the like. This is particularly true of novice analysts who are confronted with a myriad of choices in performing a calculation. The advantage of having the myriad of options available to the analyst is, however, that it improves and optimizes the design process if the appropriate ones are selected. Unfortunately, the optimum choices are not always apparent and only through the process of elimination or prior extensive experience can the optimum choices or combination of choices be selected. The knowledge of expert analysts could be integrated into a fuzzy ``front-end`` rule-based package to optimize the design process. The use of logic to capture the heuristic and human knowledge for selecting optimum solution strategies sets the framework for these proposed strategies.
An Analysis of Finite-Difference and Finite-Volume Formulations of Convervation Laws
NASA Astrophysics Data System (ADS)
Vinokur, Marcel
1989-03-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations-potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
An analysis of finite-difference and finite-volume formulations of conservation laws
NASA Astrophysics Data System (ADS)
Vinokur, Marcel
1986-06-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
An analysis of finite-difference and finite-volume formulations of conservation laws
NASA Technical Reports Server (NTRS)
Vinokur, Marcel
1986-01-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
An analysis of finite-difference and finite-volume formulations of conservation laws
NASA Technical Reports Server (NTRS)
Vinokur, Marcel
1989-01-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
Macroscopic traffic modeling with the finite difference method
Mughabghab, S.; Azarm, A.; Stock, D.
1996-03-15
A traffic congestion forecasting model (ATOP), developed in the present investigation, is described briefly. Several macroscopic models, based on the solution of the partial differential equation of conservation of vehicles by the finite difference method, were tested using actual traffic data. The functional form, as well as the parameters, of the equation of state which describes the relation between traffic speed and traffic density, were determined for a section of the Long Island Expressway. The Lax method and the forward difference technique were applied. The results of extensive tests showed that the Lax method, in addition to giving very good agreement with the traffic data, produces stable solutions.
Finite element thermal-structural analysis of cable-stiffened space structues
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Pandey, A. K.
1984-01-01
Finite element thermal-structural analyses of large, cable-stiffened space structures are presented. A computational scheme for the calculation of prestresses in the cable-stiffened structures is also described. The determination of thermal loads on orbiting space structures due to environment heating is discussed briefly. Three finite element structural analysis techniques are presented for the analysis of prestressed structures. Linear, stress stiffening, and large displacement analysis techniques were investigated. These three techniques were employed for analysis of prestressed cable structures at different prestress levels. The analyses produced similar results at small prestress, but at higher prestress, differences between the results became significant. For the cable-stiffened structures studied, the linear analysis technique may not provide acceptable results. The stress stiffening analysis technique may yield results of acceptable accuracy depending upon the level of prestress. The large displacement analysis technique produced accurate results over a wide range of prestress and is recommended as a general analysis technique for thermal-structural analysis of cable-stiffened space structures.
Seismic imaging using finite-differences and parallel computers
Ober, C.C.
1997-12-31
A key to reducing the risks and costs of associated with oil and gas exploration is the fast, accurate imaging of complex geologies, such as salt domes in the Gulf of Mexico and overthrust regions in US onshore regions. Prestack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar wave equation using finite differences. As part of an ongoing ACTI project funded by the US Department of Energy, a finite difference, 3-D prestack, depth migration code has been developed. The goal of this work is to demonstrate that massively parallel computers can be used efficiently for seismic imaging, and that sufficient computing power exists (or soon will exist) to make finite difference, prestack, depth migration practical for oil and gas exploration. Several problems had to be addressed to get an efficient code for the Intel Paragon. These include efficient I/O, efficient parallel tridiagonal solves, and high single-node performance. Furthermore, to provide portable code the author has been restricted to the use of high-level programming languages (C and Fortran) and interprocessor communications using MPI. He has been using the SUNMOS operating system, which has affected many of his programming decisions. He will present images created from two verification datasets (the Marmousi Model and the SEG/EAEG 3D Salt Model). Also, he will show recent images from real datasets, and point out locations of improved imaging. Finally, he will discuss areas of current research which will hopefully improve the image quality and reduce computational costs.
Application of a finite difference technique to thermal wave propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1975-01-01
A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Next, computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.
Application of a finite difference technique to thermal wave propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1975-01-01
A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.
FDIPS: Finite Difference Iterative Potential-field Solver
NASA Astrophysics Data System (ADS)
Toth, Gabor; van der Holst, Bartholomeus; Huang, Zhenguang
2016-06-01
FDIPS is a finite difference iterative potential-field solver that can generate the 3D potential magnetic field solution based on a magnetogram. It is offered as an alternative to the spherical harmonics approach, as when the number of spherical harmonics is increased, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. FDIPS is written in Fortran 90 and uses the MPI library for parallel execution.
Compact finite difference schemes with spectral-like resolution
NASA Technical Reports Server (NTRS)
Lele, Sanjiva K.
1992-01-01
The present finite-difference schemes for the evaluation of first-order, second-order, and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes. Various boundary conditions may be invoked, and both accurate interpolation and spectral-like filtering can be accomplished by means of schemes for derivatives at mid-cell locations. This family of schemes reduces to the Pade schemes when the maximal formal accuracy constraint is imposed with a specific computational stencil. Attention is given to illustrative applications of these schemes in fluid dynamics.
A finite difference approach to microstrip antenna design
Barth, M.J.; Bevensee, R.M.; Pennock, S.T.
1986-12-01
Microstrip antennas have received increased attention in recent years, due to their size and cost advantages. Analysis of the microstrip structure has proved difficult due to the presence of the dielectric substrate, particularly for complex geometries. One possible approach to a solution is the use of a finite difference computer code to model a proposed microstrip antenna design. The models are easily constructed and altered, and code versions are available which allow input impedance or far-field patterns to be calculated. Results for some simple antenna geometries will be presented.
Finite difference time domain modeling of spiral antennas
NASA Technical Reports Server (NTRS)
Penney, Christopher W.; Beggs, John H.; Luebbers, Raymond J.
1992-01-01
The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials.
A multigrid algorithm for the cell-centered finite difference scheme
NASA Technical Reports Server (NTRS)
Ewing, Richard E.; Shen, Jian
1993-01-01
In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.
Pencil: Finite-difference Code for Compressible Hydrodynamic Flows
NASA Astrophysics Data System (ADS)
Brandenburg, Axel; Dobler, Wolfgang
2010-10-01
The Pencil code is a high-order finite-difference code for compressible hydrodynamic flows with magnetic fields. It is highly modular and can easily be adapted to different types of problems. The code runs efficiently under MPI on massively parallel shared- or distributed-memory computers, like e.g. large Beowulf clusters. The Pencil code is primarily designed to deal with weakly compressible turbulent flows. To achieve good parallelization, explicit (as opposed to compact) finite differences are used. Typical scientific targets include driven MHD turbulence in a periodic box, convection in a slab with non-periodic upper and lower boundaries, a convective star embedded in a fully nonperiodic box, accretion disc turbulence in the shearing sheet approximation, self-gravity, non-local radiation transfer, dust particle evolution with feedback on the gas, etc. A range of artificial viscosity and diffusion schemes can be invoked to deal with supersonic flows. For direct simulations regular viscosity and diffusion is being used. The code is written in well-commented Fortran90.
NASA Technical Reports Server (NTRS)
Campbell, W.
1981-01-01
A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.
Finite Difference Elastic Wave Field Simulation On GPU
NASA Astrophysics Data System (ADS)
Hu, Y.; Zhang, W.
2011-12-01
Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finite-difference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for real-time strong ground motion simulation.
Arrayed waveguide grating using the finite difference beam propagation method
NASA Astrophysics Data System (ADS)
Toledo, M. C. F.; Alayo, M. I.
2013-03-01
The purpose of this work is to analyze by simulation the coupling effects occurring in Arrayed Waveguide Grating (AWG) using the finite difference beam propagation method (FD-BPM). Conventional FD-BPM techniques do not immediately lend themselves to the analysis of large structures such as AWG. Cooper et al.1 introduced a description of the coupling between the interface of arrayed waveguides and star couplers using the numerically-assisted coupled-mode theory. However, when the arrayed waveguides are spatially close, such that, there is strong coupling between them, and coupled-mode theory is not adequate. On the other hand, Payne2 developed an exact eigenvalue equation for the super modes of a straight arrayed waveguide which involve a computational overhead. In this work, an integration of both methods is accomplished in order to describe the behavior of the propagation of light in guided curves. This new method is expected to reduce the necessary effort for simulation while also enabling the simulation of large and curved arrayed waveguides using a fully vectorial finite difference technique.
Viscoelastic Finite Difference Modeling Using Graphics Processing Units
NASA Astrophysics Data System (ADS)
Fabien-Ouellet, G.; Gloaguen, E.; Giroux, B.
2014-12-01
Full waveform seismic modeling requires a huge amount of computing power that still challenges today's technology. This limits the applicability of powerful processing approaches in seismic exploration like full-waveform inversion. This paper explores the use of Graphics Processing Units (GPU) to compute a time based finite-difference solution to the viscoelastic wave equation. The aim is to investigate whether the adoption of the GPU technology is susceptible to reduce significantly the computing time of simulations. The code presented herein is based on the freely accessible software of Bohlen (2002) in 2D provided under a General Public License (GNU) licence. This implementation is based on a second order centred differences scheme to approximate time differences and staggered grid schemes with centred difference of order 2, 4, 6, 8, and 12 for spatial derivatives. The code is fully parallel and is written using the Message Passing Interface (MPI), and it thus supports simulations of vast seismic models on a cluster of CPUs. To port the code from Bohlen (2002) on GPUs, the OpenCl framework was chosen for its ability to work on both CPUs and GPUs and its adoption by most of GPU manufacturers. In our implementation, OpenCL works in conjunction with MPI, which allows computations on a cluster of GPU for large-scale model simulations. We tested our code for model sizes between 1002 and 60002 elements. Comparison shows a decrease in computation time of more than two orders of magnitude between the GPU implementation run on a AMD Radeon HD 7950 and the CPU implementation run on a 2.26 GHz Intel Xeon Quad-Core. The speed-up varies depending on the order of the finite difference approximation and generally increases for higher orders. Increasing speed-ups are also obtained for increasing model size, which can be explained by kernel overheads and delays introduced by memory transfers to and from the GPU through the PCI-E bus. Those tests indicate that the GPU memory size
Natural convection within a vertical finite-length channel in free space
Lin, S.C.; Chang, K.P.; Hung, Y.H. )
1994-04-01
Natural convection within a vertical finite length channel in free space is studied in this article to remove assumptions that need to be made on velocity and temperature profiles at the channel entrance. For small channel aspect ratios and low Rayleigh numbers, significant deviations of the Nusselt number and temperature distributions exist due to the effects of vertical thermal diffusion and free space stratification in the channel. A new correlation was proposed on induced Reynolds number for vertical finite length channel. 8 refs.
Spatial parallelism of a 3D finite difference, velocity-stress elastic wave propagation code
Minkoff, S.E.
1999-12-01
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, finite difference simulations for 3D elastic wave propagation are expensive. The authors model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code
MINKOFF,SUSAN E.
1999-12-09
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements
NASA Technical Reports Server (NTRS)
Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.
1990-01-01
A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.
Elastic finite-difference method for irregular grids
Oprsal, I.; Zahradnik, J.
1999-01-01
Finite-difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low-velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero-valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fulfills the free-surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.
McEneaney, William M.
2004-08-15
Stochastic games under imperfect information are typically computationally intractable even in the discrete-time/discrete-state case considered here. We consider a problem where one player has perfect information.A function of a conditional probability distribution is proposed as an information state.In the problem form here, the payoff is only a function of the terminal state of the system,and the initial information state is either linear ora sum of max-plus delta functions.When the initial information state belongs to these classes, its propagation is finite-dimensional.The state feedback value function is also finite-dimensional,and obtained via dynamic programming,but has a nonstandard form due to the necessity of an expanded state variable.Under a saddle point assumption,Certainty Equivalence is obtained and the proposed function is indeed an information state.
Phase-space finite elements in a least-squares solution of the transport equation
Drumm, C.; Fan, W.; Pautz, S.
2013-07-01
The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)
3D finite-difference seismic migration with parallel computers
Ober, C.C.; Gjertsen, R.; Minkoff, S.; Womble, D.E.
1998-11-01
The ability to image complex geologies such as salt domes in the Gulf of Mexico and thrusts in mountainous regions is essential for reducing the risk associated with oil exploration. Imaging these structures, however, is computationally expensive as datasets can be terabytes in size. Traditional ray-tracing migration methods cannot handle complex velocity variations commonly found near such salt structures. Instead the authors use the full 3D acoustic wave equation, discretized via a finite difference algorithm. They reduce the cost of solving the apraxial wave equation by a number of numerical techniques including the method of fractional steps and pipelining the tridiagonal solves. The imaging code, Salvo, uses both frequency parallelism (generally 90% efficient) and spatial parallelism (65% efficient). Salvo has been tested on synthetic and real data and produces clear images of the subsurface even beneath complicated salt structures.
A finite-difference method for transonic airfoil design.
NASA Technical Reports Server (NTRS)
Steger, J. L.; Klineberg, J. M.
1972-01-01
This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.
Accurate finite difference methods for time-harmonic wave propagation
NASA Technical Reports Server (NTRS)
Harari, Isaac; Turkel, Eli
1994-01-01
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
Effects of sources on time-domain finite difference models.
Botts, Jonathan; Savioja, Lauri
2014-07-01
Recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena. This paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing. Interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals. Boundary conditions modify the matrix and thus its modal structure, and initial conditions or source signals shape the solution, but not the modal structure. Low-frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix, and previously reported artifacts are predicted from eigenvalue estimates. The role of source signals is also briefly discussed. PMID:24993210
Finite-difference modeling of commercial aircraft using TSAR
Pennock, S.T.; Poggio, A.J.
1994-11-15
Future aircraft may have systems controlled by fiber optic cables, to reduce susceptibility to electromagnetic interference. However, the digital systems associated with the fiber optic network could still experience upset due to powerful radio stations, radars, and other electromagnetic sources, with potentially serious consequences. We are modeling the electromagnetic behavior of commercial transport aircraft in support of the NASA Fly-by-Light/Power-by-Wire program, using the TSAR finite-difference time-domain code initially developed for the military. By comparing results obtained from TSAR with data taken on a Boeing 757 at the Air Force Phillips Lab., we hope to show that FDTD codes can serve as an important tool in the design and certification of U.S. commercial aircraft, helping American companies to produce safe, reliable air transportation.
Visualization of elastic wavefields computed with a finite difference code
Larsen, S.; Harris, D.
1994-11-15
The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.
Parallelization of implicit finite difference schemes in computational fluid dynamics
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel
1990-01-01
Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.
Finite difference time domain implementation of surface impedance boundary conditions
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.
Improved finite difference schemes for transonic potential calculations
NASA Technical Reports Server (NTRS)
Hafez, M.; Osher, S.; Whitlow, W., Jr.
1984-01-01
Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.
A mimetic finite difference method for the Stokes problem with elected edge bubbles
Lipnikov, K; Berirao, L
2009-01-01
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.
NASA Technical Reports Server (NTRS)
Bauld, N. R., Jr.; Goree, J. G.; Tzeng, L.-S.
1985-01-01
It is pointed out that edge delamination is a serious failure mechanism for laminated composite materials. Various numerical methods have been utilized in attempts to calculate the interlaminar stress components which precede delamination in a laminate. There are, however, discrepancies regarding the results provided by different methods, taking into account a finite-difference procedure, a perturbation procedure, and finite element approaches. The present investigation has the objective to assess the capacity of a finite difference method to predict the character and magnitude of the interlaminar stress distributions near an interface corner. A second purpose of the investigation is to determine if predictions by finite element method in-plane, interlaminar stress components near an interface corner represent actual laminate behavior.
Domain decomposition methods for nonconforming finite element spaces of Lagrange-type
NASA Technical Reports Server (NTRS)
Cowsar, Lawrence C.
1993-01-01
In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.
A finite difference solution for the propagation of sound in near sonic flows
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Lester, H. C.
1983-01-01
An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.
Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory
NASA Astrophysics Data System (ADS)
Ghosh, Swarnava; Suryanarayana, Phanish
2016-02-01
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization. We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.
AnisWave2D: User's Guide to the 2d Anisotropic Finite-DifferenceCode
Toomey, Aoife
2005-01-06
This document describes a parallel finite-difference code for modeling wave propagation in 2D, fully anisotropic materials. The code utilizes a mesh refinement scheme to improve computational efficiency. Mesh refinement allows the grid spacing to be tailored to the velocity model, so that fine grid spacing can be used in low velocity zones where the seismic wavelength is short, and coarse grid spacing can be used in zones with higher material velocities. Over-sampling of the seismic wavefield in high velocity zones is therefore avoided. The code has been implemented to run in parallel over multiple processors and allows large-scale models and models with large velocity contrasts to be simulated with ease.
Nonlinear wave propagation using three different finite difference schemes (category 2 application)
NASA Technical Reports Server (NTRS)
Pope, D. Stuart; Hardin, J. C.
1995-01-01
Three common finite difference schemes are used to examine the computation of one-dimensional nonlinear wave propagation. The schemes are studied for their responses to numerical parameters such as time step selection, boundary condition implementation, and discretization of governing equations. The performance of the schemes is compared and various numerical phenomena peculiar to each is discussed.
A finite difference model for free surface gravity drainage
Couri, F.R.; Ramey, H.J. Jr.
1993-09-01
The unconfined gravity flow of liquid with a free surface into a well is a classical well test problem which has not been well understood by either hydrologists or petroleum engineers. Paradigms have led many authors to treat an incompressible flow as compressible flow to justify the delayed yield behavior of a time-drawdown test. A finite-difference model has been developed to simulate the free surface gravity flow of an unconfined single phase, infinitely large reservoir into a well. The model was verified with experimental results in sandbox models in the literature and with classical methods applied to observation wells in the Groundwater literature. The simulator response was also compared with analytical Theis (1935) and Ramey et al. (1989) approaches for wellbore pressure at late producing times. The seepage face in the sandface and the delayed yield behavior were reproduced by the model considering a small liquid compressibility and incompressible porous medium. The potential buildup (recovery) simulated by the model evidenced a different- phenomenon from the drawdown, contrary to statements found in the Groundwater literature. Graphs of buildup potential vs time, buildup seepage face length vs time, and free surface head and sand bottom head radial profiles evidenced that the liquid refills the desaturating cone as a flat moving surface. The late time pseudo radial behavior was only approached after exaggerated long times.
An adaptive-mesh finite-difference solution method for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Luchini, Paolo
1987-02-01
An adjustable variable-spacing grid is presented which permits the addition or deletion of single points during iterative solutions of the Navier-Stokes equations by finite difference methods. The grid is designed for application to two-dimensional steady-flow problems which can be described by partial differential equations whose second derivatives are constrained to the Laplacian operator. An explicit Navier-Stokes equations solution technique defined for use with the grid incorporates a hybrid form of the convective terms. Three methods are developed for automatic modifications of the mesh during calculations.
Finite Element Analysis of a Deployable Space Structure
NASA Technical Reports Server (NTRS)
Weeks, G. E.
1983-01-01
The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.
Contraction pre-conditioner in finite-difference electromagnetic modelling
NASA Astrophysics Data System (ADS)
Yavich, Nikolay; Zhdanov, Michael S.
2016-09-01
This paper introduces a novel approach to constructing an effective pre-conditioner for finite-difference (FD) electromagnetic modelling in geophysical applications. This approach is based on introducing an FD contraction operator, similar to one developed for integral equation formulation of Maxwell's equation. The properties of the FD contraction operator were established using an FD analogue of the energy equality for the anomalous electromagnetic field. A new pre-conditioner uses a discrete Green's function of a 1-D layered background conductivity. We also developed the formulae for an estimation of the condition number of the system of FD equations pre-conditioned with the introduced FD contraction operator. Based on this estimation, we have established that the condition number is bounded by the maximum conductivity contrast between the background conductivity and actual conductivity. When there are both resistive and conductive anomalies relative to the background, the new pre-conditioner is advantageous over using the 1-D discrete Green's function directly. In our numerical experiments with both resistive and conductive anomalies, for a land geoelectrical model with 1:10 contrast, the method accelerates convergence of an iterative method (BiCGStab) by factors of 2-2.5, and in a marine example with 1:50 contrast, by a factor of 4.6, compared to direct use of the discrete 1-D Green's function as a pre-conditioner.
Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers
Wang, Jun; Luo, Ray
2009-01-01
CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271
A hybrid finite-difference and analytic element groundwater model.
Haitjema, H M; Feinstein, D T; Hunt, R J; Gusyev, M A
2010-01-01
Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models. PMID:20132324
Assessment of linear finite-difference Poisson-Boltzmann solvers.
Wang, Jun; Luo, Ray
2010-06-01
CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271
Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers.
Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray
2010-01-12
We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843
Asymptotically Correct Finite Difference Schemes for Highly Oscillatory ODEs
Arnold, Anton; Geier, Jens
2010-09-30
We are concerned with the numerical integration of ODE-initial value problems of the form {epsilon}{sup 2{phi}}{sub xx}+a(x){phi} = 0 with given a(x){>=}a{sub 0}>0 in the highly oscillatory regime 0<{epsilon}(appearing as a stationary Schroedinger equation, e.g.). In two steps we derive an accurate finite difference scheme that does not need to resolve each oscillation: With a WKB-ansatz the dominant oscillations are ''transformed out'', yielding a much smoother ODE. For the resulting oscillatory integrals we devise an asymptotic expansion both in {epsilon} and h. The resulting scheme typically has a step size restriction of h = o({radical}({epsilon})). If the phase of the WKB-transformation can be computed explicitly, then the scheme is asymptotically correct with an error bound of the order o({epsilon}{sup 3}h{sup 2}). As an application we present simulations of a 1D-model for ballistic quantum transport in a MOSFET (metal oxide semiconductor field-effect transistor).
Generating meshes for finite-difference analysis using a solid modeler
NASA Astrophysics Data System (ADS)
Laguna, G. W.; White, W. T.; Cabral, B. K.
1987-09-01
One tool used by the Engineering Research Division of LLNL to help analyze the behavior of electronic systems in hostile environments is 3D finite-difference time-domain (FDTD) computation. FDTD codes solve Maxwell's equations,the differential equations of electromagnetism, on a uniform lattice of points. It is this uniform lattice, or mesh, that distinguishes finite-difference codes from other codes. The simple mesh makes FDTD codes computationally more efficient than other codes, which enables them to run larger problems and to run faster (up to thirty times faster than finite-element codes, for example). Therefore, within the Engineering Department at LLNL, Electronics Engineering (EE) has initiated a project to develop a mesh generator that will provide meshes suitable for FDTD analysis. This report describes the results of the first year of EE's FDTD Mesh Generation Project. During this year a preliminary version of an automated mesh generator was built and used to create a mesh of an object of interest to the High-Power Microwave Program, namely an electrically detonatable land mine. The code was verified by meshing basic solids such as spheres and cylinders. Because of the design of the code, there is no software limitation to the size of meshes that can be accommodated. The algorithm with a mesh space of approximately 500,000 cells has been demonstrated. The mesh generator can detect certain objects with walls that are thinner than the width of a cell. The code has internal graphics for viewing objects as they appear prior to being converted to a finite-difference representation. Additionally, via data files, the code is coupled to two external graphics packages for visually checking the meshes, namely TAURUS on the Cray and a new code, IMAGE, on the Silicon Graphics IRIS workstation.
Generating meshes for finite-difference analysis using a solid modeler
Laguna, G.W.; White, W.T.; Cabral, B.K.
1987-09-01
One tool used by the Engineering Research Division of LLNL to help analyze the behavior of electronic systems in hostile environments is 3D finite-difference time-domain (FDTD) computation. FDTD codes solve Maxwell's equations,the differential equations of electromagnetism, on a uniform lattice of points. It is this uniform lattice, or ''mesh,'' that distinguishes finite-difference codes from other codes. The simple mesh makes FDTD codes computationally more efficient than other codes, which enables them to run larger problems and to run faster (up to thirty times faster than finite-element codes, for example). Therefore, within the Engineering Department at LLNL, Electronics Engineering (EE) has initiated a project to develop a mesh generator that will provide meshes suitable for FDTD analysis. This report describes the results of the first year of EE's FDTD Mesh Generation Project. During this year a preliminary version of an automated mesh generator was built and used to create a mesh of an object of interest to the High-Power Microwave Program, namely an electrically detonatable land mine. The code was verified by meshing basic solids such as spheres and cylinders. Because of the design of the code, there is no software limitation to the size of meshes that can be accommodated. The algorithm with a mesh space of approximately 500,000 cells has been demonstrated. The mesh generator can detect certain objects with walls that are thinner than the width of a cell. The code has internal graphics for viewing objects as they appear prior to being converted to a finite-difference representation. Additionally, via data files, the code is coupled to two external graphics packages for visually checking the meshes, namely TAURUS on the Cray and a new code, IMAGE, on the Silicon Graphics IRIS workstation.
Boiling Fluids Behave Quite Differently in Space
The boiling process is really different in space, since the vapor phase of a boiling liquid does not rise via buoyancy. Spacecraft and Earth-based systems use boiling to efficiently remove large am...
NASA Astrophysics Data System (ADS)
Moslehy, Faissal A.; Mueller, Steven A.; Davis, Richard M.
1993-10-01
This paper describes a novel application of a laser-based vibration measuring system and finite element modeling to evaluate the bond condition of Space Shuttle thermal protection system tiles. This application is based on characterizing the vibrational response of tiles when excited by an audible acoustic energy. Finite element models for tile assemblies which are comprised of tiles, SIP, and RTV layers attached to the Orbiter aluminum skin are first developed. The mathematical model considered the actual orthotropic material properties, different geometrical configurations as well as different bond conditions. The tiles' natural frequencies and mode shapes are then determined and their frequency responses due to simulated sound pressure are computed. The computed frequency response of a tile having a disbond indicates a decrease in its natural frequencies. This can be used to quickly identify the disbonded tiles. However, the exact size and location of the disbond are determined from the computed rigid- body vibrational modes. The finite element results are compared with experimentally determined frequency responses of a 17-tile test panel, where a rapid scan laser system was employed. An excellent degree of correlation between the mathematical simulation and experimental results is realized. The paper also reports on laser-based modal and shearographic testing performed on tiles of Space Shuttle Columbia. Again, the results demonstrate that experimental modal analysis, when combined with finite element modeling, can be successfully used as a reliable nondestructive, non-contact technique for tile bond verification.
Finite-difference-based dynamic modeling of MEMS bridge
NASA Astrophysics Data System (ADS)
Michael, Aron; Yu, Kevin; Kwok, Chee Yee
2005-02-01
In this paper, we present a finite difference based one-dimensional dynamic modeling, which includes electro-thermal coupled with thermo-mechanical behavior of a multi-layered micro-bridge. The electro-thermal model includes the heat transfer from the joule-heated layer to the other layers, and establishes the transient temperature gradient through the thickness of the bridge. The thermal moment and axial load resulting from the transient temperature gradient are used to couple electro-thermal with thermo-mechanical behavior. The dynamic modeling takes into account buckling, and damping effects, asymmetry residual stresses in the layers, and lateral movement at the support ends. The proposed model is applied to a tri-layer micro-bridge of 1000μm length, made of 2μm silicon dioxide sandwiched in between 2μm thick epi-silicon, and 2μm thick poly silicon, with four 400μm long legs, and springs at the four corners the bridge. The beam, and legs are 40μm, and 10μm wide respectively. Results demonstrate the bi-stability of the structure, and a large movement of 40μm between the up and down stable states can easily be obtained. Application of only 21mA electrical current for 15μs to the legs is required to switch buckled-up position to buckled-down position. An additional trapezoidal waveform electrical current of 100mA amplitude for 4μs, and 100μs falling time needs to be applied for the reverse actuation. The switching speed in both cases is less than 500μs.
3D Finite Difference Modelling of Basaltic Region
NASA Astrophysics Data System (ADS)
Engell-Sørensen, L.
2003-04-01
The main purpose of the work was to generate realistic data to be applied for testing of processing and migration tools for basaltic regions. The project is based on the three - dimensional finite difference code (FD), TIGER, made by Sintef. The FD code was optimized (parallelized) by the author, to run on parallel computers. The parallel code enables us to model large-scale realistic geological models and to apply traditional seismic and micro seismic sources. The parallel code uses multiple processors in order to manipulate subsets of large amounts of data simultaneously. The general anisotropic code uses 21 elastic coefficients. Eight independent coefficients are needed as input parameters for the general TI medium. In the FD code, the elastic wave field computation is implemented by a higher order FD solution to the elastic wave equation and the wave fields are computed on a staggered grid, shifted half a node in one or two directions. The geological model is a gridded basalt model, which covers from 24 km to 37 km of a real shot line in horizontal direction and from the water surface to the depth of 3.5 km. The 2frac {1}{2}D model has been constructed using the compound modeling software from Norsk Hydro. The vertical parameter distribution is obtained from observations in two wells. At The depth of between 1100 m to 1500 m, a basalt horizon covers the whole sub surface layers. We have shown that it is possible to simulate a line survey in realistic (3D) geological models in reasonable time by using high performance computers. The author would like to thank Norsk Hydro, Statoil, GEUS, and SINTEF for very helpful discussions and Parallab for being helpful with the new IBM, p690 Regatta system.
A finite-difference contrast source inversion method
NASA Astrophysics Data System (ADS)
Abubakar, A.; Hu, W.; van den Berg, P. M.; Habashy, T. M.
2008-12-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium.
Feldberg, S.W.
1991-01-01
Commencing in the early 60s the application of explicit finite difference (EFD) methods to the analysis of electrochemical problems paralleled the development and availability of fast, main-frame, digital computers. The appeal of the EFD method has been its simplicity of principle and of application. EFD algorithms, however, are notoriously inefficient for solving certain types of stiff problems (e.g., problems involving a wide dynamic range of time constants). In this presentation the author discusses the principles and some applications of a fast quasi-explicit finite difference (FQEFD) method in which the computational speed is enhanced, by many orders of magnitude in some cases, without compromising the user friendliness which has popularized the EFD method. The method is designed to treat electrochemical responses to a discontinuous (e.g, chronoamperometric) perturbation and utilizes the DuFort-Frankel algorithm (1) with exponentially expanding space (2) and exponentially expanding time grids. (A previously published version of the FQEFD method (3,4) was designed to treat electrochemical responses to a continuous (e.g., cyclic voltammetric) perturbation and utilizes the DuFort-Frankel (3) algorithm in conjunction with an exponentially expanding space grid and a uniform time grid. The development of the basic FQEFD equations was presented there). The protocol for introducing the expanding time grid is straightforward and is discussed. 7 refs., 1 fig. 1 tab.
Wang, Wei; Shu, Chi-Wang; Yee, H.C.; Sjögreen, Björn
2012-01-01
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.
NASA Technical Reports Server (NTRS)
Siegel, R.; Molls, F. B.
1992-01-01
Transient solutions were obtained for a square region of heat conducting semitransparent material cooling by thermal radiation. The region is in a vacuum environment, so energy is dissipated only by radiation from within the medium leaving through its boundaries. The effect of heat conduction during the transient is to partially equalize the internal temperature distribution. As the optical thickness of the region is increased, the temperature gradients increase near the boundaries and corners, unless heat conduction is large. The solution procedure must provide accurate temperature distributions in these regions to prevent error in the calculated radiation losses. Two-dimensional numerical Gaussian integration is used to obtain the local radiative source term. A finite difference procedure with variable space and time increments is used to solve the transient energy equation. Variable spacing was used to concentrate grid points in regions with large temperature gradients.
Evaluation of a thin-slot formalism for finite-difference time-domain electromagnetics codes
Turner, C.D.; Bacon, L.D.
1987-03-01
A thin-slot formalism for use with finite-difference time-domain (FDTD) electromagnetics codes has been evaluated in both two and three dimensions. This formalism allows narrow slots to be modeled in the wall of a scatterer without reducing the space grid size to the gap width. In two dimensions, the evaluation involves the calculation of the total fields near two infinitesimally thin coplanar strips separated by a gap. A method-of-moments (MoM) solution of the same problem is used as a benchmark for comparison. Results in two dimensions show that up to 10% error can be expected in total electric and magnetic fields both near (lambda/40) and far (1 lambda) from the slot. In three dimensions, the evaluation is similar. The finite-length slot is placed in a finite plate and an MoM surface patch solution is used for the benchmark. These results, although less extensive than those in two dimensions, show that slightly larger errors can be expected. Considering the approximations made near the slot in incorporating the formalism, the results are very promising. Possibilities also exist for applying this formalism to walls of arbitrary thickness and to other types of slots, such as overlapping joints. 11 refs., 25 figs., 6 tabs.
A fast finite volume method for conservative space-fractional diffusion equations in convex domains
NASA Astrophysics Data System (ADS)
Jia, Jinhong; Wang, Hong
2016-04-01
We develop a fast finite volume method for variable-coefficient, conservative space-fractional diffusion equations in convex domains via a volume-penalization approach. The method has an optimal storage and an almost linear computational complexity. The method retains second-order accuracy without requiring a Richardson extrapolation. Numerical results are presented to show the utility of the method.
Space weather at different planetary environments
NASA Astrophysics Data System (ADS)
Plainaki, Christina; Milillo, Anna; Andriopoulou, Maria; Dandouras, Iannis; Radioti, Aikaterini; Lilensten, Jean; Coustenis, Athena; Nordheim, Tom; Orsini, Stefano; Mura, Alessandro; Mangano, Valeria
2015-04-01
Different aspects of the conditions in the Sun, solar wind and magnetospheric plasmas, at various planetary systems of our Solar System, can influence the performance and reliability of space-borne technological systems. The science study of the so-called Planetary Space Weather considers different cross-disciplinary issues, including: - the interaction of solar wind/magnetospheric plasmas with planetary/satellite surfaces, ionospheres and thick (e.g. at Jupiter, Saturn, Uranus, Mars, Venus, Titan) or tenuous (e.g. Ganymede, Europa, Mercury, our Moon) atmospheres, including the generation of auroras - the satellite interactions with their neutral environments and dust - the variability of the magnetospheric regions under different solar wind conditions - radiation belts, and their interactions with atmospheres/satellites/rings, in different planetary environments - the inter-comparisons of space weather conditions in different planetary environments In this paper, a brief review of theoretical and data analysis studies regarding planetary space weather in different bodies of our Solar System is presented. The importance of such studies for the in-situ data interpretations as well as for the preparation of future space missions is outlined.
A total variation diminishing finite difference algorithm for sonic boom propagation models
NASA Technical Reports Server (NTRS)
Sparrow, Victor W.
1993-01-01
It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.
NASA Technical Reports Server (NTRS)
Gladden, Herbert J.; Ko, Ching L.; Boddy, Douglas E.
1995-01-01
A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.
A Unified Topological Layer for Finite Element Space Discretization
NASA Astrophysics Data System (ADS)
Stimpfl, Franz; Weinbub, Josef; Heinzl, René; Schwaha, Philipp; Selberherr, Siegfried
2010-09-01
A unified topological layer for mesh generation has been created to benefit from current development, to reuse existing, well tested and reliable methods, such as the Delaunay or the Advancing Front mesh generation approach, and to combine them to be able to interchange these methods, without taking a detour using file formats. In addition, by modularizing existing meshing kernels, this approach allows to not only have one meshing interface for arbitrary dimensions, but also to have the possibility at hand to independently combine different meshing strategies.
NASA Astrophysics Data System (ADS)
Kumar, Vivek; Raghurama Rao, S. V.
2008-04-01
Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally
NASA Technical Reports Server (NTRS)
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
McLeod, R.; Hawkins, R.J.; Kallman, J.S.
1991-04-01
Interest has recently grown in applying microwave modeling techniques to optical circuit modeling. One of the simplest, yet most powerful, microwave simulation techniques is the finite-difference time-domain algorithm (FDTD). In this technique, the differential form of the time-domain Maxwell's equations are discretized and all derivatives are approximated as differences. Minor algebraic manipulations on the resulting equations produces a set of update equations that produce fields at a given time step from fields at the previous time step. The FDTD algorithm, then, is quite simple. Source fields are launched into the discrete grid by some means. The FDTD equations advance these fields in time. At the boundaries of the grid, special update equations called radiation conditions are applied that approximate a continuing, infinite space. Because virtually no assumptions are made in the development of the FDTD method, the algorithm is able to represent a wide-range of physical effects. Waves can propagate in any direction, multiple reflections within structures can cause resonances, multiple modes of various polarizations can be launched, each of which may generate within the device an infinite spectrum of bound and radiation modes. The ability to model these types of general physical effects is what makes the FDTD method interesting to the field of optics. In this paper, we discuss the application of the finite-difference time-domain technique to integrated optics. Animations will be shown of the simulations of a TE coupler, TM grating, and a TE integrated detector. 3 refs., 1 fig.
Improved finite-difference computation of the van der Waals force: One-dimensional case
Pinto, Fabrizio
2009-10-15
We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate the difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.
Dynamic and thermal response finite element models of multi-body space structural configurations
NASA Technical Reports Server (NTRS)
Edighoffer, Harold H.
1987-01-01
Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.
A formula for the weight of a minimal filling of a finite metric space
Eremin, A Yu
2013-09-30
We consider the problem of finding a minimal filling for a finite metric space, that is, a weighted graph of minimal weight joining a given finite metric space. We obtain a minimax formula for the weight of the minimal filling, which we use to prove various properties of minimal fillings. Bibliography: 10 titles.
Finite element analysis of the Space Shuttle 2.5-inch frangible nut
NASA Technical Reports Server (NTRS)
McKinnis, Darin N.
1994-01-01
Finite element analysis of the Space Shuttle 2.5-inch frangible nut was conducted to improve understanding of the current design and proposed design changes to this explosively-actuated nut. The 2.5-inch frangible nut is used in two places to attach the aft end of the Space Shuttle Orbiter to the External Tank. Both 2.5-inch frangible nuts must function to complete safe separation. The 2.5-inch frangible nut contains two explosive boosters containing RDX explosive each capable of splitting the nut in half, on command from the Orbiter computers. To ensure separation, the boosters are designed to be redundant. The detonation of one booster is sufficient to split the nut in half. However, beginning in 1987 some production lots of 2.5-inch frangible nuts have demonstrated an inability to separate using only a single booster. The cause of the failure has been attributed to differences in the material properties and response of the Inconel 718 from which the 2.5-inch frangible nut is manufactured. Subsequent tests have resulted in design modifications of the boosters and frangible nut. Model development and initial analysis was conducted by Sandia National Laboratories (SNL) under funding from NASA Lyndon B. Johnson Space Center (NASA-JSC) starting in 1992. Modeling codes previously developed by SNL were transferred to NASA-JSC for further analysis on this and other devices. An explosive bolt with NASA Standard Detonator (NSD) charge, a 3/4-inch frangible nut, and the Super*Zip linear separation system are being modeled by NASA-JSC.
Finite difference identification of noisy distributed systems using scanning measurements
NASA Technical Reports Server (NTRS)
Hughes, R. O.
1975-01-01
Most of the present-day literature concerned with identification theory and techniques is directed toward lumped parameter systems, and many comprehensive surveys of the field are available. Relatively little has appeared in the literature concerning distributed identification, and even more noticeable is the scarcity of papers dealing with systems described by the one-dimensional wave equation. Perdeauville and Goodson were perhaps the first researchers with a workable but time consuming method for the identification of coefficients of the wave equation. Fairman and Shen, also considering the wave equation, used the technique of finite differencing to approximate spatial derivatives, and Poisson filter chains to approximate temporal derivatives.
2D time-domain finite-difference modeling for viscoelastic seismic wave propagation
NASA Astrophysics Data System (ADS)
Fan, Na; Zhao, Lian-Feng; Xie, Xiao-Bi; Ge, Zengxi; Yao, Zhen-Xing
2016-07-01
Real Earth media are not perfectly elastic. Instead, they attenuate propagating mechanical waves. This anelastic phenomenon in wave propagation can be modeled by a viscoelastic mechanical model consisting of several standard linear solids. Using this viscoelastic model, we approximate a constant Q over a frequency band of interest. We use a four-element viscoelastic model with a tradeoff between accuracy and computational costs to incorporate Q into 2D time-domain first-order velocity-stress wave equations. To improve the computational efficiency, we limit the Q in the model to a list of discrete values between 2 and 1000. The related stress and strain relaxation times that characterize the viscoelastic model are pre-calculated and stored in a database for use by the finite-difference calculation. A viscoelastic finite-difference scheme that is second-order in time and fourth-order in space is developed based on the MacCormack algorithm. The new method is validated by comparing the numerical result with analytical solutions that are calculated using the generalized reflection/transmission coefficient method. The synthetic seismograms exhibit greater than 95 per cent consistency in a two-layer viscoelastic model. The dispersion generated from the simulation is consistent with the Kolsky-Futterman dispersion relationship.
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.; Kreider, Kevin L.
1996-01-01
An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
NASA Astrophysics Data System (ADS)
Zehner, Björn; Hellwig, Olaf; Linke, Maik; Görz, Ines; Buske, Stefan
2016-01-01
3D geological underground models are often presented by vector data, such as triangulated networks representing boundaries of geological bodies and geological structures. Since models are to be used for numerical simulations based on the finite difference method, they have to be converted into a representation discretizing the full volume of the model into hexahedral cells. Often the simulations require a high grid resolution and are done using parallel computing. The storage of such a high-resolution raster model would require a large amount of storage space and it is difficult to create such a model using the standard geomodelling packages. Since the raster representation is only required for the calculation, but not for the geometry description, we present an algorithm and concept for rasterizing geological models on the fly for the use in finite difference codes that are parallelized by domain decomposition. As a proof of concept we implemented a rasterizer library and integrated it into seismic simulation software that is run as parallel code on a UNIX cluster using the Message Passing Interface. We can thus run the simulation with realistic and complicated surface-based geological models that are created using 3D geomodelling software, instead of using a simplified representation of the geological subsurface using mathematical functions or geometric primitives. We tested this set-up using an example model that we provide along with the implemented library.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Kreider, K. L.
1996-01-01
An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions
NASA Technical Reports Server (NTRS)
Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan
1995-01-01
The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.
NASA Technical Reports Server (NTRS)
daSilva, A.; Lin. S.-J.; Dee, D.; Joiner, J.; Atlas, Robert (Technical Monitor)
2001-01-01
The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will describe the general system formulation, the adaptive quality control and general aspects of the error covariance modeling. The NASA-NCAR GCM is a completely new model which replaces the CEOs GCM used in the previous GEOS-1/2/3 Data Assimilation systems. A particular configuration of adaptive Statistical Quality Control and the Physical-space Statistical Analysis System (PSAS) are currently implemented in DAO's operational Data Assimilation System. However, the unique finite-volume formulation of the NASA-NCAR GCM, combined with the generality of the observation-space formulation of PSAS, provides for a very simple and accurate model-analysis interface. The system assimilates a variety of conventional and satellite observations. In particular, TOVS Level 1B radiances are assimilated using a 1-D variational scheme, both in clear sky and cloudy conditions. Computationally, the fvDAS runs approximately 10 times faster than the operational GEOS-Terra system. We will show that the next-generation fvDAS has much improved observation-minus-6hr forecast (O-F) statistics, as well as 5-day forecast skills. Top of the atmosphere radiation fields are in closer agreement with CERES measurements, with realistic precipitation and moisture fields. We will also show that the finite-volume formulation of the fvDAS produce assimilated fields which are more suitable for driving constituent transport models.
NASA Technical Reports Server (NTRS)
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2015-03-01
Two square matrices of (arbitrary) order N are introduced. They are defined in terms of N arbitrary numbers zn, and of an arbitrary additional parameter (a respectively q), and provide finite-dimensional representations of the two operators acting on a function f(z) as follows: [f(z + a) - f(z)]/a respectively [f(qz) - f(z)]/[(q - 1) z]. These representations are exact—in a sense explained in the paper—when the function f(z) is a polynomial in z of degree less than N. This formalism allows to transform difference equations valid in the space of polynomials of degree less than N into corresponding matrix-vector equations. As an application of this technique, several remarkable square matrices of order N are identified, which feature explicitly N arbitrary numbers zn, or the N zeros of polynomials belonging to the Askey and q-Askey schemes. Several of these findings have a Diophantine character.
Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia
NASA Astrophysics Data System (ADS)
Mansor, Nur Jariah; Jaffar, Maheran Mohd
2014-07-01
Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.
NASA Technical Reports Server (NTRS)
Shu, Chi-Wang
1998-01-01
This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.
NASA Technical Reports Server (NTRS)
Kaul, Upender K. (Inventor)
2009-01-01
Modeling and simulation of free and forced structural vibrations is essential to an overall structural health monitoring capability. In the various embodiments, a first principles finite-difference approach is adopted in modeling a structural subsystem such as a mechanical gear by solving elastodynamic equations in generalized curvilinear coordinates. Such a capability to generate a dynamic structural response is widely applicable in a variety of structural health monitoring systems. This capability (1) will lead to an understanding of the dynamic behavior of a structural system and hence its improved design, (2) will generate a sufficiently large space of normal and damage solutions that can be used by machine learning algorithms to detect anomalous system behavior and achieve a system design optimization and (3) will lead to an optimal sensor placement strategy, based on the identification of local stress maxima all over the domain.
NASA Astrophysics Data System (ADS)
Zhu, Lu; Liu, Yuanyuan; Chen, Suhua; Hu, Fei; Chen, Zhizhang (David)
2015-04-01
Synthetic aperture imaging radiometer (SAIR) has the potential to meet the spatial resolution requirement of passive millimeter remote sensing from space. A new two-dimensional (2-D) imaging radiometer at millimeter wave (MMW) band is described in this paper; it uses a one-dimensional (1-D) synthetic aperture digital radiometer (SADR) to obtain an image on one dimension and a rotary platform to provide a scan on the second dimension. Due to the ill-posed inverse problem of SADR, we proposed a new reconstruction algorithm based on Finite Difference (FD) regularization to improve brightness temperature images. Experimental results show that the proposed 2-D MMW radiometer can give the brightness temperature images of natural scenes and the FD regularization reconstruction algorithm is able to improve the quality of brightness temperature images.
Finite difference solution for transient cooling of a radiating-conducting semitransparent layer
NASA Technical Reports Server (NTRS)
Siegel, Robert
1992-01-01
Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.
Study of two-dimensional transient cavity fields using the finite-difference time-domain technique
Crisp, J.L.
1988-06-01
This work is intended to be a study into the application of the finite-difference time-domain, or FD-TD technique, to some of the problems faced by designers of equipment used in modern accelerators. In particular it discusses using the FD-TD algorithm to study the field distribution of a simple two-dimensional cavity in both space and time. 18 refs.
Higher-Order, Space-Time Adaptive Finite Volume Methods: Algorithms, Analysis and Applications
Minion, Michael
2014-04-29
The four main goals outlined in the proposal for this project were: 1. Investigate the use of higher-order (in space and time) finite-volume methods for fluid flow problems. 2. Explore the embedding of iterative temporal methods within traditional block-structured AMR algorithms. 3. Develop parallel in time methods for ODEs and PDEs. 4. Work collaboratively with the Center for Computational Sciences and Engineering (CCSE) at Lawrence Berkeley National Lab towards incorporating new algorithms within existing DOE application codes.
High-order cyclo-difference techniques: An alternative to finite differences
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Otto, John C.
1993-01-01
The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.
Reddy, Jaggari Chandrakanth; Srikakula, Naveen Kumar; Juturu, Rajesh Kumar Reddy; Paidi, Shameen Kumar; Tedlapu, Satyendra Kumar; Mannava, Padmakanth; Khatoon, Rukhaiya
2016-01-01
Introduction Retention and esthetics are believed to play a crucial role in deciding the success of removable partial dentures. Aim To compare retention of acetal resin and cobalt–chromium clasps. Materials and Methods A finite element model was designed with an edentulous space between mandibular right second premolar and second molar. Occlusal rests were placed on distal fossa of the second premolar and mesial fossa of second molar. An undercut depth of 0.01inch was created on the mesiobuccal surface of the premolar and distobuccal surface of second molar. Three dimensional finite element model of clasp assembly was designed and assigned with the properties of two different materials namely acetal resin and cobalt–chromium in successive steps. A horizontal bar was constructed between the occlusal rests of the prosthesis. Later, variable amount of dislodging force, in increasing order, was applied at the centre of the horizontal bar and the force at which the clasp arm gets dislodged was noted with respect to each of the material. The obtained values were noted and then subsequently analyzed. Results The amount of force required to dislodge acetal resin and cobalt–chromium clasps was found to be 0.02N and 2N respectively. Conclusion The results obtained suggested that acetal resin clasp exhibited less retentive force than cobalt–chromium clasps. PMID:27437346
Finite element analysis of space debris removal by high-power lasers
NASA Astrophysics Data System (ADS)
Xue, Li; Jiang, Guanlei; Yu, Shuang; Li, Ming
2015-08-01
With the development of space station technologies, irradiation of space debris by space-based high-power lasers, can locally generate high-temperature plasmas and micro momentum, which may achieve the removal of debris through tracking down. Considered typical square-shaped space debris of material Ti with 5cm×5cm size, whose thermal conductivity, density, specific heat capacity and emissivity are 7.62W/(m·°C), 4500kg/m3, 0.52J/(kg·°C) and 0.3,respectively, based on the finite element analysis of ANSYS, each irradiation of space debris by high-power lasers with power density 106W/m2 and weapons-grade lasers with power density 3000W/m2 are simulated under space environment, and the temperature curves due to laser thermal irradiation are obtained and compared. Results show only 2s is needed for high-power lasers to make the debris temperature reach to about 10000K, which is the threshold temperature for plasmas-state conversion. While for weapons-grade lasers, it is 13min needed. Using two line elements (TLE), and combined with the coordinate transformation from celestial coordinate system to site coordinate system, the visible period of space debris is calculated as 5-10min. That is, in order to remove space debris by laser plasmas, the laser power density should be further improved. The article provides an intuitive and visual feasibility analysis method of space debris removal, and the debris material and shape, laser power density and spot characteristics are adjustable. This finite element analysis method is low-cost, repeatable and adaptable, which has an engineering-prospective applications.
High-stability Finite-Length Silicon Nanowires: A Real Space Theoretical Study
NASA Astrophysics Data System (ADS)
Koukaras, E. N.; Zdetsis, A. D.; Garoufalis, C. S.
2007-12-01
We demonstrate by real-space density functional calculations that unreconstructed low-stability finite size hydrogenated silicon nanowires could bend through relaxation under the influence of internal strains, contrary to high-stability "magic" nanowires. The strains and the resulting bending depend on the distribution and orientation of silicon dihydrides on the nanowire's surface. This and other related effects cannot be accounted for by the usual k-space supercell techniques. We also demonstrate that reconstructed (2×1) nanowires, although bend they are practically as stable as the "magic" unreconstructed nanowires. Our calculations are in full agreement with the experimental work of Ma et al. [Science 299, 1874, (2003)].
NASA Technical Reports Server (NTRS)
Byun, Chansup; Guruswamy, Guru P.
1993-01-01
This paper presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data (MIMD) parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a High Speed Civil Transport type wing-body configuration.
Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar
2014-01-01
We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils. PMID:24688360
Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar
2014-01-01
We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils. PMID:24688360
An extended pressure finite element space for two-phase incompressible flows with surface tension
NASA Astrophysics Data System (ADS)
Groß, Sven; Reusken, Arnold
2007-05-01
We consider a standard model for incompressible two-phase flows in which a localized force at the interface describes the effect of surface tension. If a level set (or VOF) method is applied then the interface, which is implicitly given by the zero level of the level set function, is in general not aligned with the triangulation that is used in the discretization of the flow problem. This non-alignment causes severe difficulties w.r.t. the discretization of the localized surface tension force and the discretization of the flow variables. In cases with large surface tension forces the pressure has a large jump across the interface. In standard finite element spaces, due to the non-alignment, the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure. In many simulations these effects cause large oscillations of the velocity close to the interface, so-called spurious velocities. In this paper, for a simplified model problem, we give an analysis that explains why known (standard) methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities. In the paper [S. Groß, A. Reusken, Finite element discretization error analysis of a surface tension force in two-phase incompressible flows, Preprint 262, IGPM, RWTH Aachen, SIAM J. Numer. Anal. (accepted for publication)], we introduce a new and accurate method for approximation of the surface tension force. In the present paper, we use the extended finite element space (XFEM), presented in [N. Moes, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Eng. 46 (1999) 131-150; T. Belytschko, N. Moes, S. Usui, C. Parimi, Arbitrary discontinuities in finite elements, Int. J. Numer. Meth. Eng. 50 (2001) 993-1013], for the discretization of the pressure. We show that the size of spurious velocities is reduced substantially, provided we
Optimization of a finite difference method for nonlinear wave equations
NASA Astrophysics Data System (ADS)
Chen, Miaochao
2013-07-01
Wave equations have important fluid dynamics background, which are extensively used in many fields, such as aviation, meteorology, maritime, water conservancy, etc. This paper is devoted to the explicit difference method for nonlinear wave equations. Firstly, a three-level and explicit difference scheme is derived. It is shown that the explicit difference scheme is uniquely solvable and convergent. Moreover, a numerical experiment is conducted to illustrate the theoretical results of the presented method.
Finite-difference evolution of a scattered laser pulse in ocean water
NASA Astrophysics Data System (ADS)
Tessendorf, J.; Piotrowski, C.; Kelly, R. L.
1988-01-01
The effects of absorption and scattering on the propagation of a finite-size laser pulse through ocean water are investigated theoretically, applying a finite-difference model based on the time-dependent radiative-transfer equation. The derivation of the finite-difference evolution algorithm is outlined; its FORTRAN numerical implementation is explained; and simulation results for simple test problems are presented in graphs. The method is shown to provide unconditional stability and physically correct propagation velocities in all directions. The need to eliminate or compensate for ray effects is indicated.
Chaudhry, S.R.; Ahmed-Zaid, S.; Demerdash, N.A.
1995-03-01
This first of two companion papers centers on applying a coupled finite-element/state-space technique to the determination of self and mutual winding inductances of a 733-MVA turbogenerator and computing its open-circuit characteristic, in the natural ABC frame of reference. In this method, the apparent self anti-mutual inductance profiles of the armature and field windings, expressed as functions of rotor position angle, are computed from a series of magnetic field solutions performed at uniformly-distributed samples of rotor positions covering the entire 360{degree} electrical cycle, using the energy perturbation method. These inductances, which are obtained at no-load for three different excitation levels, include the full effect of space harmonics introduced by the magnetic circuit geometry, winding layouts and magnetic circuit saturation. The ABC-frame/finite-element computed open-circuit characteristic is in excellent agreement with the test results. This computed no-load set of parameters forms the initial data for simulation of the full-load performance given in the companion paper, including the full impact of space harmonics and saturation on the flux linkage, current and voltage waveforms, and other performance parameters.
A non-linear constrained optimization technique for the mimetic finite difference method
Manzini, Gianmarco; Svyatskiy, Daniil; Bertolazzi, Enrico; Frego, Marco
2014-09-30
This is a strategy for the construction of monotone schemes in the framework of the mimetic finite difference method for the approximation of diffusion problems on unstructured polygonal and polyhedral meshes.
APPLICATION OF A FINITE-DIFFERENCE TECHNIQUE TO THE HUMAN RADIOFREQUENCY DOSIMETRY PROBLEM
A powerful finite difference numerical technique has been applied to the human radiofrequency dosimetry problem. The method possesses inherent advantages over the method of moments approach in that its implementation requires much less computer memory. Consequently, it has the ca...
Techniques for correcting approximate finite difference solutions. [applied to transonic flow
NASA Technical Reports Server (NTRS)
Nixon, D.
1979-01-01
A method of correcting finite-difference solutions for the effect of truncation error or the use of an approximate basic equation is presented. Applications to transonic flow problems are described and examples given.
Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.
Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue
2015-01-01
In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947
Finite-difference scheme for the numerical solution of the Schroedinger equation
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.; Ramadhani, Issa
1992-01-01
A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.
NASA Astrophysics Data System (ADS)
Lisitsa, Vadim; Tcheverda, Vladimir; Botter, Charlotte
2016-04-01
We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. In this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.
Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources
Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue
2015-01-01
In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.
1989-01-01
A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.
Zeta-function regularization approach to finite temperature effects in Kaluza-Klein space-times
Bytsenko, A.A. ); Vanzo, L.; Zerbini, S. )
1992-09-21
In the framework of heat-kernel approach to zeta-function regularization, in this paper the one-loop effective potential at finite temperature for scalar and spinor fields on Kaluza-Klein space-time of the form M[sup p] [times] M[sub c][sup n], where M[sup p] is p-dimensional Minkowski space-time is evaluated. In particular, when the compact manifold is M[sub c][sup n] = H[sup n]/[Gamma], the Selberg tracer formula associated with discrete torsion-free group [Gamma] of the n-dimensional Lobachevsky space H[sup n] is used. An explicit representation for the thermodynamic potential valid for arbitrary temperature is found. As a result a complete high temperature expansion is presented and the roles of zero modes and topological contributions is discussed.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A 1-D implementation for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique.
Exact finite difference schemes for the non-linear unidirectional wave equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1985-01-01
Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.
Choas and instabilities in finite difference approximations to nonlinear differential equations
Cloutman, L. D., LLNL
1998-07-01
The numerical solution of time-dependent ordinary and partial differential equations by finite difference techniques is a common task in computational physics and engineering The rate equations for chemical kinetics in combustion modeling are an important example. They not only are nonlinear, but they tend to be stiff, which makes their solution a challenge for transient problems. We show that one must be very careful how such equations are solved In addition to the danger of large time-marching errors, there can be unphysical chaotic solutions that remain numerically stable for a range of time steps that depends on the particular finite difference method used We point out that the solutions of the finite difference equations converge to those of the differential equations only in the limit as the time step approaches zero for stable and consistent finite difference approximations The chaotic behavior observed for finite time steps in some nonlinear difference equations is unrelated to solutions of the differential equations, but is connected with the onset of numerical instabilities of the finite difference equations This behavior suggests that the use of the theory of chaos in nonlinear iterated maps may be useful in stability anlaysis of finite difference approximations to nonlinear differential equations, providing more stringent time step limits than the formal linear stability analysis that tests only for unbounded solutions This observation implies that apparently stable numerical solutions of nonlinear differential equations by finite difference techniques may in fact be contaminated (if not dominated) by nonphysical chaotic parasitic solutions that degrade the accuracy of the numerical solution We demonstrate this phenomenon with some solutions of the logistic equation and a simple two-dimensional computational fluid dynamics example
Accurate 3-D finite difference computation of traveltimes in strongly heterogeneous media
NASA Astrophysics Data System (ADS)
Noble, M.; Gesret, A.; Belayouni, N.
2014-12-01
Seismic traveltimes and their spatial derivatives are the basis of many imaging methods such as pre-stack depth migration and tomography. A common approach to compute these quantities is to solve the eikonal equation with a finite-difference scheme. If many recently published algorithms for resolving the eikonal equation do now yield fairly accurate traveltimes for most applications, the spatial derivatives of traveltimes remain very approximate. To address this accuracy issue, we develop a new hybrid eikonal solver that combines a spherical approximation when close to the source and a plane wave approximation when far away. This algorithm reproduces properly the spherical behaviour of wave fronts in the vicinity of the source. We implement a combination of 16 local operators that enables us to handle velocity models with sharp vertical and horizontal velocity contrasts. We associate to these local operators a global fast sweeping method to take into account all possible directions of wave propagation. Our formulation allows us to introduce a variable grid spacing in all three directions of space. We demonstrate the efficiency of this algorithm in terms of computational time and the gain in accuracy of the computed traveltimes and their derivatives on several numerical examples.
NASA Astrophysics Data System (ADS)
Nikkar, Samira; Nordström, Jan
2015-06-01
A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered. By applying the energy method, well-posed boundary conditions for the continuous problem are derived. Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable conservative finite difference scheme. We show how to construct a time-dependent SAT formulation that automatically imposes boundary conditions, when and where they are required. We also prove that a uniform flow field is preserved, i.e. the Numerical Geometric Conservation Law (NGCL) holds automatically by using SBP-SAT in time and space. The developed technique is illustrated by considering an application using the linearized Euler equations: the sound generated by moving boundaries. Numerical calculations corroborate the stability and accuracy of the new fully discrete approximations.
Finite-difference methods for solving loaded parabolic equations
NASA Astrophysics Data System (ADS)
Abdullayev, V. M.; Aida-zade, K. R.
2016-01-01
Loaded partial differential equations are solved numerically. For illustrative purposes, a boundary value problem for a parabolic equation with various point loads is considered. By applying difference approximations, the problems are reduced to systems of algebraic equations of special structure, which are solved using a parametric representation involving solutions of auxiliary linear systems with tridiagonal matrices. Numerical results are presented and analyzed.
Exploring the Effectiveness of Different Approaches to Teaching Finite Mathematics
ERIC Educational Resources Information Center
Smeal, Mary; Walker, Sandra; Carter, Jamye; Simmons-Johnson, Carolyn; Balam, Esenc
2013-01-01
Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…
Viscous flow simulations in VTOL aerodynamics. [finite difference technique
NASA Technical Reports Server (NTRS)
Bower, W. W.
1978-01-01
The critical issues in viscous flow simulations, such as boundary-layer separation, entrainment, turbulence modeling, and compressibility, are discussed with regard to the ground effects problem for vertical-takeoff-and-landing (VTOL) aircraft. A simulation of the two-dimensional incompressible lift jet in ground proximity is based on solution of the Reynolds-averaged Navier-Stokes equations and a turbulence-model equation which are written in stream function-vorticity form and are solved using Hoffman's augmented-central-difference algorithm. The resulting equations and their shortcomings are discussed when the technique is extended to two-dimensional compressible and three-dimensional incompressible flows.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.
1981-01-01
Sound propagation without flow in a rectangular duct with a converging-diverging area variation was studied experimentally and theoretically. The area variation was of sufficient magnitude to produce large reflections and induce modal scattering. The rms (root-mean-squared) pressure and phase angle on both the flat and curved surface were measured and tabulated. The steady state finite element theory and the transient finite difference theory are in good agreement with the data. It is concluded that numerical finite difference and finite element theories appear ideally suited for handling duct propagation problems which encounter large area variations.
Finite Formulation for Modeling Guided Wave Structures Embedded in a Lossy Half-Space
NASA Astrophysics Data System (ADS)
Heshmatzadeh, Maryam; Bridges, Greg E.
2010-04-01
A Finite Formulation technique, the Cell Method, is applied to a transmission line embedded in a complex medium. Cell Method is a Finite Formulation numerical technique that uses a primal-dual cell complex and global (integral) variables instead of field variables (densities). A new time-harmonic finite formulation using a non-orthogonal dual mesh is presented that is based on choosing incenters of primal triangles as an alternative to barycentric dual points. In the incentric formulation, diagonal constitutive matrices are obtained and an eigenvalue problem is solved in the first step (zero-order approximation). A minimization procedure is then utilized to efficiently improve the accuracy of the zero-order solution. In this paper the effect of the non-perfectly conducting earth on the propagation constant is investigated as the location of a bare (or insulated) conductor passes through the interface of a lossy half space. It is observed that the propagation constant depends on the burial depth when it is less than the skin depth in the earth. It is shown that analytical (thin wire-based) approximations for the above-ground and buried cases fail when the conductor is close to or partially embedded in the interface.
Wave force on double cylindrical piles: a comparison between exact and finite difference solutions
NASA Astrophysics Data System (ADS)
Ali, Lotfollahi-Yaghin Mohammad; Mehdi, Moosavi Sayyid; Amin, Lotfollahi-Yaghin
2011-03-01
The wave force exerted on vertical piles of offshore structures is the main criterion in designing them. In structures with more than one large pile, the influence of piles on each other is one of the most important issues being concerned in past researches. An efficient method for determining the interaction of piles is introduced in present research. First the wave force is calculated by the exact method using the diffraction theory, then in the finite difference numerical method the force is calculated by adding the velocity potentials of each pile and integration of pressure on their surface. The results showed that the ratio of the wave force on each of the double piles to a single pile has a damped oscillation around unity in which the amplitude of oscillation decreases with the increase in the spacing parameter. Also different wave incident directions and diffraction parameters were used and the results showed that the numerical solution has acceptable accuracy when the diffraction parameter is larger than unity.
NASA Astrophysics Data System (ADS)
Česenek, Jan
2016-03-01
In this article we deal with numerical simulation of the non-stationary compressible turbulent flow. Compressible turbulent flow is described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k-omega turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.
Analytic State Space Model for an Unsteady Finite-Span Wing
NASA Astrophysics Data System (ADS)
Izraelevitz, Jacob; Zhu, Qiang; Triantafyllou, Michael
2015-11-01
Real-time control of unsteady flows, such as force control in flapping wings, requires simple wake models that easily translate into robust control designs. We analytically derive a state-space model for the unsteady trailing vortex system behind a finite aspect-ratio flapping wing. Contrary to prior models, the downwash and lift distributions over the span can be arbitrary, including tip effects. The wake vorticity is assumed to be a fully unsteady distribution, with the exception of quasi-steady (no rollup) geometry. Each discretization along the span has one to four states to represent the local unsteady wake-induced downwash, lift, and circulation. The model supports independently time-varying velocity, heave, and twist along the span. We validate this state-space model through comparison with existing analytic solutions for elliptic wings and an unsteady inviscid panel method.
Mixed finite-difference scheme for free vibration analysis of noncircular cylinders
NASA Technical Reports Server (NTRS)
Noor, A. K.; Stephens, W. B.
1973-01-01
A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.
Optimal search strategies of space-time coupled random walkers with finite lifetimes.
Campos, D; Abad, E; Méndez, V; Yuste, S B; Lindenberg, K
2015-05-01
We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers." A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate ω(m). While still alive, the creeper has a finite mean frequency ω of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an ω(m)-dependent optimal frequency ω=ω(opt) that maximizes the probability of eventual target detection. We work primarily in one-dimensional (d=1) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in d=2 domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the d=1 case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time. PMID:26066127
Optimal search strategies of space-time coupled random walkers with finite lifetimes
NASA Astrophysics Data System (ADS)
Campos, D.; Abad, E.; Méndez, V.; Yuste, S. B.; Lindenberg, K.
2015-05-01
We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers." A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate ωm. While still alive, the creeper has a finite mean frequency ω of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an ωm-dependent optimal frequency ω =ωopt that maximizes the probability of eventual target detection. We work primarily in one-dimensional (d =1 ) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in d =2 domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the d =1 case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.
NASA Technical Reports Server (NTRS)
Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)
1994-01-01
In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.
NASA Astrophysics Data System (ADS)
Reitman, L.; Wolfshtein, M.; Adler, D.
1982-11-01
A finite difference method is developed for solving the non-viscous formulation of a three-dimensional compressible flow problem for turbomachinery impellers. The numerical results and the time efficiency of this method are compared to that provided by a finite element method for this problem. The finite difference method utilizes a numerical, curvilinear, and non-orthogonal coordinate transformation and the ADI scheme. The finite difference method is utilized to solve a test problem of a centrifugal compressor impeller. It is shown that the finite difference method produces results in good agreement with the experimentally determined flow fields and is as accurate as the finite element technique. However, the finite difference method only requires about half the time in order to obtain the solution for this problem as that required by the finite element method.
Use of the finite-difference time-domain method in electromagnetic dosimetry
Sullivan, D.M.
1987-01-01
Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, the MoM requires computer storage on the order of (3N)/sup 2/, and computation time on the order of (3N)/sup 3/ where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering from metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This dissertation describes the FDTD method and evaluates it by comparing its results with analytic solutions in 2 and 3 dimensions. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. The construction of a data base to provide detailed, inhomogeneous man models for use with the FDTD method is described. Using this construction method, a model of 40,000 1.31 cm. cells is developed for use at 350 MHz, and another model consisting of 5000 2.62 cm. cells is developed for use at 100 MHz. To add more realism to the problem, a ground plane is added to the FDTD software. The needed changes to the software are described, along with a test which confirms its accuracy. Using the CRAY II supercomputer, SAR distributions in human models are calculated using incident frequencies of 100 MHz and 350 MHz for three different cases: (1) A homogeneous man model in free space, (2) an inhomogeneous man model in free space, and (3) an inhomogeneous man model standing on a ground plane.
Space-time discontinuous Galerkin finite element method for two-fluid flows
NASA Astrophysics Data System (ADS)
Sollie, W. E. H.; Bokhove, O.; van der Vegt, J. J. W.
2011-02-01
A novel numerical method for two-fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.
Kuramoto model with uniformly spaced frequencies: Finite-N asymptotics of the locking threshold.
Ottino-Löffler, Bertrand; Strogatz, Steven H
2016-06-01
We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite N, the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite N have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when N≫1. The leading correction to the infinite-N result scales like either N^{-3/2} or N^{-1}, depending on whether the frequencies are evenly spaced according to a midpoint rule or an end-point rule. These scaling laws agree with numerical results obtained by Pazó [D. Pazó, Phys. Rev. E 72, 046211 (2005)PLEEE81539-375510.1103/PhysRevE.72.046211]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics. PMID:27415267
Kuramoto model with uniformly spaced frequencies: Finite-N asymptotics of the locking threshold
NASA Astrophysics Data System (ADS)
Ottino-Löffler, Bertrand; Strogatz, Steven H.
2016-06-01
We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, N , is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case, stable phase-locked solutions are known to exist if and only if the frequency interval is narrower than a certain critical width, called the locking threshold. For infinite N , the exact value of the locking threshold was calculated 30 years ago; however, the leading corrections to it for finite N have remained unsolved analytically. Here we derive an asymptotic formula for the locking threshold when N ≫1 . The leading correction to the infinite-N result scales like either N-3 /2 or N-1, depending on whether the frequencies are evenly spaced according to a midpoint rule or an end-point rule. These scaling laws agree with numerical results obtained by Pazó [D. Pazó, Phys. Rev. E 72, 046211 (2005), 10.1103/PhysRevE.72.046211]. Moreover, our analysis yields the exact prefactors in the scaling laws, which also match the numerics.
A finite element approach for large motion dynamic analysis of multibody structures in space
NASA Technical Reports Server (NTRS)
Chang, Che-Wei
1989-01-01
A three-dimensional finite element formulation for modeling the transient dynamics of constrained multibody space sructures with truss-like configurations is presented. Convected coordinate systems are used to define rigid-body motion of individual elements in the system. These systems are located at one end of each element and are oriented such that one axis passes through the other end of the element. Deformation of each element, relative to its convected coordinate system, is defined by cubic flexural shape functions as used in finite element methods of structural analysis. The formulation is oriented toward joint dominated structures and places the generalized coordinates at the joint. A transformation matrix is derived to integrate joint degree-of-freedom into the equations of motion of the element. Based on the derivation, a general-purpose code LATDYN (Large Angle Transient DYNamics) was developed. Two examples are presented to illustrate the application of the code. For the spin-up of a flexible beam, results are compared with existing solutions available in the literature. For the deployment of one bay of a deployable space truss (the Minimast), results are verified by the geometric knowledge of the system and converged solution of a successively refined model.
Reduction of scattering to an invariant finite displacement in an ambient space-time
Segal, I. E.
1984-01-01
The scattering transformation S for a wave equation in Minkowski space M0 is reducible (rigorously in the classical case, necessarily partially heuristically in the nonlinear quantum case) to the action of a distinguished finite transformation ζ in the ambient universal cosmos M. M0 is invariantly imbedded in M, relative to any given point of observation, and the space-like surfaces x0 = s in M0 converge as s → ±∞ to finite light cones C± in M. The generator ζ of the infinite cyclic center of the connected group of all casuality-preserving transformations in M (isomorphic to SU(2,2)/Z2) carries C- into C+ and acts on solutions of relativistic wave equations as S, in an invariant bundle formulation. The establishment of S is simplified, the symmetry and regularity properties of S are enhanced, the scope of the scattering concept is extended to important equations such as those of Yang-Mills (lacking an invariant separation into free and interaction components), and the treatment of bound and scattering states is more unified. PMID:16593531
SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.
Wan, Xiaohai; Li, Zhilin
2012-06-01
Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346
Improving sub-grid scale accuracy of boundary features in regional finite-difference models
Panday, Sorab; Langevin, Christian D.
2012-01-01
As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.
NASA Technical Reports Server (NTRS)
Lee, L. C.
1976-01-01
The cross correlation of the intensity fluctuations between different frequencies and finite bandwidth effects on the intensity correlations based on the Markov approximation were calculated. Results may be applied to quite general turbulence spectra for an extended turbulent medium. Calculations of the cross-correlation function and of finite bandwidth effects are explicitly carried out for both Gaussian and Kolmogorov turbulence spectra. The increases of the correlation scale of intensity fluctuations are different for these two spectra and the difference can be used to determine whether the interstellar turbulent medium has a Gaussian or a Kolmogorov spectrum.
NASA Astrophysics Data System (ADS)
Zhang, Rui; Wen, Lihua; Naboulsi, Sam; Eason, Thomas; Vasudevan, Vijay K.; Qian, Dong
2016-05-01
A multiscale space-time finite element method based on time-discontinuous Galerkin and enrichment approach is presented in this work with a focus on improving the computational efficiencies for high cycle fatigue simulations. While the robustness of the TDG-based space-time method has been extensively demonstrated, a critical barrier for the extensive application is the large computational cost due to the additional temporal dimension and enrichment that are introduced. The present implementation focuses on two aspects: firstly, a preconditioned iterative solver is developed along with techniques for optimizing the matrix storage and operations. Secondly, parallel algorithms based on multi-core graphics processing unit are established to accelerate the progressive damage model implementation. It is shown that the computing time and memory from the accelerated space-time implementation scale with the number of degree of freedom N through {˜ }{O}(N^{1.6}) and {˜ }{O}(N) , respectively. Finally, we demonstrate the accelerated space-time FEM simulation through benchmark problems.
NASA Astrophysics Data System (ADS)
Zhang, Rui; Wen, Lihua; Naboulsi, Sam; Eason, Thomas; Vasudevan, Vijay K.; Qian, Dong
2016-08-01
A multiscale space-time finite element method based on time-discontinuous Galerkin and enrichment approach is presented in this work with a focus on improving the computational efficiencies for high cycle fatigue simulations. While the robustness of the TDG-based space-time method has been extensively demonstrated, a critical barrier for the extensive application is the large computational cost due to the additional temporal dimension and enrichment that are introduced. The present implementation focuses on two aspects: firstly, a preconditioned iterative solver is developed along with techniques for optimizing the matrix storage and operations. Secondly, parallel algorithms based on multi-core graphics processing unit are established to accelerate the progressive damage model implementation. It is shown that the computing time and memory from the accelerated space-time implementation scale with the number of degree of freedom N through ˜ O(N^{1.6}) and ˜ O(N), respectively. Finally, we demonstrate the accelerated space-time FEM simulation through benchmark problems.
Prepeliță, Sebastian; Geronazzo, Michele; Avanzini, Federico; Savioja, Lauri
2016-05-01
The scattering around the human pinna that is captured by the Head-Related Transfer Functions (HRTFs) is a complex problem that creates uncertainties in both acoustical measurements and simulations. Within the simulation framework of Finite Difference Time Domain (FDTD) with axis-aligned staircase boundaries resulting from a voxelization process, the voxelization-based uncertainty propagating in the HRTF-captured sound field is quantified for one solid and two surface voxelization algorithms. Simulated results utilizing a laser-scanned mesh of Knowles Electronics Manikin for Acoustic Research (KEMAR) show that in the context of complex geometries with local topology comparable to grid spacing such as the human pinna, the voxelization-related uncertainties in simulations emerge at lower frequencies than the generally used accuracy bandwidths. Numerical simulations show that the voxelization process induces both random error and algorithm-dependent bias in the simulated HRTF spectral features. Frequencies fr below which the random error is bounded by various dB thresholds are estimated and predicted. Particular shortcomings of the used voxelization algorithms are identified and the influence of the surface impedance on the induced errors is studied. Simulations are also validated against measurements. PMID:27250145
NASA Astrophysics Data System (ADS)
Ramadan, Omar
2014-12-01
Systematic split-step finite difference time domain (SS-FDTD) formulations, based on the general Lie-Trotter-Suzuki product formula, are presented for solving the time-dependent Maxwell equations in double-dispersive electromagnetic materials. The proposed formulations provide a unified tool for constructing a family of unconditionally stable algorithms such as the first order split-step FDTD (SS1-FDTD), the second order split-step FDTD (SS2-FDTD), and the second order alternating direction implicit FDTD (ADI-FDTD) schemes. The theoretical stability of the formulations is included and it has been demonstrated that the formulations are unconditionally stable by construction. Furthermore, the dispersion relation of the formulations is derived and it has been found that the proposed formulations are best suited for those applications where a high space resolution is needed. Two-dimensional (2-D) and 3-D numerical examples are included and it has been observed that the SS1-FDTD scheme is computationally more efficient than the ADI-FDTD counterpart, while maintaining approximately the same numerical accuracy. Moreover, the SS2-FDTD scheme allows using larger time step than the SS1-FDTD or ADI-FDTD and therefore necessitates less CPU time, while giving approximately the same numerical accuracy.
NASA Astrophysics Data System (ADS)
Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M.
2016-09-01
In this paper we construct an energy stable finite difference scheme for the amplitude expansion equations for the two-dimensional phase field crystal (PFC) model. The equations are formulated in a periodic hexagonal domain with respect to the reciprocal lattice vectors to achieve a provably unconditionally energy stable and solvable scheme. To our knowledge, this is the first such energy stable scheme for the PFC amplitude equations. The convexity of each part in the amplitude equations is analyzed, in both the semi-discrete and fully-discrete cases. Energy stability is based on a careful convexity analysis for the energy (in both the spatially continuous and discrete cases). As a result, unique solvability and unconditional energy stability are available for the resulting scheme. Moreover, we show that the scheme is point-wise stable for any time and space step sizes. An efficient multigrid solver is devised to solve the scheme, and a few numerical experiments are presented, including grain rotation and shrinkage and grain growth studies, as examples of the strength and robustness of the proposed scheme and solver.
Finite-difference time-domain studies of the optical properties of nanoshell dimers.
Oubre, C; Nordlander, P
2005-05-26
The optical properties of metallic nanoshell dimers are investigated using the finite difference time domain (FDTD) method. We discuss issues of numerical convergence specific for the dimer system. We present results for both homodimers and heterodimers. The results show that retardation effects must be taken into account for an accurate description of realistic size nanoparticle dimers. The optical properties of the nanoshell dimer are found to be strongly polarization dependent. Maximal coupling between the nanoshells in a dimer occurs when the electric field of the incident pulse is aligned parallel to the dimer axis. The wavelengths of the peaks in the extinction cross section of the dimer are shown to vary by more than 100 nm, depending on the incident electric field polarization. The calculations show that electric field enhancements in the dimer junctions depend strongly on dimer separation. The maximum field enhancements occur in the dimer junction and at the expense of a reduced electric field enhancement in other regions of space. We investigate the usefulness of nanoshell dimers substrates for SERS by integrating the fourth power of the electric field enhancements around the surfaces of the nanoparticles as a function of dimer separation and wavelength. The SERS efficiency is shown to depend strongly on dimer separation but much weaker than the fourth power of the maximum electric field enhancement at a particular point. The SERS efficiency is also found to depend strongly on the wavelength of the incident light. Maximum SERS efficiency occurs for resonant excitation of the dimer plasmons. PMID:16852215
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
ERIC Educational Resources Information Center
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene
Brinkman, D.; Heitzinger, C.; Markowich, P.A.
2014-01-15
We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.
Effects of finite volume on the KL – KS mass difference
Christ, N. H.; Feng, X.; Martinelli, G.; Sachrajda, C. T.
2015-06-24
Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the KLmore » – KS mass difference ΔMK and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less
Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces
NASA Technical Reports Server (NTRS)
Hou, Thomas Y.; Wu, Xiao-Hui; Chen, Shiyi; Zhou, Ye
1998-01-01
The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.
NASA Astrophysics Data System (ADS)
Dimitrov, Yuri M.; Vulkov, Lubin G.
2015-11-01
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed.
Fast solvers for finite difference approximations for the Stokes and Navier-Stokes equations
Shin, D.
1992-01-01
The authors consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The pressure equation method presented here for the first time, apparently, and the method, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes and incompressible Navier-Stokes at low Reynolds number. The inf-sup conditions resulting from three finite difference approximations of the Stokes equations are proven. These conditions are used to prove that the Schur complement Q[sub h] of the linear system generated by each of these approximations is bounded uniformly away from zero. For the pressure equation method, this guarantees that the conjugate gradient method applied to Q[sub h] converges in a finite number of iterations which is independent of mesh size. The fact that Q[sub h] is bounded below is used to prove convergence estimates for the solutions generated by these finite difference approximations. One of the estimates is for a staggered grid and the estimate of the scheme shows that both the pressure and the velocity parts of the solution are second-order accurate. Iterative methods are compared by the use of the regularized central differencing introduced by Strikwerda. Several finite difference approximations of the Stokes equations by the SOR method are compared and the excellence of the approximations by the regularized central differencing over the other finite difference approximation is mentioned. This difference gives rise to a linear equation with a matrix which is slightly non-symmetric. The convergence of the typical steepest descent method and conjugate gradient method, which is almost as same as the typical conjugate gradient method, applied to slightly non-symmetric positive definite matrices are proven.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.
1991-01-01
Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.
Srivastava, Vineet K.; Awasthi, Mukesh K.; Singh, Sarita
2013-12-15
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
NASA Astrophysics Data System (ADS)
Srivastava, Vineet K.; Awasthi, Mukesh K.; Singh, Sarita
2013-12-01
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers' equation on the uniform grid points. As the Burgers' equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers' equation.
Test of two methods for faulting on finite-difference calculations
Andrews, D.J.
1999-01-01
Tests of two fault boundary conditions show that each converges with second order accuracy as the finite-difference grid is refined. The first method uses split nodes so that there are disjoint grids that interact via surface traction. The 3D version described here is a generalization of a method I have used extensively in 2D; it is as accurate as the 2D version. The second method represents fault slip as inelastic strain in a fault zone. Offset of stress from its elastic value is seismic moment density. Implementation of this method is quite simple in a finite-difference scheme using velocity and stress as dependent variables.
Finite difference methods for transient signal propagation in stratified dispersive media
NASA Technical Reports Server (NTRS)
Lam, D. H.
1975-01-01
Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
A guide to differences between stochastic point-source and stochastic finite-fault simulations
Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.
2009-01-01
Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control
Ezzinbi, Khalil; Ndambomve, Patrice
2016-01-01
In this work, we consider the control system governed by some partial functional integrodifferential equations with finite delay in Banach spaces. We assume that the undelayed part admits a resolvent operator in the sense of Grimmer. Firstly, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of partial functional integrodifferential infinite dimensional control systems. Secondly, it is proved that, under generally mild conditions of cost functional, the associated Lagrange problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies. Our results extend and complement many other important results in the literature. Finally, a concrete example of application is given to illustrate the effectiveness of our main results. PMID:27540497
NASA Astrophysics Data System (ADS)
Darrall, Bradley T.
For the first time true variational principles are formulated for the analysis of the continuum problems of heat diffusion, dynamic thermoelasticity, poroelasticity, and time-dependent quantum mechanics. This is accomplished by considering the stationarity of a mixed convolved action, which can be seen as a modern counterpart to the original actions posed in Hamilton's principle and its many extensions. By including fractional derivatives, convolution integrals, and mixed variables into the definition of the action these new variational principles overcome the shortcomings of the many other variational methods based on Hamilton's principle, namely the inability to include dissipation in a consistent manner and the unjustified need to constrain variations on the primary unknowns of a system at the end of the time interval. These new variational principles then provide ideal weak forms from which novel time-space finite element methods having certain attractive properties are formulated.
Random finite set multi-target trackers: stochastic geometry for space situational awareness
NASA Astrophysics Data System (ADS)
Vo, Ba-Ngu; Vo, Ba-Tuong
2015-05-01
This paper describes the recent development in the random finite set RFS paradigm in multi-target tracking. Over the last decade the Probability Hypothesis Density filter has become synonymous with the RFS approach. As result the PHD filter is often wrongly used as a performance benchmark for the RFS approach. Since there is a suite of RFS-based multi-target tracking algorithms, benchmarking tracking performance of the RFS approach by using the PHD filter, the cheapest of these, is misleading. Such benchmarking should be performed with more sophisticated RFS algorithms. In this paper we outline the high-performance RFS-based multi-target trackers such that the Generalized Labled Multi-Bernoulli filter, and a number of efficient approximations and discuss extensions and applications of these filters. Applications to space situational awareness are discussed.
Harmonic finite-element thermoelastic analysis of space frames and trusses
Givoli, D.; Rand, O. )
1993-09-01
A numerical procedure is devised for the thermoelastic analysis of three-dimensional frame- or truss-type space structures exposed to solar radiation. Thin-walled frame or truss members with cross sections of arbitrary shape are considered. Tension-compression, bending, shear, and torsional effects due to the temperature distribution induced by the solar radiation are all taken into account. The procedure proposed involves finite element discretization in the axial direction and a harmonic analysts in the circumferential direction of each member. This procedure is an extension of the one employed previously to obtain the temperature field in trusses. A multibay frame structure serves as a model to demonstrate the performance of the proposed method. The temperature, displacement, and stress fields in the frame are found in various cases. 23 refs.
DAO's Finite-volume/Physical-space Data Assimilation System: Stratospheric Applications
NASA Technical Reports Server (NTRS)
daSilva, Arlindo; Lin, S.-J.; Einaudi, Franco (Technical Monitor)
2000-01-01
In this talk we describe the next-generation data assimilation system being developed at NASA's Data Assimilation Office (DAO), with emphasis on the applications to stratospheric forecasts and stratospheric constituent transport. This data assimilation system includes the General Circulation Model jointly developed by the DAO and the Climate and Global Dynamics Division (CGDD) at NCAR. This model is based on the finite-volume dynamical core) developed at DAO with physical parameterizations from the NCAR Climate Community Model. The Physical-space Statistical Analysis System (PSAS) is used to combine a first guess from the NASA-NCAR GCM with observational data to provide an updated estimate of the state of the atmosphere. Case studies for the (northern) Winter of 2000 will be discussed.
A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES
A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...
Finite-difference, spectral and Galerkin methods for time-dependent problems
NASA Technical Reports Server (NTRS)
Tadmor, E.
1983-01-01
Finite difference, spectral and Galerkin methods for the approximate solution of time dependent problems are surveyed. A unified discussion on their accuracy, stability and convergence is given. In particular, the dilemma of high accuracy versus stability is studied in some detail.
High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1999-01-01
Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.
Finite difference micromagnetic simulation with self-consistent currents and smooth surfaces
Cerjan, C; Gibbons, M R; Hewett, D W; Parker, G
1999-05-27
A micromagnetic algorithm has been developed using the finite difference method (FDM). Elliptic field equations are solved on the mesh using the efficient Dynamic Alternating Direction Implicit method. Smooth surfaces have been included in the FDM formulation so structures of irregular shape can be modeled. The current distribution and temperature of devices are also calculated. Keywords: Micromagnetic simulation, Magnetic dots, Read heads, Thermal Effects
FWAVE V1.0 a framework for finite difference wave equation modeling
2002-07-01
FWAVE provides a computation framework for the rapid prototyping and efficient use of finite difference wave equation solutions. The user provides single grid Fortran solver components that are integrated using opaque handles to C++ distributed data structures. Permits the scientific researcher to make of clusters and parallel computers by concentrating only on the numerical schemes.
The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel m...
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1984-01-01
Work on the construction of finite difference models of differential equations having zero truncation errors is summarized. Both linear and nonlinear unidirectional wave equations are discussed. Results regarding the construction of zero truncation error schemes for the full wave equation and Burger's equation are also briefly reported.
A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES
A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...
NASA Astrophysics Data System (ADS)
Lin, M. C.; Nieter, C.; Stoltz, P. H.; Smithe, D. N.
2009-05-01
This work introduces a conformal finite difference time domain (CFDTD) method to accurately determine the dispersion relation of an A6 relativistic magnetron. The accuracy is measured by comparing with accurate SUPERFISH calculations based on finite element method. The results show that an accuracy of 99.4% can be achieved by using only 10,000 mesh points with Dey-Mittra algorithm. By comparison, a mesh number of 360,000 is needed to preserve 99% accuracy using conventional FDTD method. This suggests one can efficiently and accurately study the hot tests of microwave tubes using CFDTD particle-in-cell method instead of conventional FDTD one.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1981-01-01
The cutoff mode instability problem associated with a transient finite difference solution to the wave equation is explained. The steady-state impedance boundary condition is found to produce acoustic reflections during the initial transient, which cause finite instabilities in the cutoff modes. The stability problem is resolved by extending the duct length to prevent transient reflections. Numerical calculations are presented at forcing frequencies above, below, and nearly at the cutoff frequency, and exit impedance models are presented for use in the practical design of turbofan inlets.
An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs
NASA Technical Reports Server (NTRS)
Warming, Robert F.; Beam, Richard M.
1989-01-01
The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.
An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs
NASA Technical Reports Server (NTRS)
Warming, Robert F.; Beam, Richard M.
1990-01-01
The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L (sub 2) stability on a finite domain.
NASA Astrophysics Data System (ADS)
Chen, Hu; Lü, Shujuan; Chen, Wenping
2016-06-01
The numerical approximation of the distributed order time fractional reaction-diffusion equation on a semi-infinite spatial domain is discussed in this paper. A fully discrete scheme based on finite difference method in time and spectral approximation using Laguerre functions in space is proposed. The scheme is unconditionally stable and convergent with order O (τ2 + Δα2 +N (1 - m) / 2), where τ, Δα, N, and m are the time-step size, step size in distributed-order variable, polynomial degree, and regularity in the space variable of the exact solution, respectively. A pseudospectral scheme is also proposed and analyzed. Some numerical examples are presented to demonstrate the efficiency of the proposed scheme.
An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1983-01-01
An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.
Same but Different: Space, Time and Narrative
ERIC Educational Resources Information Center
Bansel, Peter
2013-01-01
In this paper, I give an account of the ways in which narratives and identities change over space and time. I give an account of a mobile and changing human subject, one who does not simply express or represent her- or himself through narrative, but is constructed and reconstructed through narrative. I draw on Paul Ricoeur's concepts of "narrative…
Modeling anisotropic flow and heat transport by using mimetic finite differences
NASA Astrophysics Data System (ADS)
Chen, Tao; Clauser, Christoph; Marquart, Gabriele; Willbrand, Karen; Büsing, Henrik
2016-08-01
Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.
Modeling LiH potential-energy curves: An approach based on integration in finite space
NASA Astrophysics Data System (ADS)
Altunata, S. N.; Field, R. W.
2003-02-01
In this paper, we introduce a finite-space integration method to shed physical insight into the interactions of a Rydberg electron with a molecular ion core, as sampled by the potential-energy curves (PECs) of various electronic states of LiH. We postulate that these interactions are dominated by two independent electron-atom processes: (1) scattering of the Rydberg electron at negative energy solely off of the lithium atomic core and (2) a transition from the lithium scattering state to the lithium valence orbital necessarily accompanied by an excitation of the hydrogen atom. It is shown that the ratio of the amplitudes for the occurrences of these two processes can be obtained by means of bounded integrations inside a small region of space where the electron-electron repulsion term in the Hamiltonian is dominant. Our theory and approximations are verified by a comparison of derived potential-energy curves with those produced by ab initio calculations as well as another empirical model that uses the Fermi approximation. It is observed that the complicated features of the PECs, which reflect the nodal structure of the Rydberg orbitals, are reproduced well within our treatment.
A priori tests of a new dynamic subgrid-scale model for finite-difference large-eddy simulations
NASA Astrophysics Data System (ADS)
Salvetti, M. V.; Banerjee, S.
1995-11-01
This work focuses on subgrid-scale (SGS) modeling for finite-difference large-eddy simulations, employing filters in physical space. When a filter in physical space is used, an overlap is allowed between the unresolved and the resolved scales. For such a filter, all the three terms in the classical decomposition of the SGS stress tensor are present: the Leonard and cross-terms, due to the overlap between scales, and the true SGS Reynolds tensor, expressing the pure effect of the small scales. A dynamic subgrid-scale stress model is proposed, for finite-difference large-eddy simulation of incompressible and compressible flows in which the Leonard and cross-parts of the SGS stress tensor are assumed to be proportional to the resolved part (the ``modified Leonard term''), which is computed explicity. The SGS Reynolds stress is modeled by the eddy-viscosity Smagorinsky model. The two unknown parameters in this model are computed dynamically, as in Germano et al. [Phys. Fluids A 3, 1790 (1991)], but using a least squares technique. The model is tested using direct numerical simulation data for fully developed turbulent incompressible flows in presence of solid boundaries and free surfaces, and for compressible homogeneous turbulence. A ``box filter'' in physical space is used. Other SGS models are also tested, viz. the dynamic model of Germano et al. (DSM), and its compressible extension by Moin et al. [Phys. Fluids A 3, 2746 (1991)], and the dynamic mixed model in Zang et al. [Phys. Fluids A 5, 3186 (1993)] (DMM) and its compressible version developed here. Results on the behavior of the different models with regard to energy exchanges and correlation with the exact SGS stresses are presented for different filter widths. In particular high correlation is found between the modified Leonard and cross-terms thus justifying the basic assumption made in the model.
NASA Astrophysics Data System (ADS)
Mejdoubi, Abdelilah; Brosseau, Christian
2006-03-01
Currently, there is a great interest in tailoring the polarization properties of composite materials with the goal of controlling the dielectric behavior. This paper reports finite-difference time-domain (FDTD) modeling of the dielectric behavior of two-dimensional (2D) lossless two-phase heterostructures. More specifically, we present extensive results of 2D FDTD computations on the quasistatic effective permittivity of a single inclusion, with arbitrarily complex geometry (regular polygons and fractals), embedded in a plane. The uniaxial perfectly matched layer-absorbing boundary condition is found adequate for truncating the boundary of the 2D space because it leads to only very small backreflections. The effectiveness of the method is demonstrated by the variety of geometries modeled, i.e., regular polygons and fractals, and permittivity contrast ratios which allows us to distinguish between effects of surface fraction and effects of morphology. Our calculations show that geometrical effects can give rise to significant modifications of the surface fraction dependence of the permittivity. The results are compared with Maxwell-Garnett (MG) and symmetric Bruggeman (SBG) formulas. As expected the effective permittivity in the situations considered here deviates from the MG and SBG results at high surface fractions and/or high permittivity ratios between the inclusion and the host medium. In addition, the results show that a two-phase composite containing a fractal-boundary inclusion, e.g., Koch's snowflake, can have a permittivity which is several tens of percent lower between the first and the fourth iteration of the structure at a fixed perimeter-to-surface ratio. This feature is consistent with the fact that as the surface fraction becomes higher, the inclusion rough boundaries dominate the overall geometry. We believe that simplified modeling such as the modeling done here can serve as a useful purpose in understanding the interplay between the structure and
NASA Astrophysics Data System (ADS)
MacKinnon, R. J.; Carey, G. F.
1988-03-01
An analysis of material interface discontinuities is developed and applied in finite difference theory to determine mathematically rigorous averaging techniques for material properties. This result is compared with other averaging techniques, particularly harmonic averaging, which is often applied in practice. We also develop a class of formulas of high accuracy for post-processing the difference formula to compute derivatives (fluxes, stresses), and conduct supporting numerical studies.
NASA Technical Reports Server (NTRS)
Chen, G.; Zheng, Q.; Coleman, M.; Weerakoon, S.
1983-01-01
This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.
1981-01-01
Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.
Marchiolli, Marcelo A.; Ruzzi, Maurizio; Galetti, Diogenes
2005-10-15
By means of a mod(N)-invariant operator basis, s-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and their properties are discussed in details. The discrete Glauber-Sudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of s-parametrized phase-space functions where, in particular, a hierarchical process among them is promptly established. In addition, a phase-space description of quantum tomography and quantum teleportation is presented and new results are obtained.
Phase space matching and finite lifetime effects for top-pair production close to threshold
Hoang, Andre H.; Reisser, Christoph J.; Ruiz-Femenia, Pedro
2010-07-01
The top-pair tt production cross section close to threshold in e{sup +}e{sup -} collisions is strongly affected by the small lifetime of the top quark. Since the cross section is defined through final states containing the top decay products, a consistent definition of the cross section depends on prescriptions of how these final states are accounted for the cross section. Experimentally, these prescriptions are implemented, for example, through cuts on kinematic quantities such as the reconstructed top quark invariant masses. As long as these cuts do not reject final states that can arise from the decay of a top and an antitop quark with a small off-shellness compatible with the nonrelativistic power counting, they can be implemented through imaginary phase space matching conditions in nonrelativistic QCD. The prescription-dependent cross section can then be determined from the optical theorem using the e{sup +}e{sup -} forward scattering amplitude. We compute the phase space matching conditions associated to cuts on the top and antitop invariant masses at next-to-next-to-leading logarithmic order and partially at next-to-next-to-next-to-leading logarithmic order in the nonrelativistic expansion accounting also for higher order QCD effects. Together with finite lifetime and electroweak effects known from previous work, we analyze their numerical impact on the tt cross section. We show that the phase space matching contributions are essential to make reliable nonrelativistic QCD predictions, particularly for energies below the peak region, where the cross section is small. We find that irreducible background contributions associated to final states that do not come from top decays are strongly suppressed and can be neglected for the theoretical predictions.
NASA Astrophysics Data System (ADS)
Ren, B. Y.; Wang, L.; Tzou, H. S.; Yue, H. H.
2010-08-01
Electrical modeling of piezoelectric structronic systems by analog circuits has the disadvantages of huge circuit structure and low precision. However, studies of electrical simulation of segmented distributed piezoelectric structronic plate systems (PSPSs) by using output voltage signals of high-speed digital circuits to evaluate the real-time dynamic displacements are scarce in the literature. Therefore, an equivalent dynamic model based on the finite difference method (FDM) is presented to simulate the actual physical model of the segmented distributed PSPS with simply supported boundary conditions. By means of the FDM, the four-ordered dynamic partial differential equations (PDEs) of the main structure/segmented distributed sensor signals/control moments of the segmented distributed actuator of the PSPS are transformed to finite difference equations. A dynamics matrix model based on the Newmark-β integration method is established. The output voltage signal characteristics of the lower modes (m <= 3, n <= 3) with different finite difference mesh dimensions and different integration time steps are analyzed by digital signal processing (DSP) circuit simulation software. The control effects of segmented distributed actuators with different effective areas are consistent with the results of the analytical model in relevant references. Therefore, the method of digital simulation for vibration analysis of segmented distributed PSPSs presented in this paper can provide a reference for further research into the electrical simulation of PSPSs.
NASA Technical Reports Server (NTRS)
Jameson, A.
1976-01-01
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
Hunt, R.J.; Anderson, M.P.; Kelson, V.A.
1998-01-01
This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.
Dynamic Rupture Simulation of Bending Faults With a Finite Difference Approach
NASA Astrophysics Data System (ADS)
Cruz-Atienza, V. M.; Virieux, J.; Operto, S.
2002-12-01
Many questions about physical parameters governing the rupture propagation of earthquakes seem to find their answers within realistic dynamic considerations. Sophisticated constitutive relations based in laboratory experiments have lead to a better understanding of rupture evolution from its very beginning to its arrest. On the other hand, large amount of field observations as well as recent numerical simulations have also demonstrated the importance, in rupture growing, of considering more reasonable geological settings (e.g., bending and step-over fault geometries; heterogeneous surrounding media). So far, despite the development of powerful numerical tools, there still exist some numerical considerations that overstep their possibilities. Authors have solved the dynamic problem by applying the boundary integral equations method (BIEM) in order to explore the influence of fault geometry. This can be possible because of the fact that only the rupture path must be discretized, reducing the impact of numerical discretization. However, the BIEM needs the analytical solution of Green functions that can only be computed for a homogeneous space. Up to date, no interaction with heterogeneous structures can be taken in to account. In contrast, finite difference (FD) approaches have been widely used. In this case, due to the specific discretization of the elastodynamic equations through the entire domain, and the azimuthal anisotropy intrinsic to differential operators, only planar faults have been considered and numerical artefacts have to be carefully checked. In this work, we have used a recently proposed four-order staggered grid finite difference scheme to model in-plane (mode II) dynamic shear fracturing propagation with any pre-established geometry. In contrast with the classical 2-D staggered grid elementary cell in which all the elastic fields are defined in different positions (except the normal stresses), the stencil used here consider the velocity and stress
NASA Astrophysics Data System (ADS)
Kharytonov, Oleksii M.; Kiforenko, Boris M.
2011-08-01
The nuclear thermal rocket (NTR) propulsion is one of the leading promising technologies for primary space propulsion for manned exploration of the solar system due to its high specific impulse capability and sufficiently high thrust-to-weight ratio. Another benefit of NTR is its possible bimodal design, when nuclear reactor is used for generation of a jet thrust in a high-thrust mode and (with an appropriate power conversion system) as a source of electric power to supply the payload and the electric engines in a low-thrust mode. The model of the NTR thrust control was developed considering high-thrust NTR as a propulsion system of limited power and exhaust velocity. For the proposed model the control of the thrust value is accomplished by the regulation of reactor thermal power and propellant mass flow rate. The problem of joint optimization of the combination of high- and low-thrust arcs and the parameters of bimodal NTR (BNTR) propulsion system is considered for the interplanetary transfers. The interplanetary trajectory of the space vehicle is formed by the high-thrust NTR burns, which define planet-centric maneuvers and by the low-thrust heliocentric arcs where the nuclear electric propulsion (NEP) is used. The high-thrust arcs are analyzed using finite-thrust approach. The motion of the corresponding dynamical system is realized in three phase spaces concerning the departure planet-centric maneuver by means of high-thrust NTR propulsion, the low-thrust NEP heliocentric maneuver and the approach high-thrust NTR planet-centric maneuver. The phase coordinates are related at the time instants of the change of the phase spaces due to the relations between the space vehicle masses. The optimal control analysis is performed using Pontryagin's maximum principle. The numerical results are analyzed for Earth-Mars "sprint" transfer. The optimal values of the parameters that define the masses of NTR and NEP subsystems have been evaluated. It is shown that the low
Projection methods for incompressible flow problems with WENO finite difference schemes
NASA Astrophysics Data System (ADS)
de Frutos, Javier; John, Volker; Novo, Julia
2016-03-01
Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.
Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells
NASA Astrophysics Data System (ADS)
Deinega, Alexei; John, Sajeev
2012-10-01
We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric (l=0) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D (x, y, z) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.
Naveau, Adrien; Renault, Patrick; Pierrisnard, Laurent
2009-06-01
This three dimensional Finite Element Analysis study investigated stress distribution and intensity in implants restored with cemented or screwed crown. Two parameters varied: interarch space and abutment height. Highest stresses occurred at the cervical area in all models. Stresses increased mainly with vertical interarch space highness, and secondarily with abutments shortness. From a mechanical point of view, bone and prosthetics components supporting cemented crowns were not as solicited as with screwed crowns. PMID:19645311
ERIC Educational Resources Information Center
Song, Hairong; Ferrer, Emilio
2009-01-01
This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…
NASA Astrophysics Data System (ADS)
de Schryver, C.; Weithoffer, S.; Wasenmüller, U.; Wehn, N.
2012-09-01
Channel coding is a standard technique in all wireless communication systems. In addition to the typically employed methods like convolutional coding, turbo coding or low density parity check (LDPC) coding, algebraic codes are used in many cases. For example, outer BCH coding is applied in the DVB-S2 standard for satellite TV broadcasting. A key operation for BCH and the related Reed-Solomon codes are multiplications in finite fields (Galois Fields), where extension fields of prime fields are used. A lot of architectures for multiplications in finite fields have been published over the last decades. This paper examines four different multiplier architectures in detail that offer the potential for very high throughputs. We investigate the implementation performance of these multipliers on FPGA technology in the context of channel coding. We study the efficiency of the multipliers with respect to area, frequency and throughput, as well as configurability and scalability. The implementation data of the fully verified circuits are provided for a Xilinx Virtex-4 device after place and route.
NASA Astrophysics Data System (ADS)
McLeod, R.; Hawkins, R. J.; Kallman, J. S.
1991-04-01
Interest has recently grown in applying microwave modeling techniques to optical circuit modeling. One of the simplest, yet most powerful, microwave simulation techniques is the finite-difference time-domain algorithm (FDTD). In this technique, the differential form of the time-domain Maxwell's equations are discretized and all derivatives are approximated as differences. Minor algebraic manipulations on the resulting equations produces a set of update equations that produce fields at a given time step from fields at the previous time step. The FDTD algorithm, then, is quite simple. Source fields are launched into the discrete grid by some means. The FDTD equations advance these fields in time. At the boundaries of the grid, special update equations called radiation conditions are applied that approximate a continuing, infinite space. Because virtually no assumptions are made in the development of the FDTD method, the algorithm is able to represent a wide-range of physical effects. Waves can propagate in any direction, multiple reflections within structures can cause resonances, multiple modes of various polarizations can be launched, each of which may generate within the device an infinite spectrum of bound and radiation modes. The ability to model these types of general physical effects is what makes the FDTD method interesting to the field of optics. In this paper, we discuss the application of the finite-difference time-domain technique to integrated optics. Animations will be shown of the simulations of a TE coupler, TM grating, and a TE integrated detector.
A Multi-CPU/GPU implementation of RBF-generated finite differences for PDEs on a Sphere
NASA Astrophysics Data System (ADS)
Bollig, E. F.; Flyer, N.; Erlebacher, G.
2011-12-01
Numerical methods leveraging Radial Basis Functions (RBFs) are on the rise in computational science. With natural extensions into higher dimensions, functionality in the face of unstructured grids, stability for large time-steps, competitive accuracy and convergence when compared to other state-of-the-art methods, it is hard to ignore these simple-to-code alternatives. RBF-generated finite differences (RBF-FD) hold a promising future in that they have the advantages of global RBFs but have the ability to be highly parallelizable on multi-core machines. They differ from classical finite differences in that the test functions used to calculate the differentiation weights are n-dimensional RBFs rather than one-dimensional polynomials. This allows for generalization to n-dimensional space on completely scattered node layouts. We present an ongoing effort to develop fast and efficient implementations of RBF-FD for the geosciences. Specifically, we introduce a multi-CPU/GPU implementation for the solution of parabolic and hyperbolic PDEs. This work targets the NSF funded Keeneland GPU cluster, which---like many of the latest HPC systems around the world---offers significantly more GPU accelerators than CPU counterparts. We will discuss parallelization strategies, algorithms and data-structures used to span computation across the heterogeneous architecture.
NASA Astrophysics Data System (ADS)
Cunha, G.; Redonnet, S.
2014-04-01
The present article aims at highlighting the strengths and weaknesses of the so-called spectral-like optimized (explicit central) finite-difference schemes, when the latter are used for numerically approximating spatial derivatives in aeroacoustics evolution problems. With that view, we first remind how differential operators can be approximated using explicit central finite-difference schemes. The possible spectral-like optimization of the latter is then discussed, the advantages and drawbacks of such an optimization being theoretically studied, before they are numerically quantified. For doing so, two popular spectral-like optimized schemes are assessed via a direct comparison against their standard counterparts, such a comparative exercise being conducted for several academic test cases. At the end, general conclusions are drawn, which allows us discussing the way spectral-like optimized schemes shall be preferred (or not) to standard ones, when it comes to simulate real-life aeroacoustics problems.
A mapped finite difference study of noise propagation in nonuniform ducts with mean flow
NASA Technical Reports Server (NTRS)
Raad, Peter E.; White, James W.
1987-01-01
The primary objective of this work is to study noise propagation in acoustically lined variable area ducts with mean fluid flow. The method of study is numerical in nature and involves a body-fitted grid mapping procedure in conjunction with a factored-implicit finite difference technique. The mean fluid flow model used is two-dimensional, inviscid, irrotational, incompressible, and nonheat conducting. Fully-coupled solutions of the linearized gasdynamic equations are obtained for both positive and negative Mach numbers as well as for hard and soft wall conditions. The factored-implicit finite difference technique used did give rise to short wavelength perturbations, but these were dampened by the introduction of higher order artificial dissipation terms into the scheme. Results compared favorably with available numerical and experimental data.
A semi-implicit finite difference model for three-dimensional tidal circulation,
Casulli, V.; Cheng, R.T.
1992-01-01
A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.
On One-Dimensional Stretching Functions for Finite-Difference Calculations
NASA Technical Reports Server (NTRS)
Vinokur, M.
1980-01-01
The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.
NASA Technical Reports Server (NTRS)
Hannah, S. R.; Palazotto, A. N.
1978-01-01
A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.
Three-dimensional finite difference time domain modeling of the Earth-ionosphere cavity resonances
NASA Astrophysics Data System (ADS)
Yang, Heng; Pasko, Victor P.
2005-02-01
Comparison of results from a three-dimensional (3-D) finite difference time domain (FDTD) model of Schumann resonances (SR) with a set of classical eigenfrequency and quality factor solutions for laterally uniform spherically symmetric Earth-ionosphere cavity and recent SR observations during solar proton events (SPEs) and X-ray bursts demonstrate the potential and applicability of the FDTD technique for studies of realistic SR problems.
Simulation of realistic rotor blade-vortex interactions using a finite-difference technique
NASA Technical Reports Server (NTRS)
Hassan, Ahmed A.; Charles, Bruce D.
1989-01-01
A numerical finite-difference code has been used to predict helicopter blade loads during realistic self-generated three-dimensional blade-vortex interactions. The velocity field is determined via a nonlinear superposition of the rotor flowfield. Data obtained from a lifting-line helicopter/rotor trim code are used to determine the instantaneous position of the interaction vortex elements with respect to the blade. Data obtained for three rotor advance ratios show a reasonable correlation with wind tunnel data.
Transport and dispersion of pollutants in surface impoundments: a finite difference model
Yeh, G.T.
1980-07-01
A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.
Finite-difference, time-domain analysis of a folded acoustic transmission line.
Jackson, Charles M
2005-03-01
Recently designed, modern versions of renais sance woodwind instruments such as the recorder and serpent use square cross sections and a folded acoustic transmission line. Conventional microwave techniques would expect that this bend would cause unwanted reflections and impedance discontinuities. This paper analyses the folded acoustic transmission line using finite-difference, time-domain techniques and shows that the discontinuity can be compensated with by the use of a manufacturable method. PMID:15857045
A staggered mesh finite difference scheme for the computation of compressible flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1992-01-01
A simple high resolution finite difference technique is presented to approximate weak solutions to hyperbolic systems of conservation laws. The method does not rely on Riemann problem solvers and is therefore easy to extend to a wide variety of problems. The overall performance (resolution and CPU requirements) is competitive, with other state-of-the-art techniques offering sharp nonoscillatory shocks and contacts. Theoretical results confirm the reliability of the approach for linear systems and nonlinear scalar equations.
NASA Technical Reports Server (NTRS)
Abramopoulos, Frank
1988-01-01
The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.
ADI Finite Difference Discretization of the Heston-Hull-White PDE
NASA Astrophysics Data System (ADS)
Haentjens, Tinne; Hout, Karel in't.
2010-09-01
This paper concerns the efficient numerical solution of the time-dependent, three-dimensional Heston-Hull-White PDE for the fair prices of European call options. The numerical solution method described in this paper consists of a finite difference discretization on non-uniform spatial grids followed by an Alternating Direction Implicit scheme for the time discretization and extends the method recently proved effective by In't Hout & Foulon (2010) for the simpler, two-dimensional Heston PDE.
Finite-difference model for 3-D flow in bays and estuaries
Smith, Peter E.; Larock, Bruce E.
1993-01-01
This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.
Finite-difference models of ordinary differential equations - Influence of denominator functions
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.; Smith, Arthur
1990-01-01
This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.
Direct Simulations of Transition and Turbulence Using High-Order Accurate Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Rai, Man Mohan
1997-01-01
In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition may prove to be impractical. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This seminar will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. In this seminar high-order-accurate finite-difference methods for the compressible and incompressible formulations of the unsteady Navier-Stokes equations and their applications to direct simulations of turbulence and transition will be presented.
Properties of finite difference models of non-linear conservative oscillators
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1988-01-01
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
NASA Technical Reports Server (NTRS)
Lansing, Faiza S.; Rascoe, Daniel L.
1993-01-01
This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.
NASA Astrophysics Data System (ADS)
Sharapudinov, I. I.
2014-02-01
The paper deals with the space L^{p(x)} consisting of classes of real measurable functions f(x) on \\lbrack 0,1 \\rbrack with finite integral \\displaystyle\\int_0^1\\vert f(x)\\vert^{p(x)}\\,dx. If 1\\le p(x)\\le \\overline p\\lt\\infty, then the space L^{p(x)} can be made into a Banach space with the norm \\displaystyle\\Vert f\\Vert _{p(\\cdot)}=\\inf\\biggl\\{\\alpha\\,{\\gt}\\,0: \\int_0^1 \\vert{f(x)/\\alpha}\\vert^{p(x)}\\,dx\\le\
Finite difference time domain analysis of microwave ferrite devices and mobile antenna systems
NASA Astrophysics Data System (ADS)
Yildirim, Bahadir Suleyman
This dissertation presents analysis and design of shielded mobile antenna systems and microwave ferrite devices using a finite-difference time-domain method. Novel shielded antenna structures suitable for cellular communications have been analyzed and designed with emphasize on reducing excessive radiated energy absorbed in user's head and hand, while keeping the antenna performance at its peak in the presence of user. These novel antennas include a magnetically shielded antenna, a dual-resonance shielded antenna and, a shorted and truncated microstrip antenna. The effect of magnetic coating on the performance of a shielded monopole antenna is studied extensively. A parametric study is performed to analyze the dual-resonance phenomenon observed in the dual-resonance shielded antenna, optimize the antenna design within the cellular communications band, and improve the antenna performance. Input impedance, near and far fields of the dual-resonance shielded antenna are calculated using the finite-difference time-domain method. Experimental validation is also presented. In addition, performance of a shorted and truncated microstrip antenna has been investigated over a wide range of substrate parameters and dimensions. Objectives of the research work also include development of a finite-difference time-domain technique to accurately model magnetically anisotropic media, including the effect of non-uniform magnetization within the finite-size ferrite material due to demagnetizing fields. A slow wave thin film isolator and a stripline disc junction circulator are analyzed. An extensive parametric study calculates wide-band frequency-dependent parameters of these devices for various device dimensions and material parameters. Finally, a ferrite-filled stripline configuration is analyzed to study the non- linear behaviour of ferrite by introducing a modified damping factor.
NASA Astrophysics Data System (ADS)
Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang
2015-10-01
For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.
Experiments with explicit filtering for LES using a finite-difference method
NASA Technical Reports Server (NTRS)
Lund, T. S.; Kaltenbach, H. J.
1995-01-01
The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture
Mimetic finite difference method for the stokes problem on polygonal meshes
Lipnikov, K; Beirao Da Veiga, L; Gyrya, V; Manzini, G
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Numerical analysis of polarization gratings using the finite-difference time-domain method
Oh, Chulwoo; Escuti, Michael J.
2007-10-15
We report the first full numerical analysis of polarization gratings (PGs), and study their most general properties and limits by using the finite-difference time-domain (FDTD) method. In this way, we avoid limiting assumptions on material properties or grating dimensions (e.g., no paraxial approximations) and provide a more complete understanding of PG diffraction behavior. We identify the fundamental delineation between diffraction regimes (thin versus thick) for anisotropic gratings and determine the conditions for {approx_equal}100% diffraction efficiency in the framework of the coupled-wave {rho} and Q parameters. Diffraction characteristics including the efficiency, spectral response, and polarization sensitivity are investigated for the two primary types of PGs with linear and circular birefringence. The angular response and finite-grating behavior (i.e., pixelation) are also examined. Comparisons with previous analytic approximations, where applicable, show good agreement.
NASA Technical Reports Server (NTRS)
Kishoni, Doron; Taasan, Shlomo
1994-01-01
Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.
NASA Astrophysics Data System (ADS)
Ranjbar-Far, M.; Absi, J.; Mariaux, G.
2012-12-01
A new finite element model is used to investigate catastrophic failures of a thermal barrier coatings system due to crack propagation along the interfaces between the ceramic top-coat, thermally grown oxide, and bond-coat layers, as well as between the lamellas structure of the ceramic layer. The thermo-mechanical model is designed to take into account a non-homogenous temperature distribution and the effects of the residual stresses generated during the coating process. Crack propagation is simulated using the contact tool "Debond" present in the ABAQUS finite element code. Simulations are performed with a geometry corresponding to similar or dissimilar amplitudes of asperity, and for different thicknesses of the oxide layer. The numerical results have shown that crack evolution depends crucially on the ratio of the loading rate caused by growth and swelling of the oxide layer and also on the interface roughness obtained during the spraying of coatings.
Application of finite difference techniques to noise propagation in jet engine ducts
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1973-01-01
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be useful in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
Application of finite difference techniques to noise propagation in jet engine ducts
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1973-01-01
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be used in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross-section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
Flux vector splitting of the inviscid equations with application to finite difference methods
NASA Technical Reports Server (NTRS)
Steger, J. L.; Warming, R. F.
1979-01-01
The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.
Harbaugh, Arlen W.
1992-01-01
The U.S. Geological Survey's Modular Ground-Water Flow Model assumes that model nodes are in the center of cells and that transmissivity is constant within a cell. Based on these assumptions, the model calculates coefficients, called conductance, that are multiplied by head difference to determine flow between cells. Although these are common assumptions in finite-difference models, other assumptions are possible. A new option to the model program reads conductance as input data rather than calculating it. This optional lows the user to calculate conductance outside of the model. The user thus has the flexibility to define conductance using any desired assumptions. For a water-table condition, horizontal conductance must change as water level varies. To handle this situation, the new option reads conductance divided by thickness (CDT) as input data. The model calculates saturated thickness and multiplies it by CDT to obtain conductance. Thus, the user is still free from the assumptions of centered nodes and constant transmissivity in cells. The model option is written in FORTRAN77 and is fully compatible with the existing model. This report documents the new model option; it includes a description of the concepts, detailed input instructions, and a listing of the code.
NASA Technical Reports Server (NTRS)
Harten, A.; Tal-Ezer, H.
1981-01-01
An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.
NASA Technical Reports Server (NTRS)
Taflove, A.; Umashankar, K. R.
1987-01-01
The formulation and recent applications of the finite-difference time-domain (FD-TD) method for the numerical modeling of electromagnetic scattering and interaction problems are considered. It is shown that improvements in FD-TD modeling concepts and software implementation often make it a preferable choice for structures which cannot be easily treated by conventional integral equations and asymptotic approaches. Recent FD-TD modeling validations in research areas including coupling to wires and wire bundles in free space and cavities, scattering from surfaces in relativistic motion, inverse scattering, and radiation condition theory, are reviewed. Finally, the advantages and disadvantages of FD-TD, and guidelines concerning when FD-TD should and should not be used in high-frequency electromagnetic modeling problems, are summarized.
Son, Sang-Kil
2011-03-01
We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schroedinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.
NASA Technical Reports Server (NTRS)
Noor, A. K.; Stephens, W. B.
1973-01-01
Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.
An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Lessard, Victor R.
1990-01-01
The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.
NASA Astrophysics Data System (ADS)
Eyuboglu, S.; Daniels, J. J.; Lee, R.; Yeh, J. T.
2006-12-01
Ground Penetrating Radar (GPR) is a non-invasive tool commonly used to characterize the physical properties of the subsurface. The translation of the physical measurements of geologic and hydrogeologic conditions is the culmination of many geophysical investigations. When numerical modeling is applied parallel to GPR data, it allows understanding of the effects of complex electromagnetic phenomena by defining and solving problems, as well as predicting the performance of radar in a complex heterogeneous environment. Finite difference time domain (FDTD) has been widely used for numerical modeling of GPR, but most of the previous algorithms are limited in their ability to model the electrical conductivity and permittivity. In this research, a highly efficient robust algorithm was developed to enhance the effectiveness of the FDTD forward modeling in surroundings characterized by an arbitrary distribution of all electrical properties in three dimensional space. In the first part of this research, two different FDTD codes which include different absorbing boundary conditions, Enquist and Majda absorbing boundary condition (ABC) and perfectly matched layer (PML), were used and compared. In the second part, the modeling algorithm was developed for a heterogeneous half-space medium to facilitate statistical modeling of complex distributions of electrical properties in the subsurface. The results produced by the simulation compared with real GPR results reveal high accuracy using the robust algorithm to optimize three dimensional FDTD forward modeling of GPR responses in heterogeneous surroundings.
Lo, F. S.; Lee, T. H.; Lu, P. S.; Ragan-Kelley, B.; Minnich, A.; Lin, M. C.; Verboncoeur, J. P.
2014-02-15
A thermionic energy converter (TEC) is a static device that converts heat directly into electricity by boiling electrons off a hot emitter surface across a small inter-electrode gap to a cooler collector surface. The main challenge in TECs is overcoming the space charge limit, which limits the current transmitted across a gap of a given voltage and width. We have verified the feasibility of studying and developing a TEC using a bounded finite-difference time-domain particle-in-cell plasma simulation code, OOPD1, developed by Plasma Theory and Simulation Group, formerly at UC Berkeley and now at Michigan State University. In this preliminary work, a TEC has been modeled kinetically using OOPD1, and the accuracy has been verified by comparing with an analytically solvable case, giving good agreement. With further improvement of the code, one will be able to quickly and cheaply analyze space charge effects, and seek designs that mitigate the space charge effect, allowing TECs to become more efficient and cost-effective.
Appelo, D; Petersson, N A
2007-12-17
The isotropic elastic wave equation governs the propagation of seismic waves caused by earthquakes and other seismic events. It also governs the propagation of waves in solid material structures and devices, such as gas pipes, wave guides, railroad rails and disc brakes. In the vast majority of wave propagation problems arising in seismology and solid mechanics there are free surfaces. These free surfaces have, in general, complicated shapes and are rarely flat. Another feature, characterizing problems arising in these areas, is the strong heterogeneity of the media, in which the problems are posed. For example, on the characteristic length scales of seismological problems, the geological structures of the earth can be considered piecewise constant, leading to models where the values of the elastic properties are also piecewise constant. Large spatial contrasts are also found in solid mechanics devices composed of different materials welded together. The presence of curved free surfaces, together with the typical strong material heterogeneity, makes the design of stable, efficient and accurate numerical methods for the elastic wave equation challenging. Today, many different classes of numerical methods are used for the simulation of elastic waves. Early on, most of the methods were based on finite difference approximations of space and time derivatives of the equations in second order differential form (displacement formulation), see for example [1, 2]. The main problem with these early discretizations were their inability to approximate free surface boundary conditions in a stable and fully explicit manner, see e.g. [10, 11, 18, 20]. The instabilities of these early methods were especially bad for problems with materials with high ratios between the P-wave (C{sub p}) and S-wave (C{sub s}) velocities. For rectangular domains, a stable and explicit discretization of the free surface boundary conditions is presented in the paper [17] by Nilsson et al. In summary
Lee, D. W.; Joo, H. G.
2013-07-01
The methods and performance of a three-dimensional S{sub n} transport code employing the Discontinuous Finite Element Method (DFEM) and the Coarse Mesh Finite Difference (CMFD) formulation are presented. The mesh generator GMSH and a post processing visualization tool Visit are combined with the code for flexible geometry processing and versatile visualization. The CMFD method for DFEM Sn applications is formulated and the performance of the CMFD acceleration of eigenvalue calculations is demonstrated for a simple set of neutron transport problems. (authors)
A modular three-dimensional finite-difference ground-water flow model
McDonald, M.G.; Harbaugh, A.W.
1984-01-01
This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts were incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilitates development of additional capabilities because new modules or packages can be added to the program without modifying the existing modules or packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow from external stresses, such as flow to wells, areal recharge, evapotranspiration, flow to drains, and flow through riverbeds, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN '66 and will run without modification on most computers which have a FORTRAN '66 compiler. It will also run, without modification, with most extended FORTRAN '77 compilers and with minor modifications on standard FORTRAN '77 compilers. Documentation presented in this report
A modular three-dimensional finite-difference ground-water flow model
McDonald, Michael G.; Harbaugh, Arlen W.
1988-01-01
This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.
A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model
McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing, (translator); Lu, Guoping
1988-01-01
This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.
He, Huimin; Liu, Sanyang; Chen, Rudong
2016-01-01
The aim of this paper is to study a finite family of H-accretive operators and prove common zero point theorems of them in Banach space. The results presented in this paper extend and improve the corresponding results of Zegeye and Shahzad (Nonlinear Anal 66:1161-1169, 2007), Liu and He (J Math Anal Appl 385:466-476, 2012) and the related results. PMID:27386385
Constructing space difference schemes which satisfy a cell entropy inequality
NASA Technical Reports Server (NTRS)
Merriam, Marshal L.
1989-01-01
A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.
Transient analysis of printed lines using finite-difference time-domain method
Ahmed, Shahid
2012-03-29
Comprehensive studies of ultra-wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full-wave 3D finite-difference time-domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_{r} = 1) and with (ϵ_{r} > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Finally, physical interpretations of the simulation results are discussed in the paper.
Computing interaural differences through finite element modeling of idealized human heads
Cai, Tingli; Rakerd, Brad; Hartmann, William M.
2015-01-01
Acoustical interaural differences were computed for a succession of idealized shapes approximating the human head-related anatomy: sphere, ellipsoid, and ellipsoid with neck and torso. Calculations were done as a function of frequency (100–2500 Hz) and for source azimuths from 10 to 90 degrees using finite element models. The computations were compared to free-field measurements made with a manikin. Compared to a spherical head, the ellipsoid produced greater large-scale variation with frequency in both interaural time differences and interaural level differences, resulting in better agreement with the measurements. Adding a torso, represented either as a large plate or as a rectangular box below the neck, further improved the agreement by adding smaller-scale frequency variation. The comparisons permitted conjectures about the relationship between details of interaural differences and gross features of the human anatomy, such as the height of the head, and length of the neck. PMID:26428792
Nonlinear Comparison of High-Order and Optimized Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Hixon, R.
1998-01-01
The effect of reducing the formal order of accuracy of a finite-difference scheme in order to optimize its high-frequency performance is investigated using the I-D nonlinear unsteady inviscid Burgers'equation. It is found that the benefits of optimization do carry over into nonlinear applications. Both explicit and compact schemes are compared to Tam and Webb's explicit 7-point Dispersion Relation Preserving scheme as well as a Spectral-like compact scheme derived following Lele's work. Results are given for the absolute and L2 errors as a function of time.
One-dimensional transient finite difference model of an operational salinity gradient solar pond
NASA Technical Reports Server (NTRS)
Hicks, Michael C.; Golding, Peter
1992-01-01
This paper describes the modeling approach used to simulate the transient behavior of a salinity gradient solar pond. A system of finite difference equations are used to generate the time dependent temperature and salinity profiles within the pond. The stability of the pond, as determined by the capacity of the resulting salinity profile to suppress thermal convection within the primary gradient region of the pond, is continually monitored and when necessary adjustments are made to the thickness of the gradient zone. Results of the model are then compared to measurements taken during two representative seasonal periods at the University of Texas at El Paso's (UTEP's) research solar pond.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
A staggered mesh finite difference scheme for the computation of hypersonic Euler flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1991-01-01
A shock capturing finite difference method for systems of hyperbolic conservation laws is presented which avoids the need to solve Riemann problems while being competitive in performance with other current methods. A staggered spatial mesh is employed, so that complicated nonlinear waves generated at cell interfaces are averaged over cell interiors at the next time level. The full method combines to form a conservative version of the modified method of characteristics. The advantages of the method are discussed, and numerical results are presented for the two-dimensional double ellipse problem.
Finite-Difference Time-Domain solution of Maxwell's equations for the dispersive ionosphere
NASA Astrophysics Data System (ADS)
Nickisch, L. J.; Franke, P. M.
1992-10-01
The Finite-Difference Time-Domain (FDTD) technique is a conceptually simple, yet powerful, method for obtaining numerical solutions to electromagnetic propagation problems. However, the application of FDTD methods to problems in ionospheric radiowave propagation is complicated by the dispersive nature of the ionospheric plasma. In the time domain, the electric displacement is the convolution of the dielectric tensor with the electric field, and thus requires information from the entire signal history. This difficulty can be avoided by returning to the dynamical equations from which the dielectric tensor is derived. By integrating these differential equations simultaneously with the Maxwell equations, temporal dispersion is fully incorporated.
Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique
NASA Technical Reports Server (NTRS)
Nordmann, R.; Weiser, P.
1989-01-01
The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.
NASA Astrophysics Data System (ADS)
Yamamoto, Kaho; Iwai, Yosuke; Uchida, Yoshiaki; Nishiyama, Norikazu
2016-08-01
We numerically analyzed the light propagation in cholesteric liquid crystalline (CLC) droplet array by the finite-difference time-domain (FDTD) method. The FDTD method successfully reproduced the experimental light path observed in the complicated photonic structure of the CLC droplet array more accurately than the analysis of CLC droplets by geometric optics with Bragg condition, and this method help us understand the polarization of the propagating light waves. The FDTD method holds great promise for the design of various photonic devices composed of curved photonic materials like CLC droplets and microcapsules.
The electromagnetic modeling of thin apertures using the finite-difference time-domain technique
NASA Technical Reports Server (NTRS)
Demarest, Kenneth R.
1987-01-01
A technique which computes transient electromagnetic responses of narrow apertures in complex conducting scatterers was implemented as an extension of previously developed Finite-Difference Time-Domain (FDTD) computer codes. Although these apertures are narrow with respect to the wavelengths contained within the power spectrum of excitation, this technique does not require significantly more computer resources to attain the increased resolution at the apertures. In the report, an analytical technique which utilizes Babinet's principle to model the apertures is developed, and an FDTD computer code which utilizes this technique is described.
NASA Technical Reports Server (NTRS)
Tadghighi, Hormoz; Hassan, Ahmed A.; Charles, Bruce
1990-01-01
The present numerical finite-difference scheme for helicopter blade-load prediction during realistic, self-generated three-dimensional blade-vortex interactions (BVI) derives the velocity field through a nonlinear superposition of the rotor flow-field yielded by the full potential rotor flow solver RFS2 for BVI, on the one hand, over the rotational vortex flow field computed with the Biot-Savart law. Despite the accurate prediction of the acoustic waveforms, peak amplitudes are found to have been persistently underpredicted. The inclusion of BVI noise source in the acoustic analysis significantly improved the perceived noise level-corrected tone prediction.
A fully nonlinear, mixed spectral and finite difference model for thermally driven, rotating flows
NASA Technical Reports Server (NTRS)
Miller, Timothy L.; Lu, Huei-Iin; Butler, Karen A.
1992-01-01
Finite difference in time and the meridional plane, in conjunction with a spectral technique in the azimuthal direction, are used to approximate the Navier-Stokes equations in a model that can simulate a variety of thermally driven rotating flows in cylindrical and spherical geometries. Axisymmetric flow, linearized waves relative to a fixed or changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully nonlinear 3D flow, can in this way be calculated. A reexamination is conducted of the steady baroclinic wave case previously treated by Williams (1971) and Quon (1976).
Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
NASA Astrophysics Data System (ADS)
Li, Changpin; Yi, Qian; Chen, An
2016-07-01
In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor-corrector scheme. The error and stability analysis are carefully investigated. At last, numerical examples are carried out to verify the theoretical analysis. Besides, the comparisons between non-uniform and uniform meshes are given, where the non-uniform meshes show the better performance when dealing with the less smooth problems.
NASA Technical Reports Server (NTRS)
Steger, J. L.
1978-01-01
Although the Navier-Stokes equations describe most flows of interest in aerodynamics, the inviscid conservation law equations may be used for small regions with viscous forces. Thus, Euler equations and several time-accurate finite difference procedures, explicit and implicit, are discussed. Although implicit techniques require more computational work, they permit larger time steps to be taken without instability. It is noted that the Jacobian matrices for Euler equations in conservation-law form have certain eigenvalue-eigenvector properties which may be used to construct conservative-form coefficient matrices. This reduces the computation time of several implicit and semiimplicit schemes. Extensions of the basic approach to other areas are suggested.
WONDY V: a one-dimensional finite-difference wave-propagation code
Kipp, M.E.; Lawrence, R.J.
1982-06-01
WONDY V solves the finite difference analogs to the Lagrangian equations of motion in one spatial dimension (planar, cylindrical, or spherical). Simulations of explosive detonation, energy deposition, plate impact, and dynamic fracture are possible, using a variety of existing material models. In addition, WONDY has proven to be a powerful tool in the evaluation of new constitutive models. A preprocessor is available to allocate storage arrays commensurate with problem size, and automatic rezoning may be employed to improve resolution. This document provides a description of the equations solved, available material models, operating instructions, and sample problems.
Ramirez-Granados, J C; Paez, G; Strojnik, M
2012-06-01
We develop a technique to analyze pulsed thermography videos in order to detect and reconstruct subsurface defects in homogeneous and layered objects. The technique is based on the analysis of the thermal response of an object to a heat pulse. This thermal response is compared to the predictions of a finite-difference model that is systematically and progressively adjusted to minimize a cost function. With this minimization process, we obtain a depth and a thickness function that allow us to determine the three-dimensional shape, size, depth, thickness, and location of internal defects. The detected defects are reliably reconstructed with graphics of easy interpretation. PMID:22695546
A finite-difference program for stresses in anisotropic, layered plates in bending
NASA Technical Reports Server (NTRS)
Salamon, N. J.
1975-01-01
The interlaminar stresses induced in a layered laminate that is bent into a cylindrical surface are studied. The laminate is modeled as a continuum, and the resulting elasticity equations are solved using the finite difference method. The report sets forth the mathematical framework, presents some preliminary results, and provides a listing and explanation of the computer program. Significant among the results are apparent symmetry relationships that will reduce the numerical size of certain problems and an interlaminar stress behavior having a sharp rise at the free edges.
NASA Technical Reports Server (NTRS)
Osher, S.
1984-01-01
The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.
NASA Technical Reports Server (NTRS)
Van Dalsem, W. R.; Steger, J. L.
1983-01-01
A new, fast, direct-inverse, finite-difference boundary-layer code has been developed and coupled with a full-potential transonic airfoil analysis code via new inviscid-viscous interaction algorithms. The resulting code has been used to calculate transonic separated flows. The results are in good agreement with Navier-Stokes calculations and experimental data. Solutions are obtained in considerably less computer time than Navier-Stokes solutions of equal resolution. Because efficient inviscid and viscous algorithms are used, it is expected this code will also compare favorably with other codes of its type as they become available.
A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals
NASA Technical Reports Server (NTRS)
Dietzen, F. J.; Nordmann, R.
1989-01-01
A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.
Ceotto, Michele; Zhuang, Yu; Hase, William L
2013-02-01
This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator. PMID:23406107
Memory cost of absorbing conditions for the finite-difference time-domain method.
Chobeau, Pierre; Savioja, Lauri
2016-07-01
Three absorbing layers are investigated using standard rectilinear finite-difference schemes. The perfectly matched layer (PML) is compared with basic lossy layers terminated by two types of absorbing boundary conditions, all simulated using equivalent memory consumption. Lossy layers present the advantage of being scalar schemes, whereas the PML relies on a staggered scheme where both velocity and pressure are split. Although the PML gives the lowest reflection magnitudes over all frequencies and incidence angles, the most efficient lossy layer gives reflection magnitudes of the same order as the PML from mid- to high-frequency and for restricted incidence angles. PMID:27475200
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.
1993-01-01
The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.
Computation of wing-vortex interaction in transonic flow using implicit finite difference algorithm
NASA Technical Reports Server (NTRS)
Srinivasan, G.; Steger, J. L.
1981-01-01
An implicit delta form finite difference algorithm for Euler equations in conservation law form was used in preliminary calculations of three dimensional wing vortex interaction. Both steady and unsteady transonic flow wing vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two and three dimensions. Combination of these methods can reduce the overall computational time by a factor of 4.
NASA Technical Reports Server (NTRS)
Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.
1982-01-01
An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.
NASA Technical Reports Server (NTRS)
Anderson, O. L.
1974-01-01
A finite-difference procedure for computing the turbulent, swirling, compressible flow in axisymmetric ducts is described. Arbitrary distributions of heat and mass transfer at the boundaries can be treated, and the effects of struts, inlet guide vanes, and flow straightening vanes can be calculated. The calculation procedure is programmed in FORTRAN 4 and has operated successfully on the UNIVAC 1108, IBM 360, and CDC 6600 computers. The analysis which forms the basis of the procedure, a detailed description of the computer program, and the input/output formats are presented. The results of sample calculations performed with the computer program are compared with experimental data.
Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.
Liu, Haihu; Valocchi, Albert J; Zhang, Yonghao; Kang, Qinjun
2013-01-01
A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions. PMID:23410429
Ground motion simulations in Marmara (Turkey) region from 3D finite difference method
NASA Astrophysics Data System (ADS)
Aochi, Hideo; Ulrich, Thomas; Douglas, John
2016-04-01
In the framework of the European project MARSite (2012-2016), one of the main contributions from our research team was to provide ground-motion simulations for the Marmara region from various earthquake source scenarios. We adopted a 3D finite difference code, taking into account the 3D structure around the Sea of Marmara (including the bathymetry) and the sea layer. We simulated two moderate earthquakes (about Mw4.5) and found that the 3D structure improves significantly the waveforms compared to the 1D layer model. Simulations were carried out for different earthquakes (moderate point sources and large finite sources) in order to provide shake maps (Aochi and Ulrich, BSSA, 2015), to study the variability of ground-motion parameters (Douglas & Aochi, BSSA, 2016) as well as to provide synthetic seismograms for the blind inversion tests (Diao et al., GJI, 2016). The results are also planned to be integrated in broadband ground-motion simulations, tsunamis generation and simulations of triggered landslides (in progress by different partners). The simulations are freely shared among the partners via the internet and the visualization of the results is diffused on the project's homepage. All these simulations should be seen as a reference for this region, as they are based on the latest knowledge that obtained during the MARSite project, although their refinement and validation of the model parameters and the simulations are a continuing research task relying on continuing observations. The numerical code used, the models and the simulations are available on demand.
On the Definition of Surface Potentials for Finite-Difference Operators
NASA Technical Reports Server (NTRS)
Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.
Enhancing finite differences with radial basis functions: Experiments on the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Flyer, Natasha; Barnett, Gregory A.; Wicker, Louis J.
2016-07-01
Polynomials are used together with polyharmonic spline (PHS) radial basis functions (RBFs) to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretizations that can be viewed as enhancements of the classical finite differences (FD). The presented method replicates the convergence properties of FD but for arbitrary node layouts. It is tested on the 2D compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for hyperviscosity. Comparisons are done on Cartesian, hexagonal, and quasi-uniform node layouts. Consideration and guidelines are given on PHS order, polynomial degree and stencil size. The main advantages of the present method are: 1) capturing the basic physics of the problem surprisingly well, even at very coarse resolutions, 2) high-order accuracy without the need of tuning a shape parameter, and 3) the inclusion of polynomials eliminates stagnation (saturation) errors. A MATLAB code is given to calculate the differentiation weights for this novel approach.
Space-time finite-element objects: Efficiently modeling physically complex flows
Dilts, G.A.
1996-03-28
Accurate modeling of high-explosive systems requires detailed consideration of many different physical properties and processes: These diverse processes generally occur in localized regions of the problem. Thus the very partial differential equations used to mathematically model the problem change from one region of space and time to another. The numerical algorithms generally used to solve these equations are frequently conceived in terms of data values for physical field variables u{sup i} defined at a number of spatial points indexed by multi-integer subscripts x{sub J}, resulting in a number of discrete state variables u{sup i}{sub J}. Instead of using as the fundamental object a physical field, which naturally maps to an array, the authors imagine a small piece of space modeled for a small amount of time, a space-time ``element``. Within it, various physical processes occur at various times. Self-contained, it gives account of what happens within its borders. It cooperates with a set of neighbors that organize into meshes, which organize into problems. The authors achieve in the software model a decoupling between the where and the how and the what, lack of which historically has been the source of a great deal of the software overhead of modelling continuum systems, and which is a necessary consequence of writing down u{sup i}{sub J}. An efficient implementation of this idea requires a reformulation of the discretization and solution of systems of conservation laws, and careful class design. A working prototype for systems in one space dimension using Mathematica and C++ is provided.
NASA Astrophysics Data System (ADS)
Steich, David James
1995-01-01
The Finite Difference Time Domain (FDTD) method is a simple yet powerful method for numerically solving electromagnetic wave phenomenon on computers. The FDTD technique discretizes Maxwell's equations with finite difference equations. These finite difference equations, which approximate local field behavior, are applied to large spatial lattices allowing calculation of a vast array of electromagnetical phenomenon. The greatest strengths of the FDTD method are in its simplicity, efficiency, and diversity. FDTD is capable of modeling the scattering and coupling to lossy dielectrics, lossy magnetics, anisotropic media, dispersive media, and nonlinear materials for general geometric shapes. Wideband frequency information can be obtained using FDTD for both near and far field observation points in a single computational run. However, along with all of its benefits, the FDTD algorithm has some deficiencies. For most problems of interest, poor accuracy at geometry interfaces of differing media and at outer problem space boundarys where the spatial lattice must be truncated are the two largest error sources of the FDTD algorithm. Although most accuracy issues can be circumvented by expending large amounts of computer memory and cpu time, using excessive computer resources is not always possible and is never appealing. The purpose of this thesis is to generalize, analyze, and test various mainstream local Outer Radiating Boundary Conditions (ORBCs) for the FDTD method applied to Maxwell's equations in order to help gain a better understanding of present ORBC limitations. A common mathematical model is presented for the boundary conditions. Boundary conditions shown to fit the model include Mur, Superabsorption, Liao, Higdon, and Lindman ORBCs of varying orders. Simple operators are defined and then used to generate the final discretized equations for each of the boundary conditions, automatically, without requiring complicated high order equations. The procedure also allows
NASA Astrophysics Data System (ADS)
Li, H.; Zhang, Z.; Chen, X.
2012-12-01
It is widely accepted that they are oversampled in spatial grid spacing and temporal time step in the high speed medium if uniform grids are used for the numerical simulation. This oversampled grid spacing and time step will lower the efficiency of the calculation, especially high velocity contrast exists. Based on the collocated-grid finite-difference method (FDM), we present an algorithm of spatial discontinuous grid, with localized grid blocks and locally varying time steps, which will increase the efficiency of simulation of seismic wave propagation and earthquake strong ground motion. According to the velocity structure, we discretize the model into discontinuous grid blocks, and the time step of each block is determined according to the local stability. The key problem of the discontinuous grid method is the connection between grid blocks with different grid spacing. We use a transitional area overlapped by both of the finer and the coarser grids to deal with the problem. In the transitional area, the values of finer ghost points are obtained by interpolation from the coarser grid in space and time domain, while the values of coarser ghost points are obtained by downsampling from the finer grid. How to deal with coarser ghost points can influent the stability of long time simulation. After testing different downsampling methods and finally we choose the Gaussian filtering. Basically, 4th order Rung-Kutta scheme will be used for the time integral for our numerical method. For our discontinuous grid FDM, discontinuous time steps for the coarser and the finer grids will be used to increase the simulation efficiency. Numerical tests indicate that our method can provide a stable solution even for the long time simulation without any additional filtration for grid spacing ratio n=2. And for larger grid spacing ratio, Gaussian filtration could be used to preserve the stability. With the collocated-grid FDM, which is flexible and accurate in implementation of free
An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
NASA Astrophysics Data System (ADS)
Li, Xiao; Qiao, ZhongHua; Zhang, Hui
2016-09-01
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.
NASA Astrophysics Data System (ADS)
Kobus, J.; Moncrieff, D.; Wilson, S.
2001-12-01
A comparison is made of the accuracy by which the electric dipole polarizability αzz and hyperpolarizability βzzz can be calculated by using the finite basis set approach (the algebraic approximation) and finite difference method in calculations employing the Hartree-Fock model. The numerical and algebraic methods were tested on the ground states of H2, LiH, BH and FH molecules at their respective experimental equilibrium geometries. For the FH molecule at its experimental equilibrium geometry, a sequence of distributed universal even-tempered basis sets have been used to explore the convergence pattern of the total energy, dipole moment and polarizabilities. The comparison of finite difference and finite basis set methods is extended to geometries for which the nuclear separation, RFH, lies in the range 1.5-2.2 b. The methods give consistent results to within 1% or better. In the case of the FH molecule the dependence of truncation errors of the total energy, dipole moment and polarizabilities on the geometry have been studied and are shown to be negligible.
NASA Astrophysics Data System (ADS)
Kang, K.-T.; Kim, K.-Y.; Jung, H.-J.; Lee, H.-Y.; Chun, H.-J.; Lee, H.-M.; Moon, S.-H.; Kim, H.-J.
2010-03-01
The aim of this study is to evaluate the biomechanical changes after Spinous Process Osteotomy (SPO) with different amounts of facetectomy of the lumbar spine and to compare the models with SPO and intact models using finite element models. Intact spine models and one decompression models (L3-4) with SPO were developed. SPO models included three different amounts of facetectomy (25%, 50%, and 75%). After validation of the models, finite element analyses were performed to investigate the ranges of motion and disc stresses at each corresponding level among three SPO models and intact lumbar spine models. The ranges of motion in the SPO models were increased more than the intact models. According to increase of amounts of facetectomy, ranges of motion were also increased. Similar to range of motion, the von Mises stress of disc in the SPO models was higher than that of intact models. Moreover, with the increase of amount of facetectomy, the disc stress increased at each segments under various moments. The decompression procedures using spinous process osteotomy has been reported to provide better postoperative stability compared to the conventional laminectomy. However, facetectomy over 50 % is likely to attenuate this advantage.
NASA Astrophysics Data System (ADS)
Kang, K.-T.; Kim, K.-Y.; Jung, H.-J.; Lee, H.-Y.; Chun, H.-J.; Lee, H.-M.; Moon, S.-H.; Kim, H.-J.
2009-12-01
The aim of this study is to evaluate the biomechanical changes after Spinous Process Osteotomy (SPO) with different amounts of facetectomy of the lumbar spine and to compare the models with SPO and intact models using finite element models. Intact spine models and one decompression models (L3-4) with SPO were developed. SPO models included three different amounts of facetectomy (25%, 50%, and 75%). After validation of the models, finite element analyses were performed to investigate the ranges of motion and disc stresses at each corresponding level among three SPO models and intact lumbar spine models. The ranges of motion in the SPO models were increased more than the intact models. According to increase of amounts of facetectomy, ranges of motion were also increased. Similar to range of motion, the von Mises stress of disc in the SPO models was higher than that of intact models. Moreover, with the increase of amount of facetectomy, the disc stress increased at each segments under various moments. The decompression procedures using spinous process osteotomy has been reported to provide better postoperative stability compared to the conventional laminectomy. However, facetectomy over 50 % is likely to attenuate this advantage.
NASA Astrophysics Data System (ADS)
Wu, Kailiang; Tang, Huazhong
2015-10-01
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrichs splitting, the WENO reconstruction, the physical-constraints-preserving flux limiter, and the high-order strong stability preserving time discretization. They are extensions of the positivity-preserving finite difference WENO schemes for the non-relativistic Euler equations [20]. However, developing physical-constraints-preserving methods for the RHD system becomes much more difficult than the non-relativistic case because of the strongly coupling between the RHD equations, no explicit formulas of the primitive variables and the flux vectors with respect to the conservative vector, and one more physical constraint for the fluid velocity in addition to the positivity of the rest-mass density and the pressure. The key is to prove the convexity and other properties of the admissible state set and discover a concave function with respect to the conservative vector instead of the pressure which is an important ingredient to enforce the positivity-preserving property for the non-relativistic case. Several one- and two-dimensional numerical examples are used to demonstrate accuracy, robustness, and effectiveness of the proposed physical-constraints-preserving schemes in solving RHD problems with large Lorentz factor, or strong discontinuities, or low rest-mass density or pressure etc.
A moving mesh finite difference method for equilibrium radiation diffusion equations
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
A coarse-mesh nodal method-diffusive-mesh finite difference method
Joo, H.; Nichols, W.R.
1994-05-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.
A moving mesh finite difference method for equilibrium radiation diffusion equations
NASA Astrophysics Data System (ADS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor-corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
Kudryavtsev, Oleg
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments. PMID:24489518
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments. PMID:24489518
Modeling of tension-modulated strings using finite difference and digital waveguide techniques
NASA Astrophysics Data System (ADS)
Pakarinen, Jyri
2005-09-01
Tension modulation is a nonlinear phenomenon where large-amplitude string vibrations cause the tension of the string to vary. This results in an initial pitch glide and energy coupling between modes, causing for example the generation of missing harmonics. The presentation discusses two methods for numerical simulation of the tension modulation nonlinearity from the sound synthesis point of view. The tension modulation is assumed to propagate instantaneously along the string. In the digital waveguide approach, spatially distributed fractional delay filters are used in modulating the string length during run time. Energy-preserving techniques can be used in implementing the fractional delays. In the finite difference approach, time-domain interpolation is used to artificially modulate the wave propagation velocity. The generation of missing harmonics is implemented in the finite difference model by creating an additional excitation point at the string termination. In the waveguide model, the same effect can be obtained by using suitable approximations in the string elongation calculation. Synthesis results for both techniques are presented. Also, a brief comparison of the models with a discussion on stability issues is provided. [This research has been funded by the Academy of Finland (Project No. 104934), S3TK graduate school, and Tekniikan edistamissaatio.
Converged accelerated finite difference scheme for the multigroup neutron diffusion equation
Terranova, N.; Mostacci, D.; Ganapol, B. D.
2013-07-01
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)
Hurrell, Andrew M
2008-06-01
The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface. PMID:18537372
Accuracy issues in the finite difference time domain simulation of photomask scattering
NASA Astrophysics Data System (ADS)
Pistor, Thomas V.
2001-09-01
As the use of electromagnetic simulation in lithography increases, accuracy issues are uncovered and must be addressed. A proper understanding of these issues can allow the lithographer to avoid pitfalls in electromagnetic simulation and to know what can and can not be accurately simulated. This paper addresses the important accuracy issues related to the simulation of photomask scattering using the Finite Difference Time Domain (FDTD) method. Errors related to discretization and periodic boundary conditions are discussed. Discretization-related issues arise when derivatives are replaced by finite differences and when integrals are replaced by summations. These approximations can lead to mask features that do not have exact dimensions. The effects of discretization error on phase wells and thin films are shown. The reflectivity of certain thin film layers is seen to be very sensitive to the layer thickness. Simulation experiments and theory are used to determine how fine a discretization is necessary and various discretization schemes that help minimize error are presented. Boundary-condition-related errors arise from the use of periodic boundary conditions when simulating isolated mask features. The effects of periodic boundary conditions are assessed through the use of simulation experiments. All errors are associated with an ever-present trade-off between accuracy and computational resources. However, choosing the cell size wisely can, in many cases, minimize error without significantly increasing computation resource requirements.
Development of an advanced finite-difference atmospheric general circulation model
Randall, D.A.
1992-03-01
We have proposed to provide and further develop an advanced finite-difference climate model for use in CHAMMP. The model includes advanced parameterizations of cumulus convection, boundary-layer processes, cloud formation, and land-surface vegetation, as well as parameterizations of radiative transfer and gravity wave drag. Postprocessing codes and a user's guide will also be provided. This research is being conducted in collaboration with Professors C.R. Mechoso and A. Arakawa at the University of California at Los Angeles (UCLA). The following research tasks are being carried out in support of CHAMMP: (1) Provide to CHAMMP a base-line finite-difference model and postprocessing codes for further development by the CHAMMP Science Team; (2) Provide to CHAMMP improved model physics to be developed in the course of our research project; (3) Provide to CHAMMP improved computational methods for use in the model; and, (4) Investigate the performance of current and to-be-developed physical parameterizations and computational methods at very high resolution.
2015-01-01
PURPOSE The objective of this study was to evaluate the influence of various cement types on the stress distribution in monolithic zirconia crowns under maximum bite force using the finite element analysis. MATERIALS AND METHODS The models of the prepared #46 crown (deep chamfer margin) were scanned and solid models composed of the monolithic zirconia crown, cement layer, and prepared tooth were produced using the computer-aided design technology and were subsequently translated into 3-dimensional finite element models. Four models were prepared according to different cement types (zinc phosphate, polycarboxylate, glass ionomer, and resin). A load of 700 N was applied vertically on the crowns (8 loading points). Maximum principal stress was determined. RESULTS Zinc phosphate cement had a greater stress concentration in the cement layer, while polycarboxylate cement had a greater stress concentration on the distal surface of the monolithic zirconia crown and abutment tooth. Resin cement and glass ionomer cement showed similar patterns, but resin cement showed a lower stress distribution on the lingual and mesial surface of the cement layer. CONCLUSION The test results indicate that the use of different luting agents that have various elastic moduli has an impact on the stress distribution of the monolithic zirconia crowns, cement layers, and abutment tooth. Resin cement is recommended for the luting agent of the monolithic zirconia crowns. PMID:26816578
Parallelized implicit propagators for the finite-difference Schrödinger equation
NASA Astrophysics Data System (ADS)
Parker, Jonathan; Taylor, K. T.
1995-08-01
We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
NASA Astrophysics Data System (ADS)
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-05-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite-differences to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P, slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High order explicit finite-differences (FD) can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.
NASA Technical Reports Server (NTRS)
Stein, M.; Housner, J. D.
1978-01-01
A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.
NASA Astrophysics Data System (ADS)
Appadu, A. R.
2016-06-01
An unconditionally positive definite scheme has been derived in [1] to approximate a linear advection-diffusion-reaction equation which models exponential travelling waves and the coefficients of advective, diffusive and reactive terms have been chosen as one. The scheme has been baptised as Unconditionally Positive Finite Difference (UPFD). In this work, we use the UPFD scheme to solve the advection-diffusion-reaction problem in [1] and we also extend our study to three other important regimes involved in this model. The temporal step size is varied while fixing the spatial step size. We compute some errors namely; L1 error, dispersion, dissipation errors. We also study the variation of the modulus of the exact amplification factor, modulus of amplification factor of the scheme and relative phase error, all vs the phase angle for the four different regimes.
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.
1987-01-01
An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.
NASA Astrophysics Data System (ADS)
Deng, Xiaogang; Mao, Meiliang; Tu, Guohua; Liu, Huayong; Zhang, Hanxin
2011-02-01
The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ3 have no effects on the SCL, no extra errors can be introduced as δ3 = δ2. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ1 which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ1 to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.
Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation
Petersson, N A; Sjogreen, B
2012-03-26
second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a
NASA Astrophysics Data System (ADS)
Hammer, René; Pötz, Walter; Arnold, Anton
2014-01-01
A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and time-staggered leap-frog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Z-transform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semi-infinite exterior domains. Admitting only solutions in l2 which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Z-transformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stability of the whole space-time scheme. An exactly preserved functional for the norm of the Dirac spinor on the staggered grid is presented. Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energy-momentum dispersion relation on a grid.
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1998-01-01
Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.
Finite Difference Time Domain Electromagnetic Scattering from Frequency-Dependent Lossy Materials
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Beggs, John H.
1991-01-01
During this effort the tasks specified in the Statement of Work have been successfully completed. The extension of Finite Difference Time Domain (FDTD) to more complicated materials has been made. A three-dimensional FDTD code capable of modeling interactions with both dispersive dielectric and magnetic materials has been written, validated, and documented. This code is efficient and is capable of modeling interesting targets using a modest computer work station platform. However, in addition to the tasks in the Statement of Work, a significant number of other FDTD extensions and calculations have been made. RCS results for two different plate geometries have been reported. The FDTD method has been extended to computing far zone time domain results in two dimensions. Finally, the capability to model nonlinear materials has been incorporated into FDTD and validated. The FDTD computer codes developed have been supplied, along with documentation, and preprints describing the other FDTD advances have been included with this report as attachments.
Computationally efficient finite-difference modal method for the solution of Maxwell's equations.
Semenikhin, Igor; Zanuccoli, Mauro
2013-12-01
In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method. PMID:24323014
NASA Technical Reports Server (NTRS)
Lansing, F. L.
1976-01-01
A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.
Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.
NASA Astrophysics Data System (ADS)
Arias-Ramirez, Walter; Olson, Britton; Wolf, William; Lawrence Livermore National Laboratory Team; University of Campinas Team
2015-11-01
The suitability of a continuing forcing immersed boundary method (IBM) combined with a high-order finite difference method is examined on several acoustic scattering problems. A suite of two-dimensional numerical simulations of canonical cases are conducted with the aim of analyzing the error behavior associated with the IBM, through wave reflection, wave diffraction, and the shock-boundary layer interaction phenomena. The compressible Navier-Stokes equations are solved using the Miranda code developed at Lawrence Livermore National Laboratory. Comparison of analytical solution against numerical results is shown for different flow parameters. Preliminary results indicate that the continuing forcing approach has the largest error in wave reflection compared to analytical solution. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.
Exact finite-size corrections for the spanning-tree model under different boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh.; Kenna, R.
2015-02-01
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.
Seismic effects of viscous Biot-coupling: Finite difference simulations on micro-scale
NASA Astrophysics Data System (ADS)
Saenger, E. H.; Shapiro, S. A.; Keehm, Y.
2005-07-01
This paper is concerned with numerical considerations of viscous fluid effects on wave propagation in porous media. We apply a displacement-stress rotated staggered finite-difference (FD) grid technique to solve the elastodynamic wave equation. An accurate approximation of a Newtonian fluid is implemented in this technique by using a generalized Maxwell body. With this approach we consider the velocity predictions of the Biot theory for elastic waves in different digital rock samples. To distinguish between the low and the high frequency range we estimate the effective permeabilities by a flow simulation. Our numerical results indicate that the viscous Biot-coupling is visible in the numerical experiments. Moreover, the influences of other solid-fluid interactions (e.g., Squirt flow) are also discussed.
NASA Astrophysics Data System (ADS)
Vincenti, H.; Vay, J.-L.
2016-03-01
Very high order or pseudo-spectral Maxwell solvers are the method of choice to reduce discretization effects (e.g. numerical dispersion) that are inherent to low order Finite-Difference Time-Domain (FDTD) schemes. However, due to their large stencils, these solvers are often subject to truncation errors in many electromagnetic simulations. These truncation errors come from non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the simulation results. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of the errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solvers and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.
Transfer-matrix approach for finite-difference time-domain simulation of periodic structures.
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2013-11-01
Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment. PMID:24329377
NASA Astrophysics Data System (ADS)
Gupta, A.; Sbragaglia, M.; Scagliarini, A.
2015-06-01
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behavior of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" interaction model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical results are compared with the predictions of various theoretical models. The proposed numerical simulations explore problems where the capabilities of LBM were never quantified before.
El-Anwar, Mohamed I.; Yousief, Salah A.; Soliman, Tarek A.; Saleh, Mahmoud M.; Omar, Wael S.
2015-01-01
Objective This study aimed to evaluate stress patterns generated within implant-supported mandibular overdentures retained by two different attachment types: ball and socket and locator attachments. Materials and methods Commercial CAD/CAM and finite element analysis software packages were utilized to construct two 3D finite element models for the two attachment types. Unilateral masticatory compressive loads of 50, 100, and 150 N were applied vertically to the overdentures, parallel to the longitudinal axes of the implants. Loads were directed toward the central fossa in the molar region of each overdenture, that linear static analysis was carried out to find the generated stresses and deformation on each part of the studied model. Results According to FEA results the ball attachment neck is highly stressed in comparison to the locator one. On the other hand mucosa and cortical bone received less stresses under ball and socket attachment. Conclusions Locator and ball and socket attachments induce equivalent stresses on bone surrounding implants. Locator attachment performance was superior to that of the ball and socket attachment in the implants, nylon caps, and overdenture. Locator attachments are highly recommended and can increase the interval between successive maintenance sessions. PMID:26644755
GPU-accelerated 3D neutron diffusion code based on finite difference method
Xu, Q.; Yu, G.; Wang, K.
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
NASA Astrophysics Data System (ADS)
Castaldo, Raffaele; Tizzani, Pietro
2016-04-01
Many numerical models have been developed to simulate the deformation and stress changes associated to the faulting process. This aspect is an important topic in fracture mechanism. In the proposed study, we investigate the impact of the deep fault geometry and tectonic setting on the co-seismic ground deformation pattern associated to different earthquake phenomena. We exploit the impact of the structural-geological data in Finite Element environment through an optimization procedure. In this framework, we model the failure processes in a physical mechanical scenario to evaluate the kinematics associated to the Mw 6.1 L'Aquila 2009 earthquake (Italy), the Mw 5.9 Ferrara and Mw 5.8 Mirandola 2012 earthquake (Italy) and the Mw 8.3 Gorkha 2015 earthquake (Nepal). These seismic events are representative of different tectonic scenario: the normal, the reverse and thrust faulting processes, respectively. In order to simulate the kinematic of the analyzed natural phenomena, we assume, under the plane stress approximation (is defined to be a state of stress in which the normal stress, sz, and the shear stress sxz and syz, directed perpendicular to x-y plane are assumed to be zero), the linear elastic behavior of the involved media. The performed finite element procedure consist of through two stages: (i) compacting under the weight of the rock successions (gravity loading), the deformation model reaches a stable equilibrium; (ii) the co-seismic stage simulates, through a distributed slip along the active fault, the released stresses. To constrain the models solution, we exploit the DInSAR deformation velocity maps retrieved by satellite data acquired by old and new generation sensors, as ENVISAT, RADARSAT-2 and SENTINEL 1A, encompassing the studied earthquakes. More specifically, we first generate 2D several forward mechanical models, then, we compare these with the recorded ground deformation fields, in order to select the best boundaries setting and parameters. Finally
A free surface capturing discretization for the staggered grid finite difference scheme
NASA Astrophysics Data System (ADS)
Duretz, T.; May, D. A.; Yamato, P.
2016-03-01
The coupling that exists between surface processes and deformation within both the shallow crust and the deeper mantle-lithosphere has stimulated the development of computational geodynamic models that incorporate a free surface boundary condition. We introduce a treatment of this boundary condition that is suitable for staggered grid, finite difference schemes employing a structured Eulerian mesh. Our interface capturing treatment discretizes the free surface boundary condition via an interface that conforms with the edges of control volumes (e.g. a `staircase' representation) and requires only local stencil modifications to be performed. Comparisons with analytic solutions verify that the method is first-order accurate. Additional intermodel comparisons are performed between known reference models to further validate our free surface approximation. Lastly, we demonstrate the applicability of a multigrid solver to our free surface methodology and demonstrate that the local stencil modifications do not strongly influence the convergence of the iterative solver.
Seismic Analysis of a Rockfill Dam by FLAC Finite Difference Code
Miglio, Livia; Pagliaroli, Alessandro; Lanzo, Giuseppe; Miliziano, Salvatore
2008-07-08
The paper presents the results of numerical analyses carried out with FLAC finite difference code aiming at investigating the seismic response of rockfill dams. In particular the hysteretic damping model, recently incorporated within the code, coupled with a perfectly plastic yield criterion, was employed. As first step, 1D and 2D calibration analyses were performed and comparisons with the results supplied by well known linear equivalent and fully non linear codes were carried out. Then the seismic response of E1 Infiernillo rockfill dam was investigated during two weak and strong seismic events. Benefits and shortcomings of using the hysteretic damping model are discussed in the light of the results obtained from calibration studies and field-scale analyses.
NASA Astrophysics Data System (ADS)
Bhattacharya, Amitabh
2013-11-01
An efficient algorithm for simulating Stokes flow around particles is presented here, in which a second order Finite Difference method (FDM) is coupled to a Boundary Integral method (BIM). This method utilizes the strong points of FDM (i.e. localized stencil) and BIM (i.e. accurate representation of particle surface). Specifically, in each iteration, the flow field away from the particles is solved on a Cartesian FDM grid, while the traction on the particle surface (given the the velocity of the particle) is solved using BIM. The two schemes are coupled by matching the solution in an intermediate region between the particle and surrounding fluid. We validate this method by solving for flow around an array of cylinders, and find good agreement with Hasimoto's (J. Fluid Mech. 1959) analytical results.
NASA Technical Reports Server (NTRS)
Vinokur, M.
1979-01-01
The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent.
NASA Technical Reports Server (NTRS)
Schroeter, Jens; Wunsch, Carl
1986-01-01
The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.
A Finite Difference Method for Modeling Migration of Impurities in Multilayer Systems
NASA Astrophysics Data System (ADS)
Tosa, V.; Kovacs, Katalin; Mercea, P.; Piringer, O.
2008-09-01
A finite difference method to solve the one-dimensional diffusion of impurities in a multilayer system was developed for the special case in which a partition coefficient K impose a ratio of the concentrations at the interface between two adiacent layers. The fictitious point method was applied to derive the algebraic equations for the mesh points at the interface, while for the non-uniform mesh points within the layers a combined method was used. The method was tested and then applied to calculate migration of impurities from multilayer systems into liquids or solids samples, in migration experiments performed for quality testing purposes. An application was developed in the field of impurities migrations from multilayer plastic packagings into food, a problem of increasing importance in food industry.
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.; Yamaleev, Nail K.; Frankel, Steven H.
2009-01-01
A general strategy exists for constructing Energy Stable Weighted Essentially Non Oscillatory (ESWENO) finite difference schemes up to eighth-order on periodic domains. These ESWENO schemes satisfy an energy norm stability proof for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, boundary closures are developed for the fourth-order ESWENO scheme that maintain wherever possible the WENO stencil biasing properties, while satisfying the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L2 norm. Second-order, and third-order boundary closures are developed that achieve stability in diagonal and block norms, respectively. The global accuracy for the second-order closures is three, and for the third-order closures is four. A novel set of non-uniform flux interpolation points is necessary near the boundaries to simultaneously achieve 1) accuracy, 2) the SBP convention, and 3) WENO stencil biasing mechanics.
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2005-01-01
A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.
Finite-difference time-domain simulation of thermal noise in open cavities
Andreasen, Jonathan; Cao Hui; Taflove, Allen; Kumar, Prem |; Cao Changqi
2008-02-15
A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes.
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
Sha, Wei . E-mail: ws108@ahu.edu.cn; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng
2007-07-01
An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources.
Finite Difference Time Domain Analysis for a Sound Field Including a Plate in Water
NASA Astrophysics Data System (ADS)
Saito, Hideaki; Naoi, Jun; Kikuchi, Toshiaki
2004-05-01
In marine research, measures against self-noise of an observatory ship are important. Generally, the self-noise is measured after the completion of ships. It is difficult to predict this noise level beforehand. Then, an attempt is made to determine the noise emitted from various elements of a structure. The finite difference time domain method is applied to obtain sound fields, including that of a plate in water. The time behavior of the sound wave emitted from a sound source placed near the upper part of a plate is investigated. As a result, the reflected and re-radiated waves from the plate including the head wave resulting from the longitudinal and traverse waves in the plate are able to be visualized. In the case of the plate with a branch plate, the suppression of the wave which propagates at the inside of the plate with the length of the branch plate is shown.
NASA Astrophysics Data System (ADS)
Collins, M. W.
1980-03-01
The complete two-dimensional partial differential equations for developing laminar flow in a circular tube have been treated by a finite difference analysis. Property variation with temperature, especially that of viscosity, is allowed for in a flexible manner. The continuity and momentum equations, and then the energy equations, are solved by direct elimination at each axial step, and a marching procedure used in the axial direction. The stepwise energy balance is rigidly satisfied throughout by using it as a constituent equation in place of the 'explicit' wall thermal boundary condition normally used. The analysis predicts the complete developing hydrodynamic and thermal fields, together with friction factors and heat transfer coefficients. It has been tested for a range of fluid velocity and thermal boundary conditions and for various fluids, including high viscosity oils, water and air. Predictions for constant wall temperature presented here are for forced and combined convection and are compared with experimental data of Test and Zeldin and Schmidt.
A finite difference-time domain technique for modeling narrow apertures in conducting scatterers
NASA Technical Reports Server (NTRS)
Demarest, Kenneth R.
1987-01-01
The finite difference-time domain (FDTD) technique has proven to be a valuable tool for the calculation of the transient and steady state scattering characteristics of relatively complex scatterer and source configurations. In spite of its usefulness, it exhibits serious deficiencies when used to analyze geometries that contain fine detail. An FDTD technique is described that utilizes Babinet's principle to decouple the regions on both sides of the aperture. The result is an FDTD technique that is capable of modeling apertures that are much smaller than the spatial grid used in the analysis and yet is not perturbed by numerical noise when used in the 'scattered field' mode. Numerical results are presented that show the field penetration through cavity-backed apertures that are much smaller than the spatial grid used during the solution.
Simulation of the turbulent Rayleigh-Benard problem using a spectral/finite difference technique
NASA Technical Reports Server (NTRS)
Eidson, T. M.; Hussaini, M. Y.; Zang, T. A.
1986-01-01
The three-dimensional, incompressible Navier-Stokes and energy equations with the Bousinesq assumption have been directly simulated at a Rayleigh number of 3.8 x 10 to the 5th power and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were used. A spectral/finite difference numerical method was used to simulate the flow. The flow at these conditions is turbulent and a sufficiently fine mesh was used to capture all relevant flow scales. The results of the simulation are compared to experimental data to justify the conclusion that the small scale motion is adequately resolved.
A fast high-order finite difference algorithm for pricing American options
NASA Astrophysics Data System (ADS)
Tangman, D. Y.; Gopaul, A.; Bhuruth, M.
2008-12-01
We describe an improvement of Han and Wu's algorithm [H. Han, X.Wu, A fast numerical method for the Black-Scholes equation of American options, SIAM J. Numer. Anal. 41 (6) (2003) 2081-2095] for American options. A high-order optimal compact scheme is used to discretise the transformed Black-Scholes PDE under a singularity separating framework. A more accurate free boundary location based on the smooth pasting condition and the use of a non-uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem. Extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained. Comparisons with some recently proposed methods for the American options problem are carried out to show the advantage of our numerical method.
Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures.
Zhao, Yan; Argyropoulos, Christos; Hao, Yang
2008-04-28
This paper proposes a radial dependent dispersive finite-difference time-domain method for the modeling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are 'invisible' to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being 'visible'. It is also demonstrated numerically that the simplified cloak based on high-order transformations can indeed improve the cloaking performance. PMID:18545374
Skolski, J. Z. P. Vincenc Obona, J.; Römer, G. R. B. E.; Huis in 't Veld, A. J.
2014-03-14
A model predicting the formation of laser-induced periodic surface structures (LIPSSs) is presented. That is, the finite-difference time domain method is used to study the interaction of electromagnetic fields with rough surfaces. In this approach, the rough surface is modified by “ablation after each laser pulse,” according to the absorbed energy profile, in order to account for inter-pulse feedback mechanisms. LIPSSs with a periodicity significantly smaller than the laser wavelength are found to “grow” either parallel or orthogonal to the laser polarization. The change in orientation and periodicity follow from the model. LIPSSs with a periodicity larger than the wavelength of the laser radiation and complex superimposed LIPSS patterns are also predicted by the model.
Finite difference method to find period-one gait cycles of simple passive walkers
NASA Astrophysics Data System (ADS)
Dardel, Morteza; Safartoobi, Masoumeh; Pashaei, Mohammad Hadi; Ghasemi, Mohammad Hassan; Navaei, Mostafa Kazemi
2015-01-01
Passive dynamic walking refers to a class of bipedal robots that can walk down an incline with no actuation or control input. These bipeds are sensitive to initial conditions due to their style of walking. According to small basin of attraction of passive limit cycles, it is important to start with an initial condition in the basin of attraction of stable walking (limit cycle). This paper presents a study of the simplest passive walker with point and curved feet. A new approach is proposed to find proper initial conditions for a pair of stable and unstable period-one gait limit cycles. This methodology is based on finite difference method which can solve the nonlinear differential equations of motion on a discrete time. Also, to investigate the physical configurations of the walkers and the environmental influence such as the slope angle, the parameter analysis is applied. Numerical simulations reveal the performance of the presented method in finding two stable and unstable gait patterns.
Inclusion of lumped elements in finite difference time domain electromagnetic calculations
Thomas, V.A.; Jones, M.E.; Mason, R.J.
1994-12-31
A general approach for including lumped circuit elements in a finite difference, time domain (FD-TD) solution of Maxwell`s equations is presented. The methodology allows the direct access to SPICE to model the lumped circuits, while the full 3-Dimensional solution to Maxwell`s equations provides the electromagnetic field evolution. This type of approach could be used to mode a pulsed power machine by using a SPICE model for the driver and using an electromagnetic PIC code for the plasma/electromagnetics calculation. The evolution of the driver can be made self consistent with the behavior of the plasma load. Other applications are also possible, including modeling of nonlinear microwave circuits (as long as the non-linearities may be expressed in terms of a lumped element) and self-consistent calculation of very high speed computer interconnections and digital circuits.
Finite difference time domain calculation of transients in antennas with nonlinear loads
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent
1991-01-01
In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.
The arbitrary order mixed mimetic finite difference method for the diffusion equation
Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco
2016-05-01
Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less
Bensa, Julien; Bilbao, Stefan; Kronland-Martinet, Richard; Smith, Julius O
2003-08-01
A model of transverse piano string vibration, second order in time, which models frequency-dependent loss and dispersion effects is presented here. This model has many desirable properties, in particular that it can be written as a well-posed initial-boundary value problem (permitting stable finite difference schemes) and that it may be directly related to a digital waveguide model, a digital filter-based algorithm which can be used for musical sound synthesis. Techniques for the extraction of model parameters from experimental data over the full range of the grand piano are discussed, as is the link between the model parameters and the filter responses in a digital waveguide. Simulations are performed. Finally, the waveguide model is extended to the case of several coupled strings. PMID:12942987
Low-dispersion finite difference methods for acoustic waves in a pipe
NASA Technical Reports Server (NTRS)
Davis, Sanford
1991-01-01
A new algorithm for computing one-dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial-boundary-value problem. Conventional dissipation-free second-order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength. Using the signal generation by a piston in a duct as an example, transient acoustic computations are presented using a new compact three-point algorithm which allows about 60 percent fewer mesh points per wavelength. Both pulse and harmonic excitation are considered. Coupling of the acoustic signal with the pipe resonant modes is shown to generate a complex transient wave with rich harmonic content.
Day, D.R.
1993-12-31
Disposable and permanently mounted dielectric sensors were used to characterize the cure in polyester sheet molding compound (SMC) at various locations through the thickness of the part in a simulated molding environment. Using established techniques, the dielectric and temperature information were combined to yield local cure state information for each sensor. Parts under five millimeters thick were found to cure rather uniformly while parts greater than this had increasing degrees of nonuniformity in cure behavior through the thickness. These observed cure state data were compared to finite difference model predictions. The model predictions, which were confirmed by the sensor cure data, may be used to optimize part design and production by predicting the curing behavior and molding cycle time required for new structures.
Free transverse vibration of a wrinkled annular thin film by using finite difference method
NASA Astrophysics Data System (ADS)
Wang, C. G.; Liu, Y. P.; Lan, L.; Tan, H. F.
2016-02-01
This paper investigates the free transverse vibration of a wrinkled annular thin film. The non-dimensional Hamilton motion equation of the wrinkled annular thin film is established, which is solved by using the finite difference method to acquire the vibration frequency and mode. The predicted vibration characteristics are verified by the experimental measurements based on the digital image correlation (DIC) technique. The results show that wrinkles have great effects on the vibration of the annular thin film. Especially for the heavily wrinkled cases, the local-global interactive mode dominates the vibration of the annular thin film. The frequency increases as the wrinkling level increases which is mainly due to the increased nonlinear geometric stiffness. The results provide favorable supports for understanding the role of nonlinear wrinkling on the vibration of thin films.
NASA Astrophysics Data System (ADS)
Putri, Selmi; Arif, Idam; Khotimah, Siti Nurul
2015-04-01
In this study, peritoneal dialysis transport system was numerically simulated using finite difference method. The increase in the intraperitoneal pressure due to coughing has a high value outside the working area of the void volume fraction of the hydrostatic pressure θ(P). Therefore to illustrate the effects of the pressure increment, the pressure of working area is chosen between 1 and 3 mmHg. The effects of increased pressure in peritoneal tissue cause more fluid to flow into the blood vessels and lymph. Furthermore, the increased pressure in peritoneal tissue makes the volumetric flux jv and solute flux js across the tissue also increase. The more fluid flow into the blood vessels and lymph causes the fluid to flow into tissue qv and the glucose flow qs to have more negative value and also decreases the glucose concentration CG in the tissue.
NASA Astrophysics Data System (ADS)
Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.
2016-05-01
Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.
CUDA Fortran acceleration for the finite-difference time-domain method
NASA Astrophysics Data System (ADS)
Hadi, Mohammed F.; Esmaeili, Seyed A.
2013-05-01
A detailed description of programming the three-dimensional finite-difference time-domain (FDTD) method to run on graphical processing units (GPUs) using CUDA Fortran is presented. Two FDTD-to-CUDA thread-block mapping designs are investigated and their performances compared. Comparative assessment of trade-offs between GPU's shared memory and L1 cache is also discussed. This presentation is for the benefit of FDTD programmers who work exclusively with Fortran and are reluctant to port their codes to C in order to utilize GPU computing. The derived CUDA Fortran code is compared with an optimized CPU version that runs on a workstation-class CPU to present a realistic GPU to CPU run time comparison and thus help in making better informed investment decisions on FDTD code redesigns and equipment upgrades. All analyses are mirrored with CUDA C simulations to put in perspective the present state of CUDA Fortran development.
A fourth order accurate finite difference scheme for the computation of elastic waves
NASA Technical Reports Server (NTRS)
Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.
1986-01-01
A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.
Anami, Lilian Costa; da Costa Lima, Júlia Magalhães; Takahashi, Fernando Eidi; Neisser, Maximiliano Piero; Noritomi, Pedro Yoshito; Bottino, Marco Antonio
2015-04-01
The goal of this study was to evaluate the distribution of stresses generated around implants with different internal-cone abutments by photoelastic (PA) and finite element analysis (FEA). For FEA, implant and abutments with different internal-cone connections (H- hexagonal and S- solid) were scanned, 3D meshes were modeled and objects were loaded with computer software. Trabecular and cortical bones and photoelastic resin blocks were simulated. The PA was performed with photoelastic resin blocks where implants were included and different abutments were bolted. Specimens were observed in the circular polariscope with the application device attached, where loads were applied on same conditions as FEA. FEA images showed very similar stress distribution between two models with different abutments. Differences were observed between stress distribution in bone and resin blocks; PA images resembled those obtained on resin block FEA. PA images were also quantitatively analyzed by comparing the values assigned to fringes. It was observed that S abutment distributes loads more evenly to bone adjacent to an implant when compared to H abutment, for both analysis methods used. It was observed that the PA has generated very similar results to those obtained in FEA with the resin block. PMID:23750560
Stringhini, Diego José; Sommerfeld, Ricardo; Uetanabaro, Lucas Caetano; Leonardi, Denise Piotto; Araújo, Melissa Rodrigues; Rebellato, Nelson Luís Barbosa; Costa, Delson João da; Scariot, Rafaela
2016-01-01
The aim of this study was to evaluate the stress and dislodgement resistance by finite element analysis of different types of fixation in mandibular orthognathic surgery. A 3D solid finite element model of a hemi-mandible was obtained. A bilateral sagittal split osteotomy was simulated and the distal segment was advanced 5 mm forward. After the adjustment and superimposing of segments, 9 different types of osteosynthesis with 2.0 miniplates and screws were simulated: A, one 4-hole conventional straight miniplate; B, one 4-hole locking straight miniplate; C, one 4-hole conventional miniplate and one bicortical screw; D, one 4-hole locking miniplate and 1 bicortical screws; E, one 6-hole conventional straight miniplate; F, one 6-hole locking miniplate; G, two 4-hole conventional straight miniplates; H, two 4-hole locking straight miniplates; and I, 3 bicortical screws in an inverted-L pattern. In each model, forces simulating the masticatory muscles were applied. The values of stress in the plates and screws were checked. The dislodgement resistance was checked at the proximal segment since the distal segment was stable because of the screen at the occlusal tooth. The regions with the lowest and highest displacement were measured. The offset between the osteotomized segments was verified by millimeter intervals. Inverted-L with bicortical screws was the model that had the lowest dislodgment and the model with the lowest tension was the one with two conventional plates. The results suggest that the tension was better distributed in the locking miniplates, but the locking screws presented higher concentration of tension. PMID:27224561
Field Test of a Hybrid Finite-Difference and Analytic Element Regional Model.
Abrams, D B; Haitjema, H M; Feinstein, D T; Hunt, R J
2016-01-01
Regional finite-difference models often have cell sizes that are too large to sufficiently model well-stream interactions. Here, a steady-state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell-by-cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real-world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined "benchmark" MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost-effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite-difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady-state conditions. PMID:25628100
Overview of finite difference Hartree-Fock method algorithm, implementation and application
NASA Astrophysics Data System (ADS)
Kobus, J.
2012-12-01
Two-dimensional, finite difference Hartree-Fock method has been in constant usage and development over the last two decades. The method has proved stable and efficient enough to be applied to dozens of diatomic molecules, even to systems as large as the thorium fluoride. Its latest version is presented and the dependence of its accuracy on the grid size and efficiency on the overrelaxation parameters are discussed. The method has been mainly used to develop and calibrate sequences of universal even-tempered and polarization-consistent basis sets and assess basis set truncation and superposition errors. Its modified version has proved useful in testing various exchange-correlation potentials within the density functional theory. The method has turned out to be a valuable source of reference values of total energies, multipole moments, static polarizabilities and hyperpolarizabilities (αzz, βzzz, γzzzz, Az,zz and Bzz,zz) for atoms, diatomic molecules and their ions. Recently, it has been modified to allow to calculate the electrical properties of homonuclear molecules and the results for the Li2, N2, F2 and O2 systems are presented. Electrical properties of the AlF, CS, KCl diatomics and of highly ionized krypton atom (Kr+32) are reported as well. Accuracy of both the matrix Hartree-Fock employing universal even-tempered basis sets and the finite difference Hartree-Fock methods is discussed and the basis set superposition errors of the dipole polarizability and the first hyperpolarizability of the FH molecule is reexamined. Basis set superposition errors are also discussed in case of the dipole polarizability and the second hyperpolarizability of the F2 system.
NASA Astrophysics Data System (ADS)
Tsai, T. C.; Yu, H.-S.; Hsieh, M.-S.; Lai, S. H.; Yang, Y.-H.
2015-11-01
Nowadays most of supercomputers are based on the frame of PC cluster; therefore, the efficiency of parallel computing is of importance especially with the increasing computing scale. This paper proposes a high-order implicit predictor-corrector central finite difference (iPCCFD) scheme and demonstrates its high efficiency in parallel computing. Of special interests are the large scale numerical studies such as the magnetohydrodynamic (MHD) simulations in the planetary magnetosphere. An iPCCFD scheme is developed based on fifth-order central finite difference method and fourth-order implicit predictor-corrector method in combination with elimination-of-the-round-off-errors (ERE) technique. We examine several numerical studies such as one-dimensional Brio-Wu shock tube problem, two-dimensional Orszag-Tang vortex system, vortex type K-H instability, kink type K-H instability, field loop advection, and blast wave. All the simulation results are consistent with many literatures. iPCCFD can minimize the numerical instabilities and noises along with the additional diffusion terms. All of our studies present relatively small numerical errors without employing any divergence-free reconstruction. In particular, we obtain fairly stable results in the two-dimensional Brio-Wu shock tube problem which well conserves ∇ ṡ B = 0 throughout the simulation. The ERE technique removes the accumulation of roundoff errors in the uniform or non-disturbed system. We have also shown that iPCCFD is characterized by the high order of accuracy and the low numerical dissipation in the circularly polarized Alfvén wave tests. The proposed iPCCFD scheme is a parallel-efficient and high precision numerical scheme for solving the MHD equations in hyperbolic conservation systems.
Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; McDowell, David L.
2015-07-10
Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide
Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; McDowell, David L.
2015-07-10
Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight
NASA Astrophysics Data System (ADS)
Wang, Wei; Liang, Shujian; Sun, Yeqing
To investigate the biological effects of space environment in rice plants, proteomic profiles of six rice cultivars growing after twice different seed space flights were analyzed by two-dimensional difference gel electrophoresis (2-D DIGE) coupled with mass spectrometry (MS). Over 1500 protein spots were detected in each paired space/ground-control comparison and more than 800 protein spots were reproducible across all the samples. Six proteins including peroxiredoxin and rubisco were found significantly changed in most of the six cultivars after both of the seed space flights, indicating they might be associated with the responses of rice cells to the space environment. Cluster analyses were also applied using the quantitative protein expression data: cultivar hierarchical clustering and principal component analysis both indicated that the rice proteome changed its expression profiles after seed space environment exposures while protein hierarchical clustering revealed that there might be a decrease of protein expression in rice plants after seed space flights.
The effect of space charge fields due to finite length electron beams in the free-electron laser
NASA Technical Reports Server (NTRS)
Tang, C.-M.; Sprangle, P.; Freund, H.; Colson, W.
1982-01-01
The space charge electric field of a finite length electron beam in the free electron laser amplifier with a tapered wiggler is analyzed. In the free drift region between the accelerator and laser, expressions for the increase of energy spread due to the self field are presented. In the FEL interaction region, the general conditions on the importance of the self electric field in the equations of motion is obtained. A numerical example of the FEL experiment at 10.6 microns is given.
On a family of monotone finite-difference schemes of the second order of approximation
NASA Astrophysics Data System (ADS)
Gushchin, Valentin A.
2015-11-01
Using a simple model of a linear transport equation a family of hybrid monotone finite difference schemes has been constructed. By the analysis of the differential approximation it was shown that the resulting family has a secondorder approximation in the spatial variable, has minimal scheme viscosity and dispersion and monotonous. It is shown that the region of operability of the base schemes (Modified Central Difference Schemes (MCDS) and Modified Upwind Difference Schemes (MUDS)) is a non-empty set. The local criterion for switching between the base schemes is based on the sign of the product of the velocity, the first and second differences of the transferred functions at the considered point. On the solution of the Cauchy problem provides a graphical comparison of the calculation results obtained using the known schemes of the first, second and third order approximation. This work has been partly supported by Russian Foundation for Basic Research (grants No. 14-01-00428, 15-51-50023), by the program of the Presidium of RAS No. 8 and by the program No. 3 of the Department of Mathematical Sciences of RAS.
Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows
Fu, S.C.; So, R.M.C.; Leung, W.W.F.
2010-08-20
With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.
Three-dimensional finite-difference modeling of non-linear ground notion
Jones, E.M.; Olsen, K.B.
1997-08-01
We present a hybrid finite-difference technique capable of modeling non-linear soil amplification from the 3-D finite-fault radiation pattern for earthquakes in arbitrary earth models. The method is applied to model non-linear effects in the soils of the San Fernando Valley (SFV) from the 17 January 1994 M 6.7 Northridge earthquake. 0-7 Hz particle velocities are computed for an area of 17 km by 19 km immediately above the causative fault and 5 km below the surface where peak strike-parallel, strike-perpendicular, vertical, and total velocities reach values of 71 cm/s, 145 cm/s, 152 cm/s, and 180 cm/s, respectively. Selected Green`s functions and a soil model for the SFV are used to compute the approximate stress level during the earthquake, and comparison to the values for near-surface alluvium at the U.S. Nevada Test Site suggests that the non-linear regime may have been entered. We use selected values from the simulated particle velocity distribution at 5 km depth to compute the non-linear response in a soil column below a site within the Van Norman Complex in SFV, where the strongest ground motion was recorded. Since site-specific non- linear material parameters from the SFV are currently unavailable, values are taken from analyses of observed Test Site ground motions. Preliminary results show significant reduction of spectral velocities at the surface normalized to the peak source velocity due to non-linear effects when the peak velocity increases from 32 cm/s (approximately linear case) to 64 cm/s (30-92%), 93 cm/s (7-83%), and 124 cm/s (2-70%). The largest reduction occurs for frequencies above 1 Hz.
NASA Astrophysics Data System (ADS)
Marchiolli, M. A.; Mendonça, P. E. M. F.
2013-09-01
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener-Khinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelet bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar-Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory.
NASA Technical Reports Server (NTRS)
Doherty, Michael P.; Dalsania, Vithal
1990-01-01
An analysis was performed to predict the thermal distortion of the solar dynamic concentrator for Space Station Freedom in low earth orbit and to evaluate the effects of that thermal distortion on concentrator on-orbit performance. The analysis required substructural finite element modeling of critical concentrator structural subsystems, structural finite element modeling of the concentrator, mapping of thermal loading onto the structural finite element model, and the creation of specialized postprocessors to assist in interpreting results. Concentrator temperature distributions and thermally induced displacements and slope errors and the resulting receiver flux distribution profiles are discussed. Results determined for a typical orbit indicate that concentrator facet rotations are less than 0.2 mrad and that the change in facet radius due to thermal flattening is less than 5 percent. The predicted power loss due to thermal distortion effects is less than 0.3 percent. As a consequence the thermal distortions of the solar dynamic concentrator in low earth orbit will have a negligible effect on the flux distribution profiles within the receiver.
NASA Astrophysics Data System (ADS)
Tam, Christopher K. W.; Ju, Hongbin
2009-09-01
The use of finite difference schemes to compute the scattering of acoustic waves by surfaces made up of different materials with sharp surface discontinuities at the joints would, invariably, result in the generations of spurious reflected waves of numerical origin. Spurious scattered waves are produced even if a high-order scheme capable of resolving and supporting the propagation of the incident wave is used. This problem is of practical importance in jet engine duct acoustic computation. In this work, the basic reason for the generation of spurious numerical waves is first examined. It is known that when the governing partial differential equations of acoustics are discretized, one should only use the long waves of the computational scheme to represent or simulate the physical waves. The short waves of the computational scheme have entirely different propagation characteristics. They are the spurious numerical waves. A method by which high wave number components (short waves) in the wave scattering process is intentionally removed so as to minimize the scattering of spurious numerical waves is proposed. This method is implemented in several examples from computational aeroacoustics to illustrate its effectiveness, accuracy and efficiency. This method is also employed to compute the scattering of acoustic waves by scatterers, such as rigid wall acoustic liner splices, with width smaller than the computational mesh size. Good results are obtained when comparing with computed results using much smaller mesh size. The method is further extended for applications to computations of acoustic wave reflection and scattering by very small surface inhomogeneities with simple geometries.
Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks
NASA Technical Reports Server (NTRS)
Kimoto, Paul A.; Chernoff, David F.
1995-01-01
We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.
NASA Technical Reports Server (NTRS)
Melis, Matthew E.
2003-01-01
Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.
NASA Astrophysics Data System (ADS)
Melis, Matthew E.
2003-01-01
Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.
Finite-difference modeling with variable grid-size and adaptive time-step in porous media
NASA Astrophysics Data System (ADS)
Liu, Xinxin; Yin, Xingyao; Wu, Guochen
2014-04-01
Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.
Marchiolli, M.A.; Mendonça, P.E.M.F.
2013-09-15
We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar–Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener–Khinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelet bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar–Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory. -- Highlights: •Conception of a quantum-algebraic framework embracing a new uncertainty principle for unitary operators. •Determination of new restrictions upon the selective process of signals and wavelet bases. •Demonstration of looser bounds interpolating between the tightest bound and the Massar–Spindel inequality. •Construction of finite ground states properly describing the tightest bound. •Establishment of an important connection with the discrete Weyl function.
NASA Astrophysics Data System (ADS)
Min, Xiaoyi
This thesis first presents the study of the interaction of electromagnetic waves with three-dimensional heterogeneous, dielectric, magnetic, and lossy bodies by surface integral equation modeling. Based on the equivalence principle, a set of coupled surface integral equations is formulated and then solved numerically by the method of moments. Triangular elements are used to model the interfaces of the heterogeneous body, and vector basis functions are defined to expand the unknown current in the formulation. The validity of this formulation is verified by applying it to concentric spheres for which an exact solution exists. The potential applications of this formulation to a partially coated sphere and a homogeneous human body are discussed. Next, this thesis also introduces an efficient new set of integral equations for treating the scattering problem of a perfectly conducting body coated with a thin magnetically lossy layer. These electric field integral equations and magnetic field integral equations are numerically solved by the method of moments (MoM). To validate the derived integral equations, an alternative method to solve the scattering problem of an infinite circular cylinder coated with a thin magnetic lossy layer has also been developed, based on the eigenmode expansion. Results for the radar cross section and current densities via the MoM and the eigenmode expansion method are compared. The agreement is excellent. The finite difference time domain method is subsequently implemented to solve a metallic object coated with a magnetic thin layer and numerical results are compared with that by the MoM. Finally, this thesis presents an application of the finite-difference time-domain approach to the problem of electromagnetic receiving and scattering by a cavity -backed antenna situated on an infinite conducting plane. This application involves modifications of Yee's model, which applies the difference approximations of field derivatives to differential
NASA Astrophysics Data System (ADS)
Liao, Fei; Ye, Zhengyin
2015-12-01
Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al. [8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al. [9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM) [12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al. [11] presented new asymmetric and symmetric conservative forms of time metrics and
Space adaptation syndrome: multiple etiological factors and individual differences
NASA Technical Reports Server (NTRS)
Lackner, J. R.; DiZio, P.
1991-01-01
Space motion sickness is a significant operational concern in the American and Soviet space programs. Nearly 70% of all astronauts and cosmonauts are affected to some degree during their first several days of flight. It is now beginning to appear that space motion sickness like terrestrial motion sickness is the consequence of multiple etiological factors. As we come to understand basic mechanisms of spatial orientation and sensory-motor adaptation we can begin to predict etiological factors in different motion environments. Individuals vary greatly in the extent to which they are susceptible to these different factors. However, individuals seem to be relatively self-consistent in terms of their rates of adaptation to provocative stimulation and their retention of adaptation. Attempts to relate susceptibility to motion sickness during the microgravity phases of parabolic flight maneuvers to vestibular function under 1G and 0G test conditions are described.
Finite Size Effects on the Real-Space Pair Distribution Function of Nanoparticles
Gilbert, Benjamin
2008-10-01
The pair distribution function (PDF) method is a powerful approach for the analysis of the structure of nanoparticles. An important approximation used in nanoparticle PDF simulations is the incorporation of a form factor describing nanoparticle size and shape. The precise effect of the form factor on the PDF is determined by both particle shape and structure if these characteristics are both anisotropic and correlated. The correct incorporation of finite size effects is important for distinguishing and quantifying the structural consequences of small particle size in nanomaterials.
Ackleh, Azmy S; Farkas, József Z; Li, Xinyu; Ma, Baoling
2015-01-01
We consider a size-structured population model where individuals may be recruited into the population at different sizes. First- and second-order finite difference schemes are developed to approximate the solution of the model. The convergence of the approximations to a unique weak solution is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Gurtin-McCamy-type size-structured model in the weak* topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. Finally, we provide an example where supercritical Hopf-bifurcation occurs in the limiting single state-at-birth model and we apply the second-order numerical scheme to show that such bifurcation also occurs in the distributed model. PMID:24890735
Guan, Wei; Hu, Hengshan; He, Xiao
2009-04-01
Monopole acoustic logs in a homogeneous fluid-saturated porous formation can be simulated by the real-axis integration (RAI) method to analytically solve Biot's equations [(1956a) J. Acoust. Soc. Am. 28, 168-178; (1956b) J. Acoust. Soc. Am. 28, 179-191; (1962) J. Appl. Phys. 33, 1482-1498], which govern the wave propagation in poro-elastic media. Such analytical solution generally is impossible for horizontally stratified formations which are common in reality. In this paper, a velocity-stress finite-difference time-domain (FDTD) algorithm is proposed to solve the problem. This algorithm considers both the low-frequency viscous force and the high-frequency inertial force in poro-elastic media, extending its application to a wider frequency range compared to existing algorithms which are only valid in the low-frequency limit. The perfectly matched layer (PML) is applied as an absorbing boundary condition to truncate the computational region. A PML technique without splitting the fields is extended to the poro-elastic wave problem. The FDTD algorithm is validated by comparisons against the RAI method in a variety of formations with different velocities and permeabilities. The acoustic logs in a horizontally stratified porous formation are simulated with the proposed FDTD algorithm. PMID:19354370
High-Accuracy Finite Difference Equations for Simulation of Photonic Structures
Hadley, G.R.
1999-04-23
Progress towards the development of such algorithms as been reported for waveguide analysis'-3and vertical-cavity laser simulation. In all these cases, the higher accuracy order was obtained for a single spatial dimension. More recently, this concept was extended to differencing of the Helmholtz Equation on a 2-D grid, with uniform regions treated to 4th order and dielectric interfaces to 3'd order5. No attempt was made to treat corners properly. In this talk I will describe the extension of this concept to allow differencing of the Helmholtz Equation on a 2-D grid to 6* order in uniform regions and 5* order at dielectric interfaces. In addition, the first known derivation of a finite difference equation for a dielectric comer that allows correct satisfaction of all boundary conditions will be presented. This equation is only accurate to first order, but as will be shown, results in simulations that are third-order-accurate. In contrast to a previous approach3 that utilized a generalized Douglas scheme to increase the accuracy order of the difference second derivative, the present method invokes the Helmholtz Equation itself to convert derivatives of high order in a single direction into mixed
Light Scattering by Gaussian Particles: A Solution with Finite-Difference Time Domain Technique
NASA Technical Reports Server (NTRS)
Sun, W.; Nousiainen, T.; Fu, Q.; Loeb, N. G.; Videen, G.; Muinonen, K.
2003-01-01
The understanding of single-scattering properties of complex ice crystals has significance in atmospheric radiative transfer and remote-sensing applications. In this work, light scattering by irregularly shaped Gaussian ice crystals is studied with the finite-difference time-domain (FDTD) technique. For given sample particle shapes and size parameters in the resonance region, the scattering phase matrices and asymmetry factors are calculated. It is found that the deformation of the particle surface can significantly smooth the scattering phase functions and slightly reduce the asymmetry factors. The polarization properties of irregular ice crystals are also significantly different from those of spherical cloud particles. These FDTD results could provide a reference for approximate light-scattering models developed for irregular particle shapes and can have potential applications in developing a much simpler practical light scattering model for ice clouds angular-distribution models and for remote sensing of ice clouds and aerosols using polarized light. (copyright) 2003 Elsevier Science Ltd. All rights reserved.
Implicit Predictor-Corrector finite difference scheme for the ideal MHD simulations
NASA Astrophysics Data System (ADS)
Tsai, T.; Yu, H.; Lai, S.
2012-12-01
A innovative simulation code for ideal magnetohydrodynamics (MHD) is developed. We present a multiple-dimensional MHD code based on high-order implicit predictor-corrector finite difference scheme (high-order IPCFD scheme). High-order IPCFD scheme adopts high-order predictor-corrector scheme for the time integration and high-order central difference method as the spatial derivative solver. We use Elimination-of-the-Runoff-Errors (ERE) technology to avoid the numerical oscillations and numerical instability in the simulation results. In one-dimensional MHD problem, our simulation results show good agreement with the Brio & Wu MHD shock tube problem. The divergent B constraint remains fully satisfied, that is the divergent B equals to zero throughout the simulation. When solving the two-dimensional (2D) linear wave in MHD plasma, we clearly obtain the group-velocity Friedrichs diagrams of the MHD waves. Here we demonstrate 2D simulation results of rotor problem, Orszag-Tang vortex system, vortex type K-H instability, and kink type K-H instability by using our IPCFD MHD code and discuss the advantage of our simulation code.
Finite difference time domain calculation of transients in antennas with nonlinear loads
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent
1991-01-01
Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
NASA Astrophysics Data System (ADS)
Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi
2010-08-01
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.