Existing second order accurate finite difference methods have been evaluated for application to finite deformation transient dynamic response problems in solids. A new second order accurate finite difference technique has been developed. This is a ...

... order accurate finite difference technique has ... concepts of contour differences and MacCormack ... beams, with nonstructured masses and stiffened ...

A finite difference for elastic waves is introduced. The model is based on the first order system of

The present investigation is concerned with a fourth order accurate finite difference method and its

... Accession Number : ADA035698. Title : A Balanced Expansion Technique for Constructing Accurate Finite Difference Advection Schemes. ...

... Scheme for the Dynamic Response of Non-Linear Crush Zone Type ... accurate solutions for different boundary conditions. ... in the numerical solution. ...

A new procedure, called the Balanced Expansion Technique (BET), is employed to construct accurate finite difference advection schemes that, for the model equation considered, are neutrally stable. By applying BET systematically, the phase error can be mad...

Disclosed are exemplary finite difference methods for electromagnetically simulating planar multilayer structures. The exemplary finite difference methods simulate multilayer planes by combining the admittance matrices of single plane pairs and equivalent circuit models for such single plane pairs based on ...

This paper presents a class of new explicit and implicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws. These highly nonlinear schemes are obtained by applying a nonoscillatory first ...

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 electr...

... and three even-order accurate schemes -- III, IV, and V -- on the C staggered grid. ... Distribution Statement : APPROVED FOR PUBLIC RELEASE. ...

In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows

Figure. 1 shows the staggered mesh system for the spatial finite-difference formulation. In the staggered grid, the discretization of equation. (12) yields ...

... procedure utilizes explicit second order accurate finite difference methods applied to the conservation law form of the steady inviscid flow equations ...

... procedure utilizes explicit second order accurate finite difference methods applied to the conservation law form of the steady inviscid flow equations ...

... next to a hard surface in linear acoustics should be replaced with a more accurate ... one-dimensional shocked acoustic waves in ducts.85 ,M ...

A mesoscale model capable of treating variable terrain is described herein. The model, based on the hydrostatic and anelastic approximations, has been developed with a primary goal of providing, in real time, physically realistic and accurate wind fields ...

[25] G. A. Sod, A Survey of Several Finite Difference Methods for Systems of Non-linear Hyperbolic Conservation. Laws, J. Comput. Phys., Vol. 27, pp. ...

The finite-volume and finite-difference implementations of high-order accurate essentially non-oscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined f...

In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation, they use an i...

A numerical procedure was developed to compute the inviscid super/hypersonic flow fields about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equatio...

The goal of this project is to accurately predict the high altitude wave energy generated by low altitude VLF sources. We applied full-wave finite difference numerical models of the electromagnetic fields in both time and frequency domain to compute the V...

A reduced quadratic finite element method on quadrilaterals is developed for discretizing the capillary equation in regular and irregular domains. Newton's method is used to solve the resulting set of nonlinear equations for the capillary surface. Numerical experiments are conducted for square and elliptical capillaries in order to compare this high-order method to a ...

A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency ...

An explicit finite difference algorithm for the solution of quasi-linear divergence free multidimensional hyperbolic systems. The method consists of four steps per time level. The resulting scheme is fourth order accurate in both space and time though the...

... Title : Finite Element, Finite Difference, and Finite Volume Methods: Examples and their Comparisons. Descriptive Note : Final rept. Jan-Jul 95,. ...

We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and di...

One of the important phenomena that thermal-hydraulic codes such as RELAP5 must accurately calculate is heat transfer between a fluid and solid. Currently all thermal-hydraulic safety codes use the finite-difference technique to solve the transient conduction equation. This paper will examine the effect of different nodalization ...

Elementary descriptions of finite element and finite difference methods are given while the finite volume method is briefly overviewed. Examples illustrating finite element and finite difference methods are worked out. Finally, comparisons of these ...

The utility of the finite-element Galerkin technique in advection-diffusion flow problems is examined by comparison with several finite-difference schemes in one dimension. The calculations show that for relatively coarse grids, finite-element solutions are either comparable to or significantly better than those obtained from the ...

The solution to the Helmholtz equation, encountered in nuclear reactor theory, is obtained with the finite element technique, employing linear and quadratic Lagrange and cubic Hermite interpolation polynomials, and compared with the classical finite difference result. Transforming the Helmholtz equation into a weak form, the ...

Seismic monitoring requires accurate source characterization in real time. Accurate 3D earth models are essential for accurate predictions of seismic observables and source characterization. While recovering the true earth structure has always been the go...

In this paper, a nodal method applicable to fast reactor diffusion theory analysis has been developed. This method has been shown to be accurate and efficient in comparison to highly optimized finite difference techniques. The use of an analytic solution to the diffusion equation as a means of determining accurate ...

The increased power of computers and computer codes makes the use of nonlinear dynamic finite element analyses attractive for use as a tool used in the design and certification of radioactive material transportation packages. For this analysis technique to be acceptable it must be demonstrated. The technique has the ability to accurately capture the ...

Radon-222 diffusion in an anhydrous andesitic melt was investigated. The melts were glass discs formed artificially from melted volcanic materials. Solutions of the relevant diffusion equations were done by the explicit finite difference method. Results were compared to analytical solutions reported in the literature and good agreement was found. We have ...

A finite element model of turbulent motion and diffusiom in the atmospheric planetary boundary layer is presented. In preliminary results the behavior of the planetary boundary layer agrees well with the available data. The proposed simple model is more economical and efficient than the complicated existing finite difference models ...

The finite difference time domain (FDTD) method is an important tool in numerical electromagnetic simulation. There are many ways to construct a finite difference approximation such as the Taylor series expansion theorem, the filtering theory, etc. This paper aims to provide the comparison between the Taylor ...

This report deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a h...

A high-order compact finite difference scheme combined with the temporal extrapolation technique is investigated for the fourth-order fractional diffusion-wave system in this paper. The solvability, stability and convergence of the scheme are analyzed simultaneously by the energy method. Numerical experiments show that the proposed compact scheme is more ...

Millimeter and sub-millimeter wave three-dimensional open dielectric structures are characterized using the Finite Difference Time Domain (FDTD) technique. The use of FDTD method allows for the accurate characterization of these components over a very wid...

A computational plasma aerodynamics model is developed to study the performance of an experimental laser propelled lightcraft. The computational methodology is based on a time-accurate, three-dimensional, finite-difference, chemically reacting, unstructur...

Second- and fourth-order accurate finite-difference approximations of the equations governing a free surface autobarotropic fluid are compared with each other and with a second-order approximation on a one-half mesh. It is concluded that once the mesh siz...

Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate ENO scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. T...

A computer code has been written for a general finite difference solution procedure of the incompressible boundary layer equations on a body of revolution. The procedure, a fourth-order accurate extension of Keller's Box Method, is capable of treating lam...

acoustic and convective wave speeds. Although it is possi- ble to avoid this problem altogether ...... for the finite-difference metrics had to be ..... Duct Flow. Simulation. To more accurately simulate the flow entering the impeller, while also ...

The parabolic approximation method is widely recognized as useful for accurately analyzing and predicting sound transmission intensity in diverse ocean environments. One reason for its attractiveness is that solutions are marched in range, thereby avoidin...

Numerical methods are investigated for solving a system of continuity equations that contain linear and nonlinear chemistry as source and sink terms. It is shown that implicit, finite-difference approximations, when applied to the chemical kinetic terms, yield accurate results wh...

A previously developed local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation) has been modified to utilize a more accurate windward finite difference procedure in ...

... Tel-Aviv Ulni'.ersity Dist- ibutiOn I and Availabiit:y Codes Institute for Computer Applications in Science and Engineering . .... Dist Special ...

... Title : An Investigation of the Method of Finite Elements with Accuracy Comparisons to the Method of Finite Differences for Solution of the Transient ...

For what is believed to be the first time, the central adjoint variable method (CAVM) is applied to the sensitivity analysis of photonic devices using the finite-difference time-domain (FDTD) technique. The FDTD-CAVM technique obtains accurate sensitivities of any desired response with respect to the different design parameters. Our ...

A locally conformal finite-difference time-domain (LC-FDTD) scheme is proposed to accomplish the challenging task of accurately modelling electromagnetic scattering phenomena generated by the wave interaction with metallic and/or dielectric objects having complex geometries. The proposed technique is first validated by evaluating the resonant frequency of ...

Conventional numerical differentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simplified to one of the finite difference approximations based on Taylor series, and closed-form expressions of these finite difference formulas have already been presented. In this paper, we ...

A new method for solving Maxwell's equations in the time domain on two-dimensional irregular grids has been developed. The method is based on finite-difference approximations to Ampere's and Faraday's laws in both their differential and integral forms. These difference approximations are derived, in part, using ...

An accurate and unconditionally stable explicit finite difference scheme for 1D diffusion equations is derived from the lattice Boltzmann method with rest particles. The system of the lattice Boltzmann equations for the distribution of the number of the fictitious particles is rewritten as a four-level explicit ...

This report combines two ideas from the basis of finite volume and finite element numerical methods to form a accurate discontinuous finite element solution for the two dimensional Euler equations.

This paper defines discretizations of the divergence and flux operators that produce symmetric, positive-definite, and accurate approximations to steady-state diffusion problems. Because discontinuous material properties and highly distorted grids are allowed, the flux operator, rather than the gradient, is used as a fundamental operator to be discretized. Resulting ...

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 ...

... most accurate beam elements in the ABAQUS ... The beam finite element representation is shown in ... The elements of the finite element representation ...

This paper develops and analyses individual construction aspects of an efficient and accurate finite

... The finite-element method is very powerful and flexible to model complex ... the region of interest can be subdivided into finite elements accurately. ...

A numerical procedure was developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equation...

A numerical procedure has been developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second order accurate finite difference scheme is used to integrate the three dimensional Euler equ...

The goal of this project is accurate prediction of high-altitude fields generated by low-altitude VLF sources to understand their influence on radiation belt dynamics. We applied a full-wave finite difference numerical model of the electromagnetic fields ...

Accurate and reliable electromagnetic modeling codes, which may be specific or general purpose, help Lawrence Livermore National Laboratory carry out its research. However, a need for a three-dimensional coded prompted the development of a finite element code. MAXWELL3 is a general electromagnetic modeling code (solves the differential Maxwell equations in ...

A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an ...

The need for sensitivities in particular applications is becoming increasingly important in problems such as optimal design or control. In this study, the authors use ADIFOR to generate derivative code for TACO2D, a finite element heat transfer code. The study of TACO2D indicates that ADIFOR-generated derivatives yield accurate derivatives at a fraction of ...

... Title : THE EFFECT OF FINITE DIFFERENCES ON THE GROWTH RATES OF UNSTABLE WAVES IN A SIMPLE BAROCLINIC MODEL. ...

... Title : ON THE FORMULATION OF FINITE DIFFERENCE ANALOGUES OF THE DIRICHLET PROBLEM FOR POISSON'S EQUATION. ...

Calculate computational work required to model heat conduction using finite differences with explicit timestepping.

... the finite difference solutions to the ... the weak sense solution to the ... DIFFERENTIAL EQUATIONS, STOCHASTIC PROCESSES, MEASURE ...

... FINITE DIFFERENCE SOLUTION OF THE LAMINAR COMPRESSIBLE BOUNDARY LAYER EQUATIONS IN THE VON MISES VARIABLES WITH ...

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady

... Descriptors : *FINITE DIFFERENCE THEORY, *THERMAL DIFFUSION, *THERMAL CONDUCTIVITY, *PARTIAL DIFFERENTIAL EQUATIONS ...

... OF THE APPLICATION OF FINITE -DIFFERENCE TECHNIQUES TO ULF WAVES IN A SPHERICAL MODEL INHOMOGENEOUS, ANISOTROPIC ...

... 2001-11 High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD Chi-Wang Shu ...

... ADA390653. Title : High Order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD. ...

Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular ...

We present an exponential time integrator in conjunction with a finite volume discretisation in space for simulating transport by advection and diffusion including chemical reactions in highly heterogeneous porous media representative of geological reservoirs. These numerical integrators are based on the variation of constants solution and solving the linear system exactly. ...

this paper are defined in Section 3. Existing finite difference schemes in a regular grid system are checked for violations of the conservation properties in Section 4. In Section 5 we analyze existing staggered grid schemes and propose a new class of conservative schemes. Finite difference schemes for a collocated ...

A key to reducing the risks and costs 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. Pre-stack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar-wave equation using ...

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 ...

Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with ...

An algorithm is presented to solve the elastic-wave equation by replacing the partial differentials with finite differences. It enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models. The space derivatives are calculated using discrete convolution sums, while the time derivatives are replaced by ...

The process of combined conduction and radiation in a large, heat-generating, dry particulate bed in sudden contact with a semi-infinite solid is studied analytically by a successive approximation method and numerically by a finite difference method. The transient behavior of the system, in particular, the behavior of the temperature at the particulate ...

A semianalytic method developed earlier couples the overburden energy-balance solution to reservoir equations by a single differential equation applicable at the reservoir-overburden boundary. The semianalytic method is extended in this work to allow temperatures at the reservoir-overburden boundary to decrease, as well as increase, with time. Computer calculations on several test problmes show a ...

Sensitivity analysis quantifies the dependence of a system's behavior on the parameters that could possibly affect the dynamics. Calculation of sensitivities of stochastic chemical systems using Kinetic Monte Carlo and finite-difference-based methods is not only computationally intensive, but direct calculation of sensitivities by ...

Violation of energy conservation in Poisson-Boltzmann molecular dynamics, due to the limited accuracy and precision of numerical methods, is a major bottleneck preventing its wide adoption in biomolecular simulations. We explored the ideas of enforcing interface conditions by the immerse interface method and of removing charge singularity to improve the finite-difference ...

Very basic principles are reviewed in this lecture: The concepts of Finite Volumes and numerical stability (implicit and explicit).

... The finite element models for the staggered vertical grids did not perform up to their possibilities due to the boundary elements. ...

... Modifications were made on Jordan's (1985) Galerkin finite element approximation for two staggered grids. Comparisons ...

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. ...

Important characteristics of many oxidation reactions are associated with the infusion of oxygen into the metal in advance of the oxide--metal interface. The calculation of the resulting oxygen profiles generally involves the solution to the diffusion equation for a finite system with a moving boundary. While it was possible to obtain at least approximate analytical ...

There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is ...

This paper presents a practical numerical method for incompressible flows by combining the concept of the CIP method and the finite volume formulation. The method, namely VSIAM3 (Volume/Surface Integrated Average based Multi-Moment Method), employs two integrated averages, i.e. Volume Integrated Average (VIA) and Surface Integrated Average (SIA) which are generically called ...

... behavior using the Finite Difference method; examples of non ... DIFFERENCE EQUATIONS, THESES, HEAT EXCHANGERS, FINITE DIFFERENCE ...

Numerical simulations of submicron Co extruded elliptical dots were performed to illustrate the relative importance of different physical parameters on the switching behavior in the easy direction. Shape, size, magnetic moment magnitude and crystalline anisotropy, both magnitude and distribution, were varied. The simulation includes calculation of the magnetostatic, exchange ...

... Abstract : The computer program FIDO (Finite Difference Ocean acoustic model) computes the real acoustic pressure via a finite- difference ...

... Title : A Generalized Finite-Difference Formulation for the US Geological Survey Modular Three-Dimensional Finite-Difference Ground-Water Flow ...

One-pass three-dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two-pass migration, in variable velocity media. Conventional one-pass 3-D migration, done with the method of finite-difference inline and crossline splitting, however, creates large errors in imaging complex structures due to paraxial ...

A numerical formulation of high-order accuracy, based on variational methods, is proposed for the solution of multi-dimensional diffusion-convection type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that very ...

The finite element method is applied to several simple cases of steady flow of a perfect, incompressible fluid. It is shown that the finite element representation accurately reflects the behavior of the classical flow equations. Finite elements form the b...

... current and cancelled), Joint Staff and ... of Test Problems for Finite Element/Finite Difference Programs for ... Calculations using ABAQUS for the pinned ...

This paper presents unconditionally stable and conformal FDTD schemes which are based on the alternating-direction implicit finite difference time domain (ADI-FDTD) method for accurate modeling of perfectly electric conducting (PEC) objects. The proposed schemes are formulated within the framework of the matrix-vector notation of the ...

Three finite-element methods for calculating the drag coefficient for a sphere in steady, laminar flow at low or intermediate Reynolds numbers are compared. The flow equations are solved either for the stream function and the vorticity or for the velocity and pressure, with different boundary conditions applied far from the sphere. It is found that ...

Artificial neural network (ANN) methods have been researched extensively within the nuclear community for applications in systems control, diagnostics, and signal processing. We consider here the use of multilayer perceptron ANNs as an alternative to finite-difference and finite-element methods for obtaining solutions to neutron diffusion problems. This ...

By obtaining the approximate solution to the advection-diffusion equation in both one- and two-dimensions, for both purely advective (hyperbolic) and advection-dominated flows, and by comparison to finite difference results, we demonstrate, contrary to the admonition put forth by Strang and Fix (1973), that the Galerkin finite element ...

A straightforward procedure is described for accurately creating an incident focused light pulse in the 3-D finite-difference time-domain (FDTD) electromagnetic simulation of the image space of an aplanatic converging lens. In this procedure, the focused light pulse is approximated by a finite sum of plane waves, and each plane wave is ...

A simplified procedure based on the results of finite element analysis is proposed for the design of semicircular lugs under repeated axial loading. Maximum lug stresses corresponding to different failure modes are obtained by multiplying nominal stresses by stress correction factors given by design curves. Analytical limitations associated with the ...

The elliptic Monge-Amp�re equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail.In this article we build a finite ...

This paper presents a comparison of four different three-dimensional (3D) magnetotelluric (MT) modelling algorithms in terms of accuracy and computation time. Three of them use the finite difference method while the last one uses the edge finite-element method. The modelling algorithms are analysed with respect to ...

Accurate representation of different kinds of wave motion is essential for numerical models of the atmosphere, but is sensitive to details of the discretization. In this paper, numerical dispersion relations are computed for different vertical discretizations of the compressible Euler equations and compared with the analytical ...

The overall objectives of this CRADA were to assist Halliburton in analyzing a composite bridge plug and to determine why their original design was failing in the field. In Phase 1, finite element analyses were done on the original composite slip design and several alternative designs. The composite slip was the component in the bridge plug that was failing. The ...