Explicit formula of finite difference method to estimate human peripheral tissue temperatures during exposure to severe cold stress.

Science.gov (United States)

Khanday, M A; Hussain, Fida

2015-02-01

During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25 °C, 20 °C, 15 °C, 5 °C, -5 °C and -10 °C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure. Copyright © 2014 Elsevier Ltd. All rights reserved.

Synthesis of hydrocode and finite element technology for large deformation Lagrangian computation

International Nuclear Information System (INIS)

Goudreau, G.L.; Hallquist, J.O.

1979-08-01

Large deformation engineering analysis at Lawrence Livermore Laboratory has benefited from a synthesis of computational technology from the finite difference hydrocodes of the scientific weapons community and the structural finite element methodology of engineering. Two- and three-dimensional explicit and implicit Lagrangian continuum codes have been developed exploiting the strengths of each. The explicit methodology primarily exploits the primitive constant stress (or one point integration) brick element. Similarity and differences with the integral finite difference method are discussed. Choice of stress and finite strain measures, and selection of hour glass viscosity are also considered. The implicit codes also employ a Cauchy formulation, with Newton iteration and a symmetric tangent matrix. A library of finite strain material routines includes hypoelastic/plastic, hyperelastic, viscoelastic, as well as hydrodynamic behavior. Arbitrary finite element topology and a general slide-line treatment significantly extends Lagrangian hydrocode application. Computational experience spans weapons and non-weapons applications

A practical implicit finite-difference method: examples from seismic modelling

International Nuclear Information System (INIS)

Liu, Yang; Sen, Mrinal K

2009-01-01

We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method

Visualization of elastic wavefields computed with a finite difference code

Energy Technology Data Exchange (ETDEWEB)

Larsen, S. [Lawrence Livermore National Lab., CA (United States); 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.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

An implicit finite-difference operator for the Helmholtz equation

KAUST Repository

Chu, Chunlei

2012-07-01

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

A General Symbolic PDE Solver Generator: Beyond Explicit Schemes

Directory of Open Access Journals (Sweden)

K. Sheshadri

2003-01-01

Full Text Available This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1 arbitrary number of dependent variables, (2 arbitrary dimensionality, and (3 arbitrary geometry, as well as (4 developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.

Moving magnets in a micromagnetic finite-difference framework

Science.gov (United States)

Rissanen, Ilari; Laurson, Lasse

2018-05-01

We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.

Parallel Computation on Multicore Processors Using Explicit Form of the Finite Element Method and C++ Standard Libraries

Directory of Open Access Journals (Sweden)

Rek Václav

2016-11-01

Full Text Available In this paper, the form of modifications of the existing sequential code written in C or C++ programming language for the calculation of various kind of structures using the explicit form of the Finite Element Method (Dynamic Relaxation Method, Explicit Dynamics in the NEXX system is introduced. The NEXX system is the core of engineering software NEXIS, Scia Engineer, RFEM and RENEX. It has the possibilities of multithreaded running, which can now be supported at the level of native C++ programming language using standard libraries. Thanks to the high degree of abstraction that a contemporary C++ programming language provides, a respective library created in this way can be very generalized for other purposes of usage of parallelism in computational mechanics.

COVE-1: a finite difference creep collapse code for oval fuel pin cladding material

International Nuclear Information System (INIS)

Mohr, C.L.

1975-03-01

COVE-1 is a time-dependent incremental creep collapse code that estimates the change in ovality of a fuel pin cladding tube. It uses a finite difference method of solving the differential equations which describe the deflection of the tube walls as a function of time. The physical problem is nonlinear, both with respect to geometry and material properties, which requires the use of an incremental, analytical, path-dependent solution. The application of this code is intended primarily for tubes manufactured from Zircaloy. Therefore, provision has been made to include some of the effects of anisotropy in the flow equations for inelastic incremental deformations. 10 references. (U.S.)

Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

Directory of Open Access Journals (Sweden)

I. Amirali

2014-01-01

Full Text Available 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.

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad

2013-01-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

On the Stability of the Finite Difference based Lattice Boltzmann Method

KAUST Repository

El-Amin, Mohamed

2013-06-01

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

Development of Multi-Scale Finite Element Analysis Codes for High Formability Sheet Metal Generation

International Nuclear Information System (INIS)

Nnakamachi, Eiji; Kuramae, Hiroyuki; Ngoc Tam, Nguyen; Nakamura, Yasunori; Sakamoto, Hidetoshi; Morimoto, Hideo

2007-01-01

In this study, the dynamic- and static-explicit multi-scale finite element (F.E.) codes are developed by employing the homogenization method, the crystalplasticity constitutive equation and SEM-EBSD measurement based polycrystal model. These can predict the crystal morphological change and the hardening evolution at the micro level, and the macroscopic plastic anisotropy evolution. These codes are applied to analyze the asymmetrical rolling process, which is introduced to control the crystal texture of the sheet metal for generating a high formability sheet metal. These codes can predict the yield surface and the sheet formability by analyzing the strain path dependent yield, the simple sheet forming process, such as the limit dome height test and the cylindrical deep drawing problems. It shows that the shear dominant rolling process, such as the asymmetric rolling, generates ''high formability'' textures and eventually the high formability sheet. The texture evolution and the high formability of the newly generated sheet metal experimentally were confirmed by the SEM-EBSD measurement and LDH test. It is concluded that these explicit type crystallographic homogenized multi-scale F.E. code could be a comprehensive tool to predict the plastic induced texture evolution, anisotropy and formability by the rolling process and the limit dome height test analyses

Explicit dynamics for numerical simulation of crack propagation by the extended finite element method

International Nuclear Information System (INIS)

Menouillard, T.

2007-09-01

Computerized simulation is nowadays an integrating part of design and validation processes of mechanical structures. Simulation tools are more and more performing allowing a very acute description of the phenomena. Moreover, these tools are not limited to linear mechanics but are developed to describe more difficult behaviours as for instance structures damage which interests the safety domain. A dynamic or static load can thus lead to a damage, a crack and then a rupture of the structure. The fast dynamics allows to simulate 'fast' phenomena such as explosions, shocks and impacts on structure. The application domain is various. It concerns for instance the study of the lifetime and the accidents scenario of the nuclear reactor vessel. It is then very interesting, for fast dynamics codes, to be able to anticipate in a robust and stable way such phenomena: the assessment of damage in the structure and the simulation of crack propagation form an essential stake. The extended finite element method has the advantage to break away from mesh generation and from fields projection during the crack propagation. Effectively, crack is described kinematically by an appropriate strategy of enrichment of supplementary freedom degrees. Difficulties connecting the spatial discretization of this method with the temporal discretization of an explicit calculation scheme has then been revealed; these difficulties are the diagonal writing of the mass matrix and the associated stability time step. Here are presented two methods of mass matrix diagonalization based on the kinetic energy conservation, and studies of critical time steps for various enriched finite elements. The interest revealed here is that the time step is not more penalizing than those of the standard finite elements problem. Comparisons with numerical simulations on another code allow to validate the theoretical works. A crack propagation test in mixed mode has been exploited in order to verify the simulation

Complete permutation Gray code implemented by finite state machine

Directory of Open Access Journals (Sweden)

Li Peng

2014-09-01

Full Text Available An enumerating method of complete permutation array is proposed. The list of n! permutations based on Gray code defined over finite symbol set Z(n = {1, 2, …, n} is implemented by finite state machine, named as n-RPGCF. An RPGCF can be used to search permutation code and provide improved lower bounds on the maximum cardinality of a permutation code in some cases.

Syrthes thermal code and Estet or N3S fluid mechanics codes coupling; Couplage du code de thermique Syrthes et des codes de mecanique des fluides N3S et ou Estet

Energy Technology Data Exchange (ETDEWEB)

Peniguel, C [Electricite de France (EDF), 78 - Chatou (France). Direction des Etudes et Recherches; Rupp, I [SIMULOG, 78 - Guyancourt (France)

1997-06-01

EDF has developed numerical codes for modeling the conductive, radiative and convective thermal transfers and their couplings in complex industrial configurations: the convection in a fluid is solved by Estet in finite volumes or N3S in finite elements, the conduction is solved by Syrthes and the wall-to-wall thermal radiation is modelled by Syrthes with the help of a radiosity method. Syrthes controls the different heat exchanges which may occur between fluid and solid domains, using an explicit iterative method. An extension of Syrthes has been developed in order to allow the consideration of configurations where several fluid codes operate simultaneously, using ``message passing`` tools such as PVM (Parallel Virtual Machine) and the Calcium code coupler developed at EDF. Application examples are given

Algebraic coding theory over finite commutative rings

CERN Document Server

Dougherty, Steven T

2017-01-01

This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.

Implicit finite-difference simulations of seismic wave propagation

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

Implicit finite-difference simulations of seismic wave propagation

KAUST Repository

Chu, Chunlei

2012-03-01

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

Science.gov (United States)

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.

A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

Science.gov (United States)

Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen

2017-06-01

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

A simple finite-difference scheme for handling topography with the first-order wave equation

NARCIS (Netherlands)

Mulder, W.A.; Huiskes, M.J.

2017-01-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the

Numerical stability of finite difference algorithms for electrochemical kinetic simulations: Matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods and typical problems involving mixed boundary conditions

DEFF Research Database (Denmark)

Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter

1995-01-01

The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....

Aspects of Finite Element Simulation of Axi-Symmetric Hydromechanical Deep Drawing

DEFF Research Database (Denmark)

Jensen, Morten Rikard; Olovsson, Lars; Danckert, Joachim

1999-01-01

A new approach for the Finite Element modelling of the hydromechanical deep drawing process is evaluated. In the model a Finite Difference approximation of Reynold’s equation is solved for the fluid flow between the blank and the draw die in the flange region. The approach is implemented...... as a contact algorithm in an explicit Finite Element code, Exhale2D. The developed model is verified against experiments and good agreement is obtained. It is concluded that the developed model is a promising approach for simulating the hydromechanical deep drawing process using the Finite Element Method....

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Directory of Open Access Journals (Sweden)

Peng Jiang

2013-01-01

Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

Science.gov (United States)

Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk

2018-05-01

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

KAUST Repository

Gerke, Kirill M.

2018-01-17

Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

International Nuclear Information System (INIS)

Ackroyd, R.T.

1987-01-01

A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)

Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods

International Nuclear Information System (INIS)

Baker, A.R.

1982-07-01

A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

Science.gov (United States)

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

Development of explicit solution scheme for the MATRA-LMR code and test calculation

International Nuclear Information System (INIS)

Jeong, H. Y.; Ha, K. S.; Chang, W. P.; Kwon, Y. M.; Jeong, K. S.

2003-01-01

The local blockage in a subassembly of a liquid metal reactor is of particular importance because local sodium boiling could occur at the downstream of the blockage and integrity of the fuel clad could be threatened. The explicit solution scheme of MATRA-LMR code is developed to analyze the flow blockage in a subassembly of a liquid metal cooled reactor. In the present study, the capability of the code is extended to the analysis of complete blockage of one or more subchannels. The results of the developed solution scheme shows very good agreement with the results obtained from the implicit scheme for the experiments of flow channel without any blockage. The applicability of the code is also evaluated for two typical experiments in a blocked channel. Through the sensitivity study, it is shown that the explicit scheme of MATRA-LMR predicts the flow and temperature profile after blockage reasonably if the effect of wire is suitably modeled. The simple assumption in wire-forcing function is effective for the un-blocked case or for the case of blockage with lower velocity. A different type of wire-forcing function describing the velocity reduction after blockage or an accurate distributed resistance model is required for more improved predictions

Acoustic, finite-difference, time-domain technique development

International Nuclear Information System (INIS)

Kunz, K.

1994-01-01

A close analog exists between the behavior of sound waves in an ideal gas and the radiated waves of electromagnetics. This analog has been exploited to obtain an acoustic, finite-difference, time-domain (AFDTD) technique capable of treating small signal vibrations in elastic media, such as air, water, and metal, with the important feature of bending motion included in the behavior of the metal. This bending motion is particularly important when the metal is formed into sheets or plates. Bending motion does not have an analog in electromagnetics, but can be readily appended to the acoustic treatment since it appears as a single additional term in the force equation for plate motion, which is otherwise analogous to the electromagnetic wave equation. The AFDTD technique has been implemented in a code architecture that duplicates the electromagnetic, finite-difference, time-domain technique code. The main difference in the implementation is the form of the first-order coupled differential equations obtained from the wave equation. The gradient of pressure and divergence of velocity appear in these equations in the place of curls of the electric and magnetic fields. Other small changes exist as well, but the codes are essentially interchangeable. The pre- and post-processing for model construction and response-data evaluation of the electromagnetic code, in the form of the TSAR code at Lawrence Livermore National Laboratory, can be used for the acoustic version. A variety of applications is possible, pending validation of the bending phenomenon. The applications include acoustic-radiation-pattern predictions for a submerged object; mine detection analysis; structural noise analysis for cars; acoustic barrier analysis; and symphonic hall/auditorium predictions and speaker enclosure modeling

Modeling seismic wave propagation using staggered-grid mimetic finite differences

Directory of Open Access Journals (Sweden)

Freysimar Solano-Feo

2017-04-01

Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.

FINELM: a multigroup finite element diffusion code. Part II

International Nuclear Information System (INIS)

Davierwalla, D.M.

1981-05-01

The author presents the axisymmetric case in cylindrical coordinates for the finite element multigroup neutron diffusion code, FINELM. The numerical acceleration schemes incorporated viz. the Lebedev extrapolations and the coarse mesh rebalancing, space collapsing, are discussed. A few benchmark computations are presented as validation of the code. (Auth.)

On the raising and lowering difference operators for eigenvectors of the finite Fourier transform

International Nuclear Information System (INIS)

Atakishiyeva, M K; Atakishiyev, N M

2015-01-01

We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)

Integral and finite difference inequalities and applications

CERN Document Server

Pachpatte, B G

2006-01-01

The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.- Contains a variety of inequalities discovered which find numero

3-D spherical harmonics code FFT3 by the finite Fourier transformation method

International Nuclear Information System (INIS)

Kobayashi, K.

1997-01-01

In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)

Imaging x-ray sources at a finite distance in coded-mask instruments

International Nuclear Information System (INIS)

Donnarumma, Immacolata; Pacciani, Luigi; Lapshov, Igor; Evangelista, Yuri

2008-01-01

We present a method for the correction of beam divergence in finite distance sources imaging through coded-mask instruments. We discuss the defocusing artifacts induced by the finite distance showing two different approaches to remove such spurious effects. We applied our method to one-dimensional (1D) coded-mask systems, although it is also applicable in two-dimensional systems. We provide a detailed mathematical description of the adopted method and of the systematics introduced in the reconstructed image (e.g., the fraction of source flux collected in the reconstructed peak counts). The accuracy of this method was tested by simulating pointlike and extended sources at a finite distance with the instrumental setup of the SuperAGILE experiment, the 1D coded-mask x-ray imager onboard the AGILE (Astro-rivelatore Gamma a Immagini Leggero) mission. We obtained reconstructed images of good quality and high source location accuracy. Finally we show the results obtained by applying this method to real data collected during the calibration campaign of SuperAGILE. Our method was demonstrated to be a powerful tool to investigate the imaging response of the experiment, particularly the absorption due to the materials intercepting the line of sight of the instrument and the conversion between detector pixel and sky direction

Construction method of QC-LDPC codes based on multiplicative group of finite field in optical communication

Science.gov (United States)

Huang, Sheng; Ao, Xiang; Li, Yuan-yuan; Zhang, Rui

2016-09-01

In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate ( BER) is 10-6, in the same simulation environment, the net coding gain ( NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.

W7-X vacuum and finite-β magnetic field structure resolved with the HINT 3D equilibrium code

International Nuclear Information System (INIS)

Hayashi, T.; Merkel, P.; Nuehrenberg, J.; Schwenn, U.

1994-01-01

The 3D equilibrium code HINT allows the direct investigation of finite-β effects on sizes and phases of islands in genuinely 3D configurations like the W7-X stellarator planned by the Max-Planck-Institut fuer Plasmaphysik in Germany. The code does not require the existence of nested flux surfaces. This, in contrast to the inverse formulation used in the VMEC code, leads to a considerably more complex computational goal. The HINT code combines some crucial features reducing the numerical problems and the computational effort to such an extent as to allow computation of 3D equilibria at finite-β with magnetic islands. The code is based on a two-step procedure: Starting from a given B and an initial pressure, the iteration technique for the pressure advancement is differencing in an artificial time with an explicit 4th order scheme, or - alternatively for resolving the island topology - field lines starting from all gridpoints are followed long enough to allow pressure equalization along these. B.∇p 0, for fixed B. In a second step, p is kept fixed and B is advanced with an artificial time for solving ∇p - jxB = 0 under the constraint of vanishing toroidal current J. The differential equations are discretized in space with 4th order difference approximations on an Eulerian grid spanned by a rectangular box whose toroidal rotation law follows the W7-X geometry. The two sub-iteration steps are repeated until the force balance is satisfied to an appropriate accuracy. The boundaries (where the boundary conditions are prescribed) are far enough away from the last closed magnetic surface, thus guaranteeing the motion of the plasma column not being constrained by the boundary conditions. Due to the stellarator symmetry in the toroidal direction only half of an equilibrium period is computed, using modified periodic boundary conditions guaranteeing the 4th order of the spatial discretization. (author) 5 refs., 4 figs

A finite range coupled channel Born approximation code

International Nuclear Information System (INIS)

Nagel, P.; Koshel, R.D.

1978-01-01

The computer code OUKID calculates differential cross sections for direct transfer nuclear reactions in which multistep processes, arising from strongly coupled inelastic states in both the target and residual nuclei, are possible. The code is designed for heavy ion reactions where full finite range and recoil effects are important. Distorted wave functions for the elastic and inelastic scattering are calculated by solving sets of coupled differential equations using a Matrix Numerov integration procedure. These wave functions are then expanded into bases of spherical Bessel functions by the plane-wave expansion method. This approach allows the six-dimensional integrals for the transition amplitude to be reduced to products of two one-dimensional integrals. Thus, the inelastic scattering is treated in a coupled channel formalism while the transfer process is treated in a finite range born approximation formalism. (Auth.)

A General Symbolic PDE Solver Generator: Explicit Schemes

Directory of Open Access Journals (Sweden)

K. Sheshadri

2003-01-01

Full Text Available A symbolic solver generator to deal with a system of partial differential equations (PDEs in functions of an arbitrary number of variables is presented; it can also handle arbitrary domains (geometries of the independent variables. Given a system of PDEs, the solver generates a set of explicit finite-difference methods to any specified order, and a Fourier stability criterion for each method. For a method that is stable, an iteration function is generated symbolically using the PDE and its initial and boundary conditions. This iteration function is dynamically generated for every PDE problem, and its evaluation provides a solution to the PDE problem. A C++/Fortran 90 code for the iteration function is generated using the MathCode system, which results in a performance gain of the order of a thousand over Mathematica, the language that has been used to code the solver generator. Examples of stability criteria are presented that agree with known criteria; examples that demonstrate the generality of the solver and the speed enhancement of the generated C++ and Fortran 90 codes are also presented.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

Science.gov (United States)

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Explicit dynamics for numerical simulation of crack propagation by the extended finite element method; Dynamique explicite pour la simulation numerique de propagation de fissure par la methode des elements finis etendus

Energy Technology Data Exchange (ETDEWEB)

Menouillard, T

2007-09-15

Computerized simulation is nowadays an integrating part of design and validation processes of mechanical structures. Simulation tools are more and more performing allowing a very acute description of the phenomena. Moreover, these tools are not limited to linear mechanics but are developed to describe more difficult behaviours as for instance structures damage which interests the safety domain. A dynamic or static load can thus lead to a damage, a crack and then a rupture of the structure. The fast dynamics allows to simulate 'fast' phenomena such as explosions, shocks and impacts on structure. The application domain is various. It concerns for instance the study of the lifetime and the accidents scenario of the nuclear reactor vessel. It is then very interesting, for fast dynamics codes, to be able to anticipate in a robust and stable way such phenomena: the assessment of damage in the structure and the simulation of crack propagation form an essential stake. The extended finite element method has the advantage to break away from mesh generation and from fields projection during the crack propagation. Effectively, crack is described kinematically by an appropriate strategy of enrichment of supplementary freedom degrees. Difficulties connecting the spatial discretization of this method with the temporal discretization of an explicit calculation scheme has then been revealed; these difficulties are the diagonal writing of the mass matrix and the associated stability time step. Here are presented two methods of mass matrix diagonalization based on the kinetic energy conservation, and studies of critical time steps for various enriched finite elements. The interest revealed here is that the time step is not more penalizing than those of the standard finite elements problem. Comparisons with numerical simulations on another code allow to validate the theoretical works. A crack propagation test in mixed mode has been exploited in order to verify the simulation

An induction-based magnetohydrodynamic 3D code for finite magnetic Reynolds number liquid-metal flows in fusion blankets

International Nuclear Information System (INIS)

Kawczynski, Charlie; Smolentsev, Sergey; Abdou, Mohamed

2016-01-01

Highlights: • A new induction-based magnetohydrodynamic code was developed using a finite difference method. • The code was benchmarked against purely hydrodynamic and MHD flows for low and finite magnetic Reynolds number. • Possible applications of the new code include liquid-metal MHD flows in the breeder blanket during unsteady events in the plasma. - Abstract: Most numerical analysis performed in the past for MHD flows in liquid-metal blankets were based on the assumption of low magnetic Reynolds number and involved numerical codes that utilized electric potential as the main electromagnetic variable. One limitation of this approach is that such codes cannot be applied to truly unsteady processes, for example, MHD flows of liquid-metal breeder/coolant during unsteady events in plasma, such as major plasma disruptions, edge-localized modes and vertical displacements, when changes in plasmas occur at millisecond timescales. Our newly developed code MOONS (Magnetohydrodynamic Object-Oriented Numerical Solver) uses the magnetic field as the main electromagnetic variable to relax the limitations of the low magnetic Reynolds number approximation for more realistic fusion reactor environments. The new code, written in Fortran, implements a 3D finite-difference method and is capable of simulating multi-material domains. The constrained transport method was implemented to evolve the magnetic field in time and assure that the magnetic field remains solenoidal within machine accuracy at every time step. Various verification tests have been performed including purely hydrodynamic flows and MHD flows at low and finite magnetic Reynolds numbers. Test results have demonstrated very good accuracy against known analytic solutions and other numerical data.

An induction-based magnetohydrodynamic 3D code for finite magnetic Reynolds number liquid-metal flows in fusion blankets

Energy Technology Data Exchange (ETDEWEB)

Kawczynski, Charlie; Smolentsev, Sergey, E-mail: sergey@fusion.ucla.edu; Abdou, Mohamed

2016-11-01

Highlights: • A new induction-based magnetohydrodynamic code was developed using a finite difference method. • The code was benchmarked against purely hydrodynamic and MHD flows for low and finite magnetic Reynolds number. • Possible applications of the new code include liquid-metal MHD flows in the breeder blanket during unsteady events in the plasma. - Abstract: Most numerical analysis performed in the past for MHD flows in liquid-metal blankets were based on the assumption of low magnetic Reynolds number and involved numerical codes that utilized electric potential as the main electromagnetic variable. One limitation of this approach is that such codes cannot be applied to truly unsteady processes, for example, MHD flows of liquid-metal breeder/coolant during unsteady events in plasma, such as major plasma disruptions, edge-localized modes and vertical displacements, when changes in plasmas occur at millisecond timescales. Our newly developed code MOONS (Magnetohydrodynamic Object-Oriented Numerical Solver) uses the magnetic field as the main electromagnetic variable to relax the limitations of the low magnetic Reynolds number approximation for more realistic fusion reactor environments. The new code, written in Fortran, implements a 3D finite-difference method and is capable of simulating multi-material domains. The constrained transport method was implemented to evolve the magnetic field in time and assure that the magnetic field remains solenoidal within machine accuracy at every time step. Various verification tests have been performed including purely hydrodynamic flows and MHD flows at low and finite magnetic Reynolds numbers. Test results have demonstrated very good accuracy against known analytic solutions and other numerical data.

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1975-10-01

The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level

Implicit time-dependent finite different algorithm for quench simulation

International Nuclear Information System (INIS)

Koizumi, Norikiyo; Takahashi, Yoshikazu; Tsuji, Hiroshi

1994-12-01

A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)

Using finite mixture models in thermal-hydraulics system code uncertainty analysis

Energy Technology Data Exchange (ETDEWEB)

Carlos, S., E-mail: scarlos@iqn.upv.es [Department d’Enginyeria Química i Nuclear, Universitat Politècnica de València, Camí de Vera s.n, 46022 València (Spain); Sánchez, A. [Department d’Estadística Aplicada i Qualitat, Universitat Politècnica de València, Camí de Vera s.n, 46022 València (Spain); Ginestar, D. [Department de Matemàtica Aplicada, Universitat Politècnica de València, Camí de Vera s.n, 46022 València (Spain); Martorell, S. [Department d’Enginyeria Química i Nuclear, Universitat Politècnica de València, Camí de Vera s.n, 46022 València (Spain)

2013-09-15

Highlights: • Best estimate codes simulation needs uncertainty quantification. • The output variables can present multimodal probability distributions. • The analysis of multimodal distribution is performed using finite mixture models. • Two methods to reconstruct output variable probability distribution are used. -- Abstract: Nuclear Power Plant safety analysis is mainly based on the use of best estimate (BE) codes that predict the plant behavior under normal or accidental conditions. As the BE codes introduce uncertainties due to uncertainty in input parameters and modeling, it is necessary to perform uncertainty assessment (UA), and eventually sensitivity analysis (SA), of the results obtained. These analyses are part of the appropriate treatment of uncertainties imposed by current regulation based on the adoption of the best estimate plus uncertainty (BEPU) approach. The most popular approach for uncertainty assessment, based on Wilks’ method, obtains a tolerance/confidence interval, but it does not completely characterize the output variable behavior, which is required for an extended UA and SA. However, the development of standard UA and SA impose high computational cost due to the large number of simulations needed. In order to obtain more information about the output variable and, at the same time, to keep computational cost as low as possible, there has been a recent shift toward developing metamodels (model of model), or surrogate models, that approximate or emulate complex computer codes. In this way, there exist different techniques to reconstruct the probability distribution using the information provided by a sample of values as, for example, the finite mixture models. In this paper, the Expectation Maximization and the k-means algorithms are used to obtain a finite mixture model that reconstructs the output variable probability distribution from data obtained with RELAP-5 simulations. Both methodologies have been applied to a separated

A simple finite-difference scheme for handling topography with the second-order wave equation

NARCIS (Netherlands)

Mulder, W.A.

2017-01-01

The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free

A finite element code for electric motor design

Science.gov (United States)

Campbell, C. Warren

1994-01-01

FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.

Finite difference time domain modelling of particle accelerators

International Nuclear Information System (INIS)

Jurgens, T.G.; Harfoush, F.A.

1989-03-01

Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs

Coupling of the SYRTHES thermal code with the ESTET or N3S fluid mechanics codes; Couplage du code de thermique SYRTHES et des codes de mecanique des fluides ESTET ou N3S

Energy Technology Data Exchange (ETDEWEB)

Peniguel, C [Electricite de France (EDF), 78 - Chatou (France). Direction des Etudes et Recherches; Rupp, I [Simulog, 78 (France)

1998-12-31

Thermal aspects take place in several industrial applications in which Electricite de France (EdF) is concerned. In most cases, several physical phenomena like conduction, radiation and convection are involved in thermal transfers. The aim of this paper is to present a numerical tool adapted to industrial configurations and which uses the coupling between fluid convection (resolved with ESTET in finite-volumes or with N3S in finite-elements) and radiant heat transfers between walls (resolved with SYRTHES using a radiosity method). SYRTHES manages the different thermal exchanges that can occur between fluid and solid domains thanks to an explicit iterative method. An extension of SYRTHES has been developed which allows to take into account simultaneously several fluid codes using `message passing` computer tools like Parallel Virtual Machine (PVM) and the code coupling software CALCIUM developed by the Direction of Studies and Researches (DER) of EdF. Various examples illustrate the interest of such a numerical tool. (J.S.) 12 refs.

Coupling of the SYRTHES thermal code with the ESTET or N3S fluid mechanics codes; Couplage du code de thermique SYRTHES et des codes de mecanique des fluides ESTET ou N3S

Energy Technology Data Exchange (ETDEWEB)

Peniguel, C. [Electricite de France (EDF), 78 - Chatou (France). Direction des Etudes et Recherches; Rupp, I. [Simulog, 78 (France)

1997-12-31

Thermal aspects take place in several industrial applications in which Electricite de France (EdF) is concerned. In most cases, several physical phenomena like conduction, radiation and convection are involved in thermal transfers. The aim of this paper is to present a numerical tool adapted to industrial configurations and which uses the coupling between fluid convection (resolved with ESTET in finite-volumes or with N3S in finite-elements) and radiant heat transfers between walls (resolved with SYRTHES using a radiosity method). SYRTHES manages the different thermal exchanges that can occur between fluid and solid domains thanks to an explicit iterative method. An extension of SYRTHES has been developed which allows to take into account simultaneously several fluid codes using `message passing` computer tools like Parallel Virtual Machine (PVM) and the code coupling software CALCIUM developed by the Direction of Studies and Researches (DER) of EdF. Various examples illustrate the interest of such a numerical tool. (J.S.) 12 refs.

Computational Aero-Acoustic Using High-order Finite-Difference Schemes

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2007-01-01

are solved using the in-house flow solver EllipSys2D/3D which is a second-order finite volume code. The acoustic solution is found by solving the acoustic equations using high-order finite difference schemes. The incompressible flow equations and the acoustic equations are solved at the same time levels......In this paper, a high-order technique to accurately predict flow-generated noise is introduced. The technique consists of solving the viscous incompressible flow equations and inviscid acoustic equations using a incompressible/compressible splitting technique. The incompressible flow equations...

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1977-11-01

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P 1 ) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently

Residual fatigue life evaluation of rail at squats seeds using 3D explicit finite element analysis

NARCIS (Netherlands)

Deng, X.; Naeimi, M.; Li, Z.; Qian, Z.

2014-01-01

A modeling procedure to predict the residual fatigue life of rail at squats seeds is developed in this article. Two models are involved: a 3D explicit Finite Element (FE) model to compute the stress and strain at squats in rail, and the J-S fatigue damage model to determine the residual fatigue life

Three-dimensional modeling with finite element codes

Energy Technology Data Exchange (ETDEWEB)

Druce, R.L.

1986-01-17

This paper describes work done to model magnetostatic field problems in three dimensions. Finite element codes, available at LLNL, and pre- and post-processors were used in the solution of the mathematical model, the output from which agreed well with the experimentally obtained data. The geometry used in this work was a cylinder with ports in the periphery and no current sources in the space modeled. 6 refs., 8 figs.

SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

Energy Technology Data Exchange (ETDEWEB)

Stone, C.M.

1997-07-01

SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived from the transient dynamic code PRONTO 2D. The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided. 43 refs., 22 figs.

Mechanical modelling of PCI with FRAGEMA and CEA finite element codes

International Nuclear Information System (INIS)

Joseph, J.; Bernard, Ph.; Atabek, R.; Chantant, M.

1983-01-01

In the framework of their common program, CEA and FRAGEMA have undertaken the mechanical modelization of PCI. In the first step two different codes, TITUS and VERDON, have been tested by FRAGEMA and CEA respectively. Whereas the two codes use a finite element method to describe the thermomechanical behaviour of a fuel element, input models are not the same for the two codes: to take into account the presence of cracks in UO 2 , an axisymmetric two dimensional mesh pattern and the Druecker-Prager criterion are used in VERDON and a 3D equivalent method in TITUS. Two rods have been studied with these two methods: PRISCA 04bis and PRISCA 104 which were ramped in SILOE. The results show that the stresses and strains are the same with the two codes. These methods are further applied to the complete series of the common ramp test rods program of FRAGEMA and CEA. (author)

Structural dynamics in LMFBR containment analysis. A brief survey of computational methods and codes

International Nuclear Information System (INIS)

Chang, Y.W.

1977-01-01

This paper gives a brief survey of the computational methods and codes available for LMFBR containment analysis. The various numerical methods commonly used in the computer codes are compared. It provides the reactor engineers to up-to-date information on the development of structural dynamics in LMFBR containment analysis. It can also be used as a basis for the selection of the numerical method in the future code development. First, the commonly used finite-difference expressions in the Lagrangian codes will be compared. Sample calculations will be used as a basis for discussing and comparing the accuracy of the various finite-difference representations. The distortion of the meshes will also be compared; the techniques used for eliminating the numerical instabilities will be discussed and compared using examples. Next, the numerical methods used in the Eulerian formulation will be compared, first among themselves and then with the Lagrangian formulations. Special emphasis is placed on the effect of mass diffusion of the Eulerian calculation on the propagation of discontinuities. Implicit and explicit numerical integrations will be discussed and results obtained from these two techniques will be compared. Then, the finite-element methods are compared with the finite-difference methods. The advantages and disadvantages of the two methods will be discussed in detail, together with the versatility and ease of application of the method to containment analysis having complex geometries. It will also be shown that the finite-element equations for a constant-pressure fluid element is identical to the finite-difference equations using contour integrations. Finally, conclusions based on this study will be given

Interactive finite difference preprocessor for three-dimensional fluid flow systems. [PREFLO

Energy Technology Data Exchange (ETDEWEB)

Kleinstreuer, C. (Rensselaer Polytechnic Inst., Troy, NY); Patterson, M.R.

1981-06-01

A preprocessor, called PREFLO, consisting of data processing modules combined with a flexible finite difference grid generator is described. This economical, interactive computer code is a useful research tool contributing significantly to the accurate analysis and modeling of large and/or geometrically complex flow systems. PREFLO (PREprocessor for fluid FLOw problems), written in FORTRAN IV, consists of four modules which in turn call various subroutines. The main programs accomplish the following tasks: (1) system identification and selection of appropriate finite difference algorithms; (2) input devices for storage of natural flow boundaries; (3) interactive generation of finite difference meshes and display of computer graphics; (4) preparation of all data files for the source program. The computation of the velocity field near a power plant site is outlined to illustrate the capabilities and application of PREFLO.

Verification of the DEFENS Code through the CANDU Problems with Rectangular Geometry

Energy Technology Data Exchange (ETDEWEB)

Ryu, Eun Hyun; Song, Yong Mann [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2014-05-15

Because a finite element method (FEM) based code can explicitly describe the core geometry, it has an advantage in a core analysis such as the CANDU core. For the reactor physics calculation in the CANDU core, the RFSP-IST code is used for the core analysis, and the RFSP-IST code is based on the finite difference method (FDM). Thus, the convergence with the mesh size and the geometry shape is not consistent. In this research, the convergence with the mesh size of the RFSP code is investigated, a method comparison between the FEM and FDM is done for the usefulness of the FEM based code with the same rectangular geometry. The target problems are the imaginary core and initial core with the uniform parameter, which is produced by the WIMS-IST code based on the parameters of Wolsong unit 1. The reference solution is generated by running the multi-group calculation of the McCARD code. In this research, the convergence of the RFSP code is investigated and the DEFENS code is compared with the RFSP code for the imaginary and initial cores. The accuracy of the DEFENS code and the disadvantage of the RFSP code are verified.

Prediction of residual stress using explicit finite element method

Directory of Open Access Journals (Sweden)

W.A. Siswanto

2015-12-01

Full Text Available This paper presents the residual stress behaviour under various values of friction coefficients and scratching displacement amplitudes. The investigation is based on numerical solution using explicit finite element method in quasi-static condition. Two different aeroengine materials, i.e. Super CMV (Cr-Mo-V and Titanium alloys (Ti-6Al-4V, are examined. The usage of FEM analysis in plate under normal contact is validated with Hertzian theoretical solution in terms of contact pressure distributions. The residual stress distributions along with normal and shear stresses on elastic and plastic regimes of the materials are studied for a simple cylinder-on-flat contact configuration model subjected to normal loading, scratching and followed by unloading. The investigated friction coefficients are 0.3, 0.6 and 0.9, while scratching displacement amplitudes are 0.05 mm, 0.10 mm and 0.20 mm respectively. It is found that friction coefficient of 0.6 results in higher residual stress for both materials. Meanwhile, the predicted residual stress is proportional to the scratching displacement amplitude, higher displacement amplitude, resulting in higher residual stress. It is found that less residual stress is predicted on Super CMV material compared to Ti-6Al-4V material because of its high yield stress and ultimate strength. Super CMV material with friction coefficient of 0.3 and scratching displacement amplitude of 0.10 mm is recommended to be used in contact engineering applications due to its minimum possibility of fatigue.

A code for obtaining temperature distribution by finite element method

International Nuclear Information System (INIS)

Bloch, M.

1984-01-01

The ELEFIB Fortran language computer code using finite element method for calculating temperature distribution of linear and two dimensional problems, in permanent region or in the transient phase of heat transfer, is presented. The formulation of equations uses the Galerkin method. Some examples are shown and the results are compared with other papers. The comparative evaluation shows that the elaborated code gives good values. (M.C.K.) [pt

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II. [LMFBR

Energy Technology Data Exchange (ETDEWEB)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1977-11-01

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.

TACO: a finite element heat transfer code

International Nuclear Information System (INIS)

Mason, W.E. Jr.

1980-02-01

TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code

Recent progress on weight distributions of cyclic codes over finite fields

Directory of Open Access Journals (Sweden)

Hai Q. Dinh

2015-01-01

Full Text Available Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions.

Hydrological model in STEALTH 2-D code

International Nuclear Information System (INIS)

Hart, R.; Hofmann, R.

1979-10-01

Porous media fluid flow logic has been added to the two-dimensional version of the STEALTH explicit finite-difference code. It is a first-order hydrological model based upon Darcy's Law. Anisotropic permeability can be prescribed through x and y directional permeabilities. The fluid flow equations are formulated for either two-dimensional translation symmetry or two-dimensional axial symmetry. The addition of the hydrological model to STEALTH is a first step toward analyzing a physical system's response to the coupling of thermal, mechanical, and fluid flow phenomena

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

KAUST Repository

Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai

2012-01-01

It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

KAUST Repository

Osman, Hossam Omar

2012-06-17

It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

Use of a finite difference code for the prediction of the ability of sub-floor ventilation strategies to reduce indoor radon concentrations

International Nuclear Information System (INIS)

Cohilis, P.; Wouters, P.; L'Heureux, D.

1992-01-01

This paper concerns the use of a numerical code, based on the finite difference method, for the evaluation of 222 Rn mitigation strategies in dwellings. It is supposed that 222 Rn transport from soil into a dwelling occurs mainly by pressure-driven air flow. The program calculates the pressure fields under the buildings, supposing a laminar air flow in the soil and adopting the steady-state condition. The simple data structure of the code allows one to describe even complex configurations in an easy way. Clear alphanumerical and graphical outputs are delivered. The calculations presented in the paper illustrate the possibilities of the program. An interesting consequence of the linear assumption implicit in the equations of the model is considered, and a comparison with laboratory measurements is presented. (author)

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

Science.gov (United States)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Optimized Finite-Difference Coefficients for Hydroacoustic Modeling

Science.gov (United States)

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.

GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations.

Science.gov (United States)

Strbac, V; Pierce, D M; Vander Sloten, J; Famaey, N

2017-12-01

Finite element (FE) simulations are increasingly valuable in assessing and improving the performance of biomedical devices and procedures. Due to high computational demands such simulations may become difficult or even infeasible, especially when considering nearly incompressible and anisotropic material models prevalent in analyses of soft tissues. Implementations of GPGPU-based explicit FEs predominantly cover isotropic materials, e.g. the neo-Hookean model. To elucidate the computational expense of anisotropic materials, we implement the Gasser-Ogden-Holzapfel dispersed, fiber-reinforced model and compare solution times against the neo-Hookean model. Implementations of GPGPU-based explicit FEs conventionally rely on single-point (under) integration. To elucidate the expense of full and selective-reduced integration (more reliable) we implement both and compare corresponding solution times against those generated using underintegration. To better understand the advancement of hardware, we compare results generated using representative Nvidia GPGPUs from three recent generations: Fermi (C2075), Kepler (K20c), and Maxwell (GTX980). We explore scaling by solving the same boundary value problem (an extension-inflation test on a segment of human aorta) with progressively larger FE meshes. Our results demonstrate substantial improvements in simulation speeds relative to two benchmark FE codes (up to 300[Formula: see text] while maintaining accuracy), and thus open many avenues to novel applications in biomechanics and medicine.

An Explicit Construction of a sequence of codes attaining the Tsfasman-Vladut-Zink Bound:The first steps

DEFF Research Database (Denmark)

Høholdt, Tom; Voss, Cornelia

1997-01-01

We present a sequence of codes attaining the Tsfasman-Vladut-Zink bound. The construction is based on the tower of Artin-Schreier extensions described by Garcia and Stichtenoth (1995). We also determine the dual codes. The first steps of the constructions are explicitly given as generator matrices...

The finite-difference time-domain method for electromagnetics with Matlab simulations

CERN Document Server

Elsherbeni, Atef Z

2016-01-01

This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices.

Quantum Kronecker sum-product low-density parity-check codes with finite rate

Science.gov (United States)

Kovalev, Alexey A.; Pryadko, Leonid P.

2013-07-01

We introduce an ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many thus defined codes have a finite rate and limited-weight stabilizer generators, an analog of classical low-density parity-check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have a wider range of parameters; in particular, they can have a higher rate while preserving the estimated error threshold.

Quantum mean-field decoding algorithm for error-correcting codes

International Nuclear Information System (INIS)

Inoue, Jun-ichi; Saika, Yohei; Okada, Masato

2009-01-01

We numerically examine a quantum version of TAP (Thouless-Anderson-Palmer)-like mean-field algorithm for the problem of error-correcting codes. For a class of the so-called Sourlas error-correcting codes, we check the usefulness to retrieve the original bit-sequence (message) with a finite length. The decoding dynamics is derived explicitly and we evaluate the average-case performance through the bit-error rate (BER).

Improvement of implicit finite element code performance in deep drawing simulations by dynamics contributions

NARCIS (Netherlands)

Meinders, Vincent T.; van den Boogaard, Antonius H.; Huetink, Han

2003-01-01

To intensify the use of implicit finite element codes for solving large scale problems, the computation time of these codes has to be decreased drastically. A method is developed which decreases the computational time of implicit codes by factors. The method is based on introducing inertia effects

FEAST: a two-dimensional non-linear finite element code for calculating stresses

International Nuclear Information System (INIS)

Tayal, M.

1986-06-01

The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%

A framework for developing finite element codes for multi-disciplinary applications.

OpenAIRE

Dadvand, Pooyan

2007-01-01

The world of computing simulation has experienced great progresses in recent years and requires more exigent multidisciplinary challenges to satisfy the new upcoming demands. Increasing the importance of solving multi-disciplinary problems makes developers put more attention to these problems and deal with difficulties involved in developing software in this area. Conventional finite element codes have several difficulties in dealing with multi-disciplinary problems. Many of these codes are d...

Finite element methods in a simulation code for offshore wind turbines

Science.gov (United States)

Kurz, Wolfgang

1994-06-01

Offshore installation of wind turbines will become important for electricity supply in future. Wind conditions above sea are more favorable than on land and appropriate locations on land are limited and restricted. The dynamic behavior of advanced wind turbines is investigated with digital simulations to reduce time and cost in development and design phase. A wind turbine can be described and simulated as a multi-body system containing rigid and flexible bodies. Simulation of the non-linear motion of such a mechanical system using a multi-body system code is much faster than using a finite element code. However, a modal representation of the deformation field has to be incorporated in the multi-body system approach. The equations of motion of flexible bodies due to deformation are generated by finite element calculations. At Delft University of Technology the simulation code DUWECS has been developed which simulates the non-linear behavior of wind turbines in time domain. The wind turbine is divided in subcomponents which are represented by modules (e.g. rotor, tower etc.).

Numerical homogenization of concrete microstructures without explicit meshes

International Nuclear Information System (INIS)

Sanahuja, Julien; Toulemonde, Charles

2011-01-01

Life management of electric hydro or nuclear power plants requires to estimate long-term concrete properties on facilities, for obvious safety and serviceability reasons. Decades-old structures are foreseen to be operational for several more decades. As a large number of different concrete formulations are found in EDF facilities, empirical models based on many experiments cannot be an option for a large fleet of power plant buildings. To build predictive models, homogenization techniques offer an appealing alternative. To properly upscale creep, especially at long term, a rather precise description of the microstructure is required. However, the complexity of the morphology of concrete poses several challenges. In particular, concrete is formulated to maximize the packing density of the granular skeleton, leading to aggregates spanning several length scales with small inter particle spacings. Thus, explicit meshing of realistic concrete microstructures is either out of reach of current meshing algorithms or would produce a number of degrees of freedom far higher than the current generic FEM codes capabilities. This paper proposes a method to deal with complex matrix-inclusions microstructures such as the ones encountered at the mortar or concrete scales, without explicitly meshing them. The microstructure is superimposed to an independent mesh, which is a regular Cartesian grid. This inevitably yields so called 'gray elements', spanning across multiple phases. As the reliability of the estimate of the effective properties highly depends on the behavior affected to these gray elements, special attention is paid to them. As far as the question of the solvers is concerned, generic FEM codes are found to lack efficiency: they cannot reach high enough levels of discretization with classical free meshes, and they do not take advantage of the regular structure of the mesh. Thus, a specific finite differences/finite volumes solver has been developed. At first, generic off

Development of three-dimensional transport code by the double finite element method

International Nuclear Information System (INIS)

Fujimura, Toichiro

1985-01-01

Development of a three-dimensional neutron transport code by the double finite element method is described. Both of the Galerkin and variational methods are adopted to solve the problem, and then the characteristics of them are compared. Computational results of the collocation method, developed as a technique for the vaviational one, are illustrated in comparison with those of an Ssub(n) code. (author)

On the equivalence of cyclic and quasi-cyclic codes over finite fields

Directory of Open Access Journals (Sweden)

Kenza Guenda

2017-07-01

Full Text Available This paper studies the equivalence problem for cyclic codes of length $p^r$ and quasi-cyclic codes of length $p^rl$. In particular, we generalize the results of Huffman, Job, and Pless (J. Combin. Theory. A, 62, 183--215, 1993, who considered the special case $p^2$. This is achieved by explicitly giving the permutations by which two cyclic codes of prime power length are equivalent. This allows us to obtain an algorithm which solves the problem of equivalency for cyclic codes of length $p^r$ in polynomial time. Further, we characterize the set by which two quasi-cyclic codes of length $p^rl$ can be equivalent, and prove that the affine group is one of its subsets.

Finite-difference modeling of commercial aircraft using TSAR

Energy Technology Data Exchange (ETDEWEB)

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.

The weight hierarchies and chain condition of a class of codes from varieties over finite fields

Science.gov (United States)

Wu, Xinen; Feng, Gui-Liang; Rao, T. R. N.

1996-01-01

The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.

Intercomparison of the finite difference and nodal discrete ordinates and surface flux transport methods for a LWR pool-reactor benchmark problem in X-Y geometry

International Nuclear Information System (INIS)

O'Dell, R.D.; Stepanek, J.; Wagner, M.R.

1983-01-01

The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included

FLASH: A finite element computer code for variably saturated flow

International Nuclear Information System (INIS)

Baca, R.G.; Magnuson, S.O.

1992-05-01

A numerical model was developed for use in performance assessment studies at the INEL. The numerical model, referred to as the FLASH computer code, is designed to simulate two-dimensional fluid flow in fractured-porous media. The code is specifically designed to model variably saturated flow in an arid site vadose zone and saturated flow in an unconfined aquifer. In addition, the code also has the capability to simulate heat conduction in the vadose zone. This report presents the following: description of the conceptual frame-work and mathematical theory; derivations of the finite element techniques and algorithms; computational examples that illustrate the capability of the code; and input instructions for the general use of the code. The FLASH computer code is aimed at providing environmental scientists at the INEL with a predictive tool for the subsurface water pathway. This numerical model is expected to be widely used in performance assessments for: (1) the Remedial Investigation/Feasibility Study process and (2) compliance studies required by the US Department of Energy Order 5820.2A

Finite difference time domain solution of electromagnetic scattering on the hypercube

International Nuclear Information System (INIS)

Calalo, R.H.; Lyons, J.R.; Imbriale, W.A.

1988-01-01

Electromagnetic fields interacting with a dielectric or conducting structure produce scattered electromagnetic fields. To model the fields produced by complicated, volumetric structures, the finite difference time domain (FDTD) method employs an iterative solution to Maxwell's time dependent curl equations. Implementations of the FDTD method intensively use memory and perform numerous calculations per time step iteration. The authors have implemented an FDTD code on the California Institute of Technology/Jet Propulsion Laboratory Mark III Hypercube. This code allows to solve problems requiring as many as 2,048,000 unit cells on a 32 node Hypercube. For smaller problems, the code produces solutions in a fraction of the time to solve the same problems on sequential computers

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

Science.gov (United States)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

FEHM, Finite Element Heat and Mass Transfer Code

International Nuclear Information System (INIS)

Zyvoloski, G.A.

2002-01-01

1 - Description of program or function: FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities. 2 - Methods: FEHM uses a preconditioned conjugate gradient solution of coupled linear equations and a fully implicit, fully coupled Newton Raphson solution of nonlinear equations. It has the capability of simulating transport using either a advection/diffusion solution or a particle tracking method. 3 - Restriction on the complexity of the problem: Disk space and machine memory are the only limitations

Numerical study on two-point contact by an explicit integration finite element method : A contribution to the modeling of flange squeal

NARCIS (Netherlands)

Yang, Z.; Li, Z.; Dollevoet, R.P.B.J.; Tournay, H; Grassie, S

2015-01-01

The precise mechanism which activates squeal, especially flange squeal has not been fully explained. The complex non-Hertzian contact and the broad-band high frequency feature bring great challenges to the modelling work of flange squeal. In this paper, an explicit integration finite element method

Advances in dynamic relaxation techniques for nonlinear finite element analysis

International Nuclear Information System (INIS)

Sauve, R.G.; Metzger, D.R.

1995-01-01

Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

Random geometry capability in RMC code for explicit analysis of polytype particle/pebble and applications to HTR-10 benchmark

International Nuclear Information System (INIS)

Liu, Shichang; Li, Zeguang; Wang, Kan; Cheng, Quan; She, Ding

2018-01-01

Highlights: •A new random geometry was developed in RMC for mixed and polytype particle/pebble. •This capability was applied to the full core calculations of HTR-10 benchmark. •Reactivity, temperature coefficient and control rod worth of HTR-10 were compared. •This method can explicitly model different packing fraction of different pebbles. •Monte Carlo code with this method can simulate polytype particle/pebble type reactor. -- Abstract: With the increasing demands of high fidelity neutronics analysis and the development of computer technology, Monte Carlo method is becoming more and more attractive in accurate simulation of pebble bed High Temperature gas-cooled Reactor (HTR), owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. For the double-heterogeneous geometry of pebble bed, traditional Monte Carlo codes can treat it by explicit geometry description. However, packing methods such as Random Sequential Addition (RSA) can only produce a sphere packing up to 38% volume packing fraction, while Discrete Element Method (DEM) is troublesome and also time consuming. Moreover, traditional Monte Carlo codes are difficult and inconvenient to simulate the mixed and polytype particles or pebbles. A new random geometry method was developed in Monte Carlo code RMC to simulate the particle transport in polytype particle/pebble in double heterogeneous geometry systems. This method was verified by some test cases, and applied to the full core calculations of HTR-10 benchmark. The reactivity, temperature coefficient and control rod worth of HTR-10 were compared for full core and initial core in helium and air atmosphere respectively, and the results agree well with the benchmark results and experimental results. This work would provide an efficient tool for the innovative design of pebble bed, prism HTRs and molten salt reactors with polytype particles or pebbles using Monte Carlo method.

Anisotropic constitutive equation for use in finite difference wave propagation calculations. [Incorporation into TOODY code

Energy Technology Data Exchange (ETDEWEB)

Swegle, J.W.; Hicks, D.L.

1979-05-01

An anisotropic constitutive relation was incorporated into the Lagrangian finite-difference wavecode TOODY. The details of the implementation of the constitutive relation in the wavecode and an example of its use are discussed. 4 figures, 1 table.

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation

Science.gov (United States)

Ghil, M.; Balgovind, R.

1979-01-01

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

A simple finite-difference scheme for handling topography with the first-order wave equation

Science.gov (United States)

Mulder, W. A.; Huiskes, M. J.

2017-07-01

One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.

Finite element and finite difference methods in electromagnetic scattering

CERN Document Server

Morgan, MA

2013-01-01

This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca

FINELM: a multigroup finite element diffusion code. Part I

International Nuclear Information System (INIS)

Davierwalla, D.M.

1980-12-01

The author presents a two dimensional code for multigroup diffusion using the finite element method. It was realized that the extensive connectivity which contributes significantly to the accuracy, results in a matrix which, although symmetric and positive definite, is wide band and possesses an irregular profile. Hence, it was decided to introduce sparsity techniques into the code. The introduction of the R-Z geometry lead to a great deal of changes in the code since the rotational invariance of the removal matrices in X-Y geometry did not carry over in R-Z geometry. Rectangular elements were introduced to remedy the inability of the triangles to model essentially one dimensional problems such as slab geometry. The matter is discussed briefly in the text in the section on benchmark problems. This report is restricted to the general theory of the triangular elements and to the sparsity techniques viz. incomplete disections. The latter makes the size of the problem that can be handled independent of core memory and dependent only on disc storage capacity which is virtually unlimited. (Auth.)

INGEN: a general-purpose mesh generator for finite element codes

International Nuclear Information System (INIS)

Cook, W.A.

1979-05-01

INGEN is a general-purpose mesh generator for two- and three-dimensional finite element codes. The basic parts of the code are surface and three-dimensional region generators that use linear-blending interpolation formulas. These generators are based on an i, j, k index scheme that is used to number nodal points, construct elements, and develop displacement and traction boundary conditions. This code can generate truss elements (2 modal points); plane stress, plane strain, and axisymmetry two-dimensional continuum elements (4 to 8 nodal points); plate elements (4 to 8 nodal points); and three-dimensional continuum elements (8 to 21 nodal points). The traction loads generated are consistent with the element generated. The expansion--contraction option is of special interest. This option makes it possible to change an existing mesh such that some regions are refined and others are made coarser than the original mesh. 9 figures

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

KAUST Repository

Chu, Chunlei

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.

Finite difference program for calculating hydride bed wall temperature profiles

International Nuclear Information System (INIS)

Klein, J.E.

1992-01-01

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

Structural code benchmarking for the analysis of impact response of nuclear material shipping casks

International Nuclear Information System (INIS)

Glass, R.E.

1984-01-01

The Transportation Technology Center at Sandia National Laboratories has initiated a program to benchmark thermal and structural codes that are available to the nuclear material transportation community. The program consists of the following five phrases: (1) code inventory and review, (2) development of a cask-like set of problems, (3) multiple independent numerical analyses of the problems, (4) transfer of information, and (5) performance of experiments to obtain data for comparison with the numerical analyses. This paper will summarize the results obtained by the independent numerical analyses. The analyses indicate the variability that can be expected both due to differences in user-controlled parameters and from code-to-code differences. The results show that in purely elastic analyses, differences can be attributed to user controlled parameters. Model problems involving elastic/plastic material behavior and large deformations, however, have greater variability with significant differences reported for implicit and explicit integration schemes in finite element programs. This variability demonstrates the need to obtain experimental data to properly benchmark codes utilizing elastic/plastic material models and large deformation capability

Industrial applications of N3S finite element code

International Nuclear Information System (INIS)

Chabard, J.P.; Pot, G.; Martin, A.

1993-12-01

The Research and Development Division of EDF (French utilities) has been working since 1982 on N3S, a 3D finite element code for simulating turbulent incompressible flows (Chabard et al., 1992) which has many applications nowadays dealing with internal flows, thermal hydraulics (Delenne and Pot, 1993), turbomachinery (Combes and Rieutord, 1992). The size of these applications is larger and larger: calculations until 350 000 nodes are in progress (around 2 000 000 unknowns). To achieve so large applications, an important work has been done on the choice of efficient algorithms and on their implementation in order to reduce CPU time and memory allocation. The paper presents the central algorithm of the code, focusing on time and memory optimization. As an illustration, validation test cases and a recent industrial application are discussed. (authors). 11 figs., 2 tabs., 11 refs

Finite element simulation of ironing process under warm conditions

Directory of Open Access Journals (Sweden)

Swadesh Kumar Singh

2014-01-01

Full Text Available Metal forming is one of the most important steps in manufacturing of a large variety of products. Ironing in deep drawing is done by adjusting the clearance between the punch and the die and allow the material flow over the punch. In the present investigation effect of extent of ironing behavior on the characteristics of the product like thickness distribution with respect to temperature was studied. With the help of finite element simulation using explicit finite element code LS-DYNA the stress in the drawn cup were predicted in the drawn cup. To increase the accuracy in the simulation process, numbers of integration points were increased in the thickness direction and it was found that there is very close prediction of finite element results to that of experimental ones.

Axisym finite element code: modifications for pellet-cladding mechanical interaction analysis

International Nuclear Information System (INIS)

Engelman, G.P.

1978-10-01

Local strain concentrations in nuclear fuel rods are known to be potential sites for failure initiation. Assessment of such strain concentrations requires a two-dimensional analysis of stress and strain in both the fuel and the cladding during pellet-cladding mechanical interaction. To provide such a capability in the FRAP (Fuel Rod Analysis Program) codes, the AXISYM code (a small finite element program developed at the Idaho National Engineering Laboratory) was modified to perform a detailed fuel rod deformation analysis. This report describes the modifications which were made to the AXISYM code to adapt it for fuel rod analysis and presents comparisons made between the two-dimensional AXISYM code and the FRACAS-II code. FRACAS-II is the one-dimensional (generalized plane strain) fuel rod mechanical deformation subcode used in the FRAP codes. Predictions of these two codes should be comparable away from the fuel pellet free ends if the state of deformation at the pellet midplane is near that of generalized plane strain. The excellent agreement obtained in these comparisons checks both the correctness of the AXISYM code modifications as well as the validity of the assumption of generalized plane strain upon which the FRACAS-II subcode is based

Multi Scale Finite Element Analyses By Using SEM-EBSD Crystallographic Modeling and Parallel Computing

International Nuclear Information System (INIS)

Nakamachi, Eiji

2005-01-01

A crystallographic homogenization procedure is introduced to the conventional static-explicit and dynamic-explicit finite element formulation to develop a multi scale - double scale - analysis code to predict the plastic strain induced texture evolution, yield loci and formability of sheet metal. The double-scale structure consists of a crystal aggregation - micro-structure - and a macroscopic elastic plastic continuum. At first, we measure crystal morphologies by using SEM-EBSD apparatus, and define a unit cell of micro structure, which satisfy the periodicity condition in the real scale of polycrystal. Next, this crystallographic homogenization FE code is applied to 3N pure-iron and 'Benchmark' aluminum A6022 polycrystal sheets. It reveals that the initial crystal orientation distribution - the texture - affects very much to a plastic strain induced texture and anisotropic hardening evolutions and sheet deformation. Since, the multi-scale finite element analysis requires a large computation time, a parallel computing technique by using PC cluster is developed for a quick calculation. In this parallelization scheme, a dynamic workload balancing technique is introduced for quick and efficient calculations

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Science.gov (United States)

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.

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

Science.gov (United States)

Zuchowski, Loïc; Brun, Michael; De Martin, Florent

2018-05-01

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

Implicit and fully implicit exponential finite difference methods

Indian Academy of Sciences (India)

Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue

Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution

Directory of Open Access Journals (Sweden)

Marco Carbone

2015-02-01

Full Text Available The increasing imperviousness of urban areas reduces the infiltration and evapotranspiration capacity of urban catchments and results in increased runoff. In the last few decades, several solutions and techniques have been proposed to prevent such impacts by restoring the hydrological cycle. A limiting factor in spreading the use of such systems is the lack of proper modelling tools for design, especially for the infiltration processes in a growing medium. In this research, a physically-based model, employing the explicit Finite Volume Method (FVM, is proposed for modelling infiltration into growing media. The model solves a modified version of the Richards equation using a formulation which takes into account the main characteristics of green infrastructure substrates. The proposed model was verified against the HYDRUS-1D software and the comparison of results confirmed the suitability of the proposed model for correctly describing the hydraulic behaviour of soil substrates.

PRIAM: A self consistent finite element code for particle simulation in electromagnetic fields

International Nuclear Information System (INIS)

Le Meur, G.; Touze, F.

1990-06-01

A 2 1/2 dimensional, relativistic particle simulation code is described. A short review of the used mixed finite element method is given. The treatment of the driving terms (charge and current densities), initial, boundary conditions are exposed. Graphical results are shown

A finite landscape?

International Nuclear Information System (INIS)

Acharya, B.S.; Douglas, M.R.

2006-06-01

We present evidence that the number of string/M theory vacua consistent with experiments is finite. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems. (author)

A sliding point contact model for the finite element structures code EURDYN

International Nuclear Information System (INIS)

Smith, B.L.

1986-01-01

A method is developed by which sliding point contact between two moving deformable structures may be incorporated within a lumped mass finite element formulation based on displacements. The method relies on a simple mechanical interpretation of the contact constraint in terms of equivalent nodal forces and avoids the use of nodal connectivity via a master slave arrangement or pseudo contact element. The methodology has been iplemented into the EURDYN finite element program for the (2D axisymmetric) version coupled to the hydro code SEURBNUK. Sample calculations are presented illustrating the use of the model in various contact situations. Effects due to separation and impact of structures are also included. (author)

Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation

International Nuclear Information System (INIS)

Sha, Wei; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng

2007-01-01

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

Evaluation of finite element codes for demonstrating the performance of radioactive material packages in hypothetical accident drop scenarios

International Nuclear Information System (INIS)

Tso, C.F.; Hueggenberg, R.

2004-01-01

Drop testing and analysis are the two methods for demonstrating the performance of packages in hypothetical drop accident scenarios. The exact purpose of the tests and the analyses, and the relative prominence of the two in the license application, may depend on the Competent Authority and will vary between countries. The Finite Element Method (FEM) is a powerful analysis tool. A reliable finite element (FE) code when used correctly and appropriately, will allow a package's behaviour to be simulated reliably. With improvements in computing power, and in sophistication and reliability of FE codes, it is likely that FEM calculations will increasingly be used as evidence of drop test performance when seeking Competent Authority approval. What is lacking at the moment, however, is a standardised method of assessing a FE code in order to determine whether it is sufficiently reliable or pessimistic. To this end, the project Evaluation of Codes for Analysing the Drop Test Performance of Radioactive Material Transport Containers, funded by the European Commission Directorate-General XVII (now Directorate-General for Energy and Transport) and jointly performed by Arup and Gesellschaft fuer Nuklear-Behaelter mbH, was carried out in 1998. The work consisted of three components: Survey of existing finite element software, with a view to finding codes that may be capable of analysing drop test performance of radioactive material packages, and to produce an inventory of them. Develop a set of benchmark problems to evaluate software used for analysing the drop test performance of packages. Evaluate the finite element codes by testing them against the benchmarks This paper presents a summary of this work

Evaluation of finite element codes for demonstrating the performance of radioactive material packages in hypothetical accident drop scenarios

Energy Technology Data Exchange (ETDEWEB)

Tso, C.F. [Arup (United Kingdom); Hueggenberg, R. [Gesellschaft fuer Nuklear-Behaelter mbH (Germany)

2004-07-01

Drop testing and analysis are the two methods for demonstrating the performance of packages in hypothetical drop accident scenarios. The exact purpose of the tests and the analyses, and the relative prominence of the two in the license application, may depend on the Competent Authority and will vary between countries. The Finite Element Method (FEM) is a powerful analysis tool. A reliable finite element (FE) code when used correctly and appropriately, will allow a package's behaviour to be simulated reliably. With improvements in computing power, and in sophistication and reliability of FE codes, it is likely that FEM calculations will increasingly be used as evidence of drop test performance when seeking Competent Authority approval. What is lacking at the moment, however, is a standardised method of assessing a FE code in order to determine whether it is sufficiently reliable or pessimistic. To this end, the project Evaluation of Codes for Analysing the Drop Test Performance of Radioactive Material Transport Containers, funded by the European Commission Directorate-General XVII (now Directorate-General for Energy and Transport) and jointly performed by Arup and Gesellschaft fuer Nuklear-Behaelter mbH, was carried out in 1998. The work consisted of three components: Survey of existing finite element software, with a view to finding codes that may be capable of analysing drop test performance of radioactive material packages, and to produce an inventory of them. Develop a set of benchmark problems to evaluate software used for analysing the drop test performance of packages. Evaluate the finite element codes by testing them against the benchmarks This paper presents a summary of this work.

Star formation, using 3-D explicit Eulerian hydrodynamics

International Nuclear Information System (INIS)

Williams, H.A.

1988-01-01

Evolutions of rapidly rotating, self-gravitating objects initially in axisymmetric equilibrium have been studied using a 3-D Newtonian hydrodynamic computer code with an eye toward understanding angular momentum transport in dynamically evolving protostars. First, a number of evolutions have been modeled using an existing explicit, Eulerian, finite difference code that is accurate to first-order in its spatial differences. The bar-mode dynamic instability has been explored by considering several models with different degrees of compressibility. This instability occurs in models with different degrees of comprresibility. This instability occurs in models having β > β d ≡ 0.27, where β is the ratio of the rotational to the gravitational potential energy. A two-armed spiral, with a well-defined pattern speed and growth rate that match the pattern speed and growth rate predicted by linear theory, develops from each of the axisymmetric equilibria. The models with greater compressibility exhibit spirals which are more tightly wound. As the nonaxisymmetric distortion become large in an extended evolution, the object does not undergo binary fission as had been thought earlier. Instead, the spiral elongates and then wraps up on itself, forming a central pulsating triaxial object surrounded by a more diffuse ring-like disk. Angular momentum and mass are dynamically redistributed by gravitational torques during the evolution, and β is reduced below β d . Since this gravitational-rotational dynamic instability is a general feature of gaseous systems, this study may have application to theta galaxies and to rapidly rotating neutron stars, as well as to protostars

The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion

International Nuclear Information System (INIS)

Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.

2006-01-01

Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)

Codes Over Hyperfields

Directory of Open Access Journals (Sweden)

Atamewoue Surdive

2017-12-01

Full Text Available In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices. We also demonstrate that codes over finite Krasner hyperfields are more interesting for code theory than codes over classical finite fields.

Electron-phonon coupling from finite differences

Science.gov (United States)

Monserrat, Bartomeu

2018-02-01

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

Development of a three-dimensional neutron transport code DFEM based on the double finite element method

International Nuclear Information System (INIS)

Fujimura, Toichiro

1996-01-01

A three-dimensional neutron transport code DFEM has been developed by the double finite element method to analyze reactor cores with complex geometry as large fast reactors. Solution algorithm is based on the double finite element method in which the space and angle finite elements are employed. A reactor core system can be divided into some triangular and/or quadrangular prism elements, and the spatial distribution of neutron flux in each element is approximated with linear basis functions. As for the angular variables, various basis functions are applied, and their characteristics were clarified by comparison. In order to enhance the accuracy, a general method is derived to remedy the truncation errors at reflective boundaries, which are inherent in the conventional FEM. An adaptive acceleration method and the source extrapolation method were applied to accelerate the convergence of the iterations. The code structure is outlined and explanations are given on how to prepare input data. A sample input list is shown for reference. The eigenvalue and flux distribution for real scale fast reactors and the NEA benchmark problems were presented and discussed in comparison with the results of other transport codes. (author)

Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases

NARCIS (Netherlands)

Bulygin, S.; Pellikaan, G.R.; Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C.

2009-01-01

In this short note we show how one can decode linear error-correcting codes up to half the minimum distance via solving a system of polynomial equations over a finite field. We also explicitly present the reduced Gröbner basis for the system considered.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

Science.gov (United States)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Finite mixture models for sensitivity analysis of thermal hydraulic codes for passive safety systems analysis

Energy Technology Data Exchange (ETDEWEB)

Di Maio, Francesco, E-mail: francesco.dimaio@polimi.it [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Nicola, Giancarlo [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Zio, Enrico [Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Chair on System Science and Energetic Challenge Fondation EDF, Ecole Centrale Paris and Supelec, Paris (France); Yu, Yu [School of Nuclear Science and Engineering, North China Electric Power University, 102206 Beijing (China)

2015-08-15

Highlights: • Uncertainties of TH codes affect the system failure probability quantification. • We present Finite Mixture Models (FMMs) for sensitivity analysis of TH codes. • FMMs approximate the pdf of the output of a TH code with a limited number of simulations. • The approach is tested on a Passive Containment Cooling System of an AP1000 reactor. • The novel approach overcomes the results of a standard variance decomposition method. - Abstract: For safety analysis of Nuclear Power Plants (NPPs), Best Estimate (BE) Thermal Hydraulic (TH) codes are used to predict system response in normal and accidental conditions. The assessment of the uncertainties of TH codes is a critical issue for system failure probability quantification. In this paper, we consider passive safety systems of advanced NPPs and present a novel approach of Sensitivity Analysis (SA). The approach is based on Finite Mixture Models (FMMs) to approximate the probability density function (i.e., the uncertainty) of the output of the passive safety system TH code with a limited number of simulations. We propose a novel Sensitivity Analysis (SA) method for keeping the computational cost low: an Expectation Maximization (EM) algorithm is used to calculate the saliency of the TH code input variables for identifying those that most affect the system functional failure. The novel approach is compared with a standard variance decomposition method on a case study considering a Passive Containment Cooling System (PCCS) of an Advanced Pressurized reactor AP1000.

Stability analysis of single-phase thermosyphon loops by finite difference numerical methods

International Nuclear Information System (INIS)

Ambrosini, W.

1998-01-01

In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs

FEHMN 1.0: Finite element heat and mass transfer code

International Nuclear Information System (INIS)

Zyvoloski, G.; Dash, Z.; Kelkar, S.

1991-04-01

A computer code is described which can simulate non-isothermal multiphase multicomponent flow in porous media. It is applicable to natural-state studies of geothermal systems and ground-water flow. The equations of heat and mass transfer for multiphase flow in porous and permeable media are solved using the finite element method. The permeability and porosity of the medium are allowed to depend on pressure and temperature. The code also has provisions for movable air and water phases and noncoupled tracers; that is, tracer solutions that do not affect the heat and mass transfer solutions. The tracers can be passive or reactive. The code can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. A summary of the equations in the model and the numerical solution procedure are provided in this report. A user's guide and sample problems are also included. The main use of FEHMN will be to assist in the understanding of flow fields in the saturated zone below the proposed Yucca Mountain Repository. 33 refs., 27 figs., 12 tabs

Free material stiffness design of laminated composite structures using commercial finite element analysis codes

DEFF Research Database (Denmark)

Henrichsen, Søren Randrup; Lindgaard, Esben; Lund, Erik

2015-01-01

In this work optimum stiffness design of laminated composite structures is performed using the commercially available programs ANSYS and MATLAB. Within these programs a Free Material Optimization algorithm is implemented based on an optimality condition and a heuristic update scheme. The heuristic...... update scheme is needed because commercially available finite element analysis software is used. When using a commercial finite element analysis code it is not straight forward to implement a computationally efficient gradient based optimization algorithm. Examples considered in this work are a clamped......, where full access to the finite element analysis core is granted. This comparison displays the possibility of using commercially available programs for stiffness design of laminated composite structures....

Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

Energy Technology Data Exchange (ETDEWEB)

Kim, K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petersson, N. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rodgers, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-10-25

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei

2012-05-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation

Energy Technology Data Exchange (ETDEWEB)

Matausek, M V [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1972-07-01

A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the

A Meta-Analysis Suggests Different Neural Correlates for Implicit and Explicit Learning.

Science.gov (United States)

Loonis, Roman F; Brincat, Scott L; Antzoulatos, Evan G; Miller, Earl K

2017-10-11

A meta-analysis of non-human primates performing three different tasks (Object-Match, Category-Match, and Category-Saccade associations) revealed signatures of explicit and implicit learning. Performance improved equally following correct and error trials in the Match (explicit) tasks, but it improved more after correct trials in the Saccade (implicit) task, a signature of explicit versus implicit learning. Likewise, error-related negativity, a marker for error processing, was greater in the Match (explicit) tasks. All tasks showed an increase in alpha/beta (10-30 Hz) synchrony after correct choices. However, only the implicit task showed an increase in theta (3-7 Hz) synchrony after correct choices that decreased with learning. In contrast, in the explicit tasks, alpha/beta synchrony increased with learning and decreased thereafter. Our results suggest that explicit versus implicit learning engages different neural mechanisms that rely on different patterns of oscillatory synchrony. Copyright © 2017 Elsevier Inc. All rights reserved.

A Finite Difference Scheme for Double-Diffusive Unsteady Free Convection from a Curved Surface to a Saturated Porous Medium with a Non-Newtonian Fluid

KAUST Repository

El-Amin, Mohamed

2011-05-14

In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

FLAME: A finite element computer code for contaminant transport n variably-saturated media

International Nuclear Information System (INIS)

Baca, R.G.; Magnuson, S.O.

1992-06-01

A numerical model was developed for use in performance assessment studies at the INEL. The numerical model referred to as the FLAME computer code, is designed to simulate subsurface contaminant transport in a variably-saturated media. The code can be applied to model two-dimensional contaminant transport in an and site vadose zone or in an unconfined aquifer. In addition, the code has the capability to describe transport processes in a porous media with discrete fractures. This report presents the following: description of the conceptual framework and mathematical theory, derivations of the finite element techniques and algorithms, computational examples that illustrate the capability of the code, and input instructions for the general use of the code. The development of the FLAME computer code is aimed at providing environmental scientists at the INEL with a predictive tool for the subsurface water pathway. This numerical model is expected to be widely used in performance assessments for: (1) the Remedial Investigation/Feasibility Study process and (2) compliance studies required by the US Department of energy Order 5820.2A

FLAME: A finite element computer code for contaminant transport n variably-saturated media

Energy Technology Data Exchange (ETDEWEB)

Baca, R.G.; Magnuson, S.O.

1992-06-01

A numerical model was developed for use in performance assessment studies at the INEL. The numerical model referred to as the FLAME computer code, is designed to simulate subsurface contaminant transport in a variably-saturated media. The code can be applied to model two-dimensional contaminant transport in an and site vadose zone or in an unconfined aquifer. In addition, the code has the capability to describe transport processes in a porous media with discrete fractures. This report presents the following: description of the conceptual framework and mathematical theory, derivations of the finite element techniques and algorithms, computational examples that illustrate the capability of the code, and input instructions for the general use of the code. The development of the FLAME computer code is aimed at providing environmental scientists at the INEL with a predictive tool for the subsurface water pathway. This numerical model is expected to be widely used in performance assessments for: (1) the Remedial Investigation/Feasibility Study process and (2) compliance studies required by the US Department of energy Order 5820.2A.

Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method

International Nuclear Information System (INIS)

Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong

2014-01-01

In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)

Non-binary Hybrid LDPC Codes: Structure, Decoding and Optimization

OpenAIRE

Sassatelli, Lucile; Declercq, David

2007-01-01

In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes Hybrid LDPC codes. Although efficient optimization techniques exist for binary LDPC codes and more recently for non-binary LDPC codes, they both exhibit drawbacks due to different reasons. Our goal is to capitalize on the advantages of both families by building codes with binary (or small finite set order) and non-bin...

An outgoing energy flux boundary condition for finite difference ICRP antenna models

International Nuclear Information System (INIS)

Batchelor, D.B.; Carter, M.D.

1992-11-01

For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods

DIF3D: a code to solve one-, two-, and three-dimensional finite-difference diffusion theory problems

International Nuclear Information System (INIS)

Derstine, K.L.

1984-04-01

The mathematical development and numerical solution of the finite-difference equations are summarized. The report provides a guide for user application and details the programming structure of DIF3D. Guidelines are included for implementing the DIF3D export package on several large scale computers. Optimized iteration methods for the solution of large-scale fast-reactor finite-difference diffusion theory calculations are presented, along with their theoretical basis. The computational and data management considerations that went into their formulation are discussed. The methods utilized include a variant of the Chebyshev acceleration technique applied to the outer fission source iterations and an optimized block successive overrelaxation method for the within-group iterations. A nodal solution option intended for analysis of LMFBR designs in two- and three-dimensional hexagonal geometries is incorporated in the DIF3D package and is documented in a companion report, ANL-83-1

Age Differences in Explicit and Implicit Age Attitudes Across the Life Span.

Science.gov (United States)

Chopik, William J; Giasson, Hannah L

2017-08-01

Biased judgments about others can operate both within and outside of our conscious awareness. However, little attention has been paid to how implicit and explicit attitudes differ across the life span, particularly with respect to age bias. In the current study, we examined age differences in implicit and explicit attitudes towards older individuals. Participants (N = 704,151) ranging from age 15 to 94 completed the Implicit Association Test and explicit self-report measures of bias against older adults. The associations between age bias and several demographic characteristics (e.g., gender, education) were also examined. A preference for younger people was found among participants of all ages; however, implicit and explicit attitudes showed divergent associations with age. Implicit preference for younger people was highest among older adults; explicit preference for younger people was lowest among older adults. Examining age differences in implicit and explicit attitudes sheds light into the development and complexities of aging perceptions in different age groups. The current study's findings are discussed in the context of applications to and implications of reducing prejudice toward older adults. © The Author 2017. Published by Oxford University Press on behalf of The Gerontological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

HEATING-7, Multidimensional Finite-Difference Heat Conduction Analysis

International Nuclear Information System (INIS)

2000-01-01

problems, surface fluxes may be plotted with H7TECPLOT which requires the proprietary software TECPLOT. HEATING 7.3 runs under Windows95 and WindowsNT on PC's. No future modifications are planned for HEATING7. See README.1ST for more information. 2 - Method of solution: Three steady-state solution techniques are available: point-successive over-relaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion.) The solution of the system of equations arising from the implicit techniques is accomplished by point-successive over-relaxation iteration and includes procedures to estimate the optimum acceleration parameter. 3 - Restrictions on the complexity of the problem: All surfaces in a model must be parallel to one of the coordinate axes which makes modeling complex geometries difficult. Transient change of phase problems can only be solved with one of the explicit techniques - an implicit change-of-phase capability has not been implemented

A full-fledged micromagnetic code in fewer than 70 lines of NumPy

International Nuclear Information System (INIS)

Abert, Claas; Bruckner, Florian; Vogler, Christoph; Windl, Roman; Thanhoffer, Raphael; Suess, Dieter

2015-01-01

We present a complete micromagnetic finite-difference code in fewer than 70 lines of Python. The code makes a large use of the NumPy library and computes the exchange field by finite differences and the demagnetization field with a fast convolution algorithm. Since the magnetization in finite-difference micromagnetics is represented by a multi-dimensional array and the NumPy library features a rich interface for this data structure, the code we present is an ideal starting point for the development of novel algorithms. - Highlights: • A very concise but complete micromagnetic code written in Python is presented. • An introduction to finite-difference micromagnetics is provided. • The code is a perfect starting point for the development of novel algorithms

Group foliation of finite difference equations

Science.gov (United States)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

Science.gov (United States)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

Three-Dimensional Finite Difference Simulation of Ground Motions from the August 24, 2014 South Napa Earthquake

Energy Technology Data Exchange (ETDEWEB)

Rodgers, Arthur J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States); Dreger, Douglas S. [Univ. of California, Berkeley, CA (United States); Pitarka, Arben [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-06-15

We performed three-dimensional (3D) anelastic ground motion simulations of the South Napa earthquake to investigate the performance of different finite rupture models and the effects of 3D structure on the observed wavefield. We considered rupture models reported by Dreger et al. (2015), Ji et al., (2015), Wei et al. (2015) and Melgar et al. (2015). We used the SW4 anelastic finite difference code developed at Lawrence Livermore National Laboratory (Petersson and Sjogreen, 2013) and distributed by the Computational Infrastructure for Geodynamics. This code can compute the seismic response for fully 3D sub-surface models, including surface topography and linear anelasticity. We use the 3D geologic/seismic model of the San Francisco Bay Area developed by the United States Geological Survey (Aagaard et al., 2008, 2010). Evaluation of earlier versions of this model indicated that the structure can reproduce main features of observed waveforms from moderate earthquakes (Rodgers et al., 2008; Kim et al., 2010). Simulations were performed for a domain covering local distances (< 25 km) and resolution providing simulated ground motions valid to 1 Hz.

A novel QC-LDPC code based on the finite field multiplicative group for optical communications

Science.gov (United States)

Yuan, Jian-guo; Xu, Liang; Tong, Qing-zhen

2013-09-01

A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) code is proposed based on the finite field multiplicative group, which has easier construction, more flexible code-length code-rate adjustment and lower encoding/decoding complexity. Moreover, a regular QC-LDPC(5334,4962) code is constructed. The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise (AWGN) channel with iterative decoding sum-product algorithm (SPA). At the bit error rate (BER) of 10-6, the net coding gain (NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB, 0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975, the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method, respectively. So it is more suitable for optical communication systems.

Comparison between a finite difference model (PUMA) and a finite element model (DELFIN) for simulation of the reactor of the atomic power plant of Atucha I

International Nuclear Information System (INIS)

Grant, C.R.

1996-01-01

The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs

DYNA3D2000*, Explicit 3-D Hydrodynamic FEM Program

International Nuclear Information System (INIS)

Lin, J.

2002-01-01

1 - Description of program or function: DYNA3D2000 is a nonlinear explicit finite element code for analyzing 3-D structures and solid continuum. The code is vectorized and available on several computer platforms. The element library includes continuum, shell, beam, truss and spring/damper elements to allow maximum flexibility in modeling physical problems. Many materials are available to represent a wide range of material behavior, including elasticity, plasticity, composites, thermal effects and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, including frictional sliding, single surface contact and automatic contact generation. 2 - Method of solution: Discretization of a continuous model transforms partial differential equations into algebraic equations. A numerical solution is then obtained by solving these algebraic equations through a direct time marching scheme. 3 - Restrictions on the complexity of the problem: Recent software improvements have eliminated most of the user identified limitations with dynamic memory allocation and a very large format description that has pushed potential problem sizes beyond the reach of most users. The dominant restrictions remain in code execution speed and robustness, which the developers constantly strive to improve

Validation of the 3D finite element transport theory code EVENT for shielding applications

International Nuclear Information System (INIS)

Warner, Paul; Oliveira, R.E. de

2000-01-01

This paper is concerned with the validation of the 3D deterministic neutral-particle transport theory code EVENT for shielding applications. The code is based on the finite element-spherical harmonics (FE-P N ) method which has been extensively developed over the last decade. A general multi-group, anisotropic scattering formalism enables the code to address realistic steady state and time dependent, multi-dimensional coupled neutron/gamma radiation transport problems involving high scattering and deep penetration alike. The powerful geometrical flexibility and competitive computational effort makes the code an attractive tool for shielding applications. In recognition of this, EVENT is currently in the process of being adopted by the UK nuclear industry. The theory behind EVENT is described and its numerical implementation is outlined. Numerical results obtained by the code are compared with predictions of the Monte Carlo code MCBEND and also with the results from benchmark shielding experiments. In particular, results are presented for the ASPIS experimental configuration for both neutron and gamma ray calculations using the BUGLE 96 nuclear data library. (author)

Modeling turbine-missile impacts using the HONDO finite-element code

International Nuclear Information System (INIS)

Schuler, K.W.

1981-11-01

Calculations have been performed using the dynamic finite element code HONDO to simulate a full scale rocket sled test. In the test a rocket sled was used to launch at a velocity of 150 m/s (490 ft/s), a 1527 kg (3366 lb) fragment of a steam turbine rotor disk into a structure which was a simplified model of a steam turbine casing. In the calculations the material behavior of and boundary conditions on the target structure were varied to assess its energy absorbing characteristics. Comparisons are made between the calculations and observations of missile velocity and strain histories of various points of the target structure

Simulation of coupled flow and mechanical deformation using IMplicit Pressure-Displacement Explicit Saturation (IMPDES) scheme

KAUST Repository

El-Amin, Mohamed

2012-01-01

The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.

Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

Energy Technology Data Exchange (ETDEWEB)

Kim, S. [Purdue Univ., West Lafayette, IN (United States)

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.

Space-Time Convolutional Codes over Finite Fields and Rings for Systems with Large Diversity Order

Directory of Open Access Journals (Sweden)

B. F. Uchôa-Filho

2008-06-01

Full Text Available We propose a convolutional encoder over the finite ring of integers modulo pk,ℤpk, where p is a prime number and k is any positive integer, to generate a space-time convolutional code (STCC. Under this structure, we prove three properties related to the generator matrix of the convolutional code that can be used to simplify the code search procedure for STCCs over ℤpk. Some STCCs of large diversity order (≥4 designed under the trace criterion for n=2,3, and 4 transmit antennas are presented for various PSK signal constellations.

Dynamic pulse buckling of cylindrical shells under axial impact: A benchmark study of 2D and 3D finite element calculations

International Nuclear Information System (INIS)

Hoffman, E.L.; Ammerman, D.J.

1995-01-01

A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several 2D and 3D finite element simulations of the event. The purpose of the work is to investigate the performance of various analysis codes and element types on a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry. During the pulse buckling tests, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. Numerical simulations of the test were performed using PRONTO, a Sandia developed transient dynamics analysis code, and ABAQUS/Explicit with both shell and continuum elements. The calculations are compared to the tests with respect to deformed shape and impact load history

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering—Application to circular footing and deep tunnel in saturated ground

Directory of Open Access Journals (Sweden)

Simon Heru Prassetyo

2018-04-01

Full Text Available Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical (H-M interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit (ADE scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in non-uniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourth-order finite difference (FD approximation to the spatial derivatives of the axisymmetric fluid–diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua (FLAC. This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%–50% that of FLAC's basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%�

Modelling 3-D mechanical phenomena in a 1-D industrial finite element code: results and perspectives

International Nuclear Information System (INIS)

Guicheret-Retel, V.; Trivaudey, F.; Boubakar, M.L.; Masson, R.; Thevenin, Ph.

2005-01-01

Assessing fuel rod integrity in PWR reactors must enjoin two opposite goals: a one-dimensional finite element code (axial revolution symmetry) is needed to provide industrial results at the scale of the reactor core, while the main risk of cladding failure [e.g. pellet-cladding interaction (PCI)] is based on fully three-dimensional phenomena. First, parametric three-dimensional elastic calculations were performed to identify the relevant parameters (fragment number, contact pellet-cladding conditions, etc.) as regards PCI. Axial fragment number as well as friction coefficient are shown to play a major role in PCI as opposed to other parameters. Next, the main limitations of the one-dimensional hypothesis of the finite element code CYRANO3 are identified. To overcome these limitations, both two- and three-dimensional emulations of CYRANO3 were developed. These developments are shown to significantly improve the results provided by CYRANO3. (authors)

Finite difference techniques for nonlinear hyperbolic conservation laws

International Nuclear Information System (INIS)

Sanders, R.

1985-01-01

The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references

Finite difference solution of the time dependent neutron group diffusion equations

International Nuclear Information System (INIS)

Hendricks, J.S.; Henry, A.F.

1975-08-01

In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods

Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers

Science.gov (United States)

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.

Coding Partitions

Directory of Open Access Journals (Sweden)

Fabio Burderi

2007-05-01

Full Text Available Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD, we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ``unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguouscomponent and other (if any totally ambiguouscomponents. In the case the code is finite, we give an algorithm for computing its canonical partition. This, in particular, allows to decide whether a given partition of a finite code X is a coding partition. This last problem is then approached in the case the code is a rational set. We prove its decidability under the hypothesis that the partition contains a finite number of classes and each class is a rational set. Moreover we conjecture that the canonical partition satisfies such a hypothesis. Finally we consider also some relationships between coding partitions and varieties of codes.

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

Finite element solution of two dimensional time dependent heat equation

International Nuclear Information System (INIS)

Maaz

1999-01-01

A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)

Finite element analysis for the impact behaviour of a cask interacting with a rigid pin

International Nuclear Information System (INIS)

Altes, J.; Geiser, H.; Voelzer, W.; Frenk, A.; Deeken, G.

1993-01-01

Full scale drop tests of casks to be licensed as type B packages according to the IAEA regulations for the safe transport of radioactive materials are expensive. Therefore efforts are being made to use computer codes for calculating the impact behaviour. But these codes have to be verified by experiments. Codes available for these calculations are for example DYNA3D and ABAQUS. In the paper results of both codes are compared. A 11 t ductile cast iron cask (type MOSAIK) without impact limiters was analysed dropping from a height of 1 m with its top onto a cylindrical steel pin. The results of the finite element calculations with both codes show good agreement. The ABAQUS results using the implicit method are in accordance with the explicit method, for which considerably shorter CPU times are noted. (author)

SPLOSH III. A code for calculating reactivity and flow transients in CSGHWR

International Nuclear Information System (INIS)

Halsall, M.J.; Course, A.F.; Sidell, J.

1979-09-01

SPLOSH is a time dependent, one dimensional, finite difference (in time and space) coupled neutron kinetics and thermal hydraulics code for studying pressurised faults and control transients in water reactor systems. An axial single channel model with equally spaced mesh intervals is used to represent the neutronics of the reactor core. A radial finite difference model is used for heat conduction through the fuel pin, gas gap and can. Appropriate convective, boiling or post-dryout heat transfer correlations are used at the can-coolant interface. The hydraulics model includes the important features of the SGHWR primary loop including 'slave' channels in parallel with the 'mean' channel. Standard mass, energy and momentum equations are solved explicitly. Circuit features modelled include pumps, spray cooling and the SGHWR steam drum. Perturbations to almost any feature of the circuit model may be specified by the user although blowdown calculations resulting in critical or reversed flows are not permitted. Automatic reactor trips may be defined and the ensuing actions of moderator dumping and rod firing can be specified. (UK)

Developmental Differences in Implicit and Explicit Memory Performance.

Science.gov (United States)

Perez, Lori A.; Peynircioglu, Zehra F.; Blaxton, Teresa A.

1998-01-01

Compared perceptual and conceptual implicit and explicit memory performance of preschool, elementary, and college students. Found that conceptual explicit memory improved with age. Perceptual explicit memory and implicit memory showed no developmental change. Perceptual processing during study led to better performance than conceptual processing…

Monte Carlo method implemented in a finite element code with application to dynamic vacuum in particle accelerators

CERN Document Server

Garion, C

2009-01-01

Modern particle accelerators require UHV conditions during their operation. In the accelerating cavities, breakdowns can occur, releasing large amount of gas into the vacuum chamber. To determine the pressure profile along the cavity as a function of time, the time-dependent behaviour of the gas has to be simulated. To do that, it is useful to apply accurate three-dimensional method, such as Test Particles Monte Carlo. In this paper, a time-dependent Test Particles Monte Carlo is used. It has been implemented in a Finite Element code, CASTEM. The principle is to track a sample of molecules during time. The complex geometry of the cavities can be created either in the FE code or in a CAD software (CATIA in our case). The interface between the two softwares to export the geometry from CATIA to CASTEM is given. The algorithm of particle tracking for collisionless flow in the FE code is shown. Thermal outgassing, pumping surfaces and electron and/or ion stimulated desorption can all be generated as well as differ...

Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.

Science.gov (United States)

Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S

2013-01-01

This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.

Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads

Directory of Open Access Journals (Sweden)

Y. S. Kong

2013-01-01

Full Text Available This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability.

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

Science.gov (United States)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

SQA of finite element method (FEM) codes used for analyses of pit storage/transport packages

Energy Technology Data Exchange (ETDEWEB)

Russel, E. [Lawrence Livermore National Lab., CA (United States)

1997-11-01

This report contains viewgraphs on the software quality assurance of finite element method codes used for analyses of pit storage and transport projects. This methodology utilizes the ISO 9000-3: Guideline for application of 9001 to the development, supply, and maintenance of software, for establishing well-defined software engineering processes to consistently maintain high quality management approaches.

Generalized rate-code model for neuron ensembles with finite populations

International Nuclear Information System (INIS)

Hasegawa, Hideo

2007-01-01

We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the Fokker-Planck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as Γ, inverse-Gaussian-like, and log-normal-like distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finite-unit stochastic systems. In the AMM, the original N-dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons

Individual differences in explicit and implicit visuomotor learning and working memory capacity.

Science.gov (United States)

Christou, Antonios I; Miall, R Chris; McNab, Fiona; Galea, Joseph M

2016-11-08

The theoretical basis for the association between high working memory capacity (WMC) and enhanced visuomotor adaptation is unknown. Visuomotor adaptation involves interplay between explicit and implicit systems. We examined whether the positive association between adaptation and WMC is specific to the explicit component of adaptation. Experiment 1 replicated the positive correlation between WMC and adaptation, but revealed this was specific to the explicit component of adaptation, and apparently driven by a sub-group of participants who did not show any explicit adaptation in the correct direction. A negative correlation was observed between WMC and implicit learning. Experiments 2 and 3 showed that when the task restricted the development of an explicit strategy, high WMC was no longer associated with enhanced adaptation. This work reveals that the benefit of high WMC is specifically linked to an individual's capacity to use an explicit strategy. It also reveals an important contribution of individual differences in determining how adaptation is performed.

Comparison of explicit finite element and mechanical simulation of the proximal femur during dynamic drop-tower testing.

Science.gov (United States)

Ariza, O; Gilchrist, S; Widmer, R P; Guy, P; Ferguson, S J; Cripton, P A; Helgason, B

2015-01-21

Current screening techniques based on areal bone mineral density (aBMD) measurements are unable to identify the majority of people who sustain hip fractures. Biomechanical examination of such events may help determine what predisposes a hip to be susceptible to fracture. Recently, drop-tower simulations of in-vitro sideways falls have allowed the study of the mechanical response of the proximal human femur at realistic impact speeds. This technique has created an opportunity to validate explicit finite element (FE) models against dynamic test data. This study compared the outcomes of 15 human femoral specimens fractured using a drop tower with complementary specimen-specific explicit FE analysis. Correlation coefficient and root mean square error (RMSE) were found to be moderate for whole bone stiffness comparison (R(2)=0.3476 and 22.85% respectively). No correlation was found between experimentally and computationally predicted peak force, however, energy absorption comparison produced moderate correlation and RMSE (R(2)=0.4781 and 29.14% respectively). By comparing predicted strain maps to high speed video data we demonstrated the ability of the FE models to detect vulnerable portions of the bones. Based on our observations, we conclude that there exists a need to extend the current apparent level material models for bone to cover higher strain rates than previously tested experimentally. Copyright © 2014 Elsevier Ltd. All rights reserved.

Mechanical modelization of PCI with Fragema and CEA finite element codes

International Nuclear Information System (INIS)

Bernard, P.; Joseph, J.; Atabek, R.; Chantant, M.

1982-03-01

In order to modelize the PCI phenomenon during a power ramp test two finite element codes have been used by FRAGEMA and CEA, TITUS and VERDON. The results given, by the 3D equivalent method developed with TITUS, and VERDON are equivalent, in particular the strains and the equivalent Von Mises stresses at the pellet to pellet interface are quite similar. An evaluation was made to explain experimental ramp tests results. These results come from FRISCA 04bis and FRISCA 104 rods which were ramp tested in SILOE. The choice of the equivalent Von Mises stress seems to be quite a good criterion to explain the failure threshold

Results from the Metis code participation to the Hydrocoin exercise

International Nuclear Information System (INIS)

Raimbault, P.

1987-04-01

The METIS code, developed at the ENSMP is a 2D finite element radionuclide transport and groundwater flow model based on the hypothesis of an equivalent porous medium with an explicit description of the main fractures. It is integrated in the global risk assessment code MELODIE for nuclear waste repositories in geological formations. The participation of the METIS code to the HYDROCOIN exercise is of prime importance for its development and its incorporation in the performance assessment procedure in France. Results from HYDROCOIN cases show that the code can handle correctly fractured media, high permeability contrast formations and buoyancy effects. A 3D version of the code has been developed for carrying comparisons of field experiments and groundwater flow models in HYDROCOIN level 2. In order to carry out the exercise, several pre and post-processing programs were developed and integrated in a conversational module. They include: contour plots, velocity field representations, interpolations, particule tracking routines and uncertainty and sensitivity analysis modules

PLASTEF: a code for the numerical simulation of thermoelastoplastic behaviour of materials using the finite element method

International Nuclear Information System (INIS)

Basombrio, F.G.; Sanchez Sarmiento, G.

1978-01-01

A general code for solving two-dimensional thermo-elastoplastic problems in geometries of arbitrary shape using the finite element method, is presented. The initial stress incremental procedure was adopted, for given histories of load and temperature. Some classical applications are included. (Auth.)

Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach

Science.gov (United States)

Shen, Yanfeng; Cesnik, Carlos E. S.

2016-04-01

This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.

Numerical simulation of temperature distribution using finite difference equations and estimation of the grain size during friction stir processing

International Nuclear Information System (INIS)

Arora, H.S.; Singh, H.; Dhindaw, B.K.

2012-01-01

Highlights: ► Magnesium alloy AE42 was friction stir processed under different cooling conditions. ► Heat flow model was developed using finite difference heat equations. ► Generalized MATLAB code was developed for solving heat flow model. ► Regression equation for estimation of grain size was developed. - Abstract: The present investigation is aimed at developing a heat flow model to simulate temperature history during friction stir processing (FSP). A new approach of developing implicit form of finite difference heat equations solved using MATLAB code was used. A magnesium based alloy AE42 was friction stir processed (FSPed) at different FSP parameters and cooling conditions. Temperature history was continuously recorded in the nugget zone during FSP using data acquisition system and k type thermocouples. The developed code was validated at different FSP parameters and cooling conditions during FSP experimentation. The temperature history at different locations in the nugget zone at different instants of time was further utilized for the estimation of grain growth rate and final average grain size of the FSPed specimen. A regression equation relating the final grain size, maximum temperature during FSP and the cooling rate was developed. The metallurgical characterization was done using optical microscopy, SEM, and FIB-SIM analysis. The simulated temperature profiles and final average grain size were found to be in good agreement with the experimental results. The presence of fine precipitate particles generated in situ in the investigated magnesium alloy also contributed in the evolution of fine grain structure through Zener pining effect at the grain boundaries.

Comparison of ASME Code NB-3200 and NB-3600 results for fatigue analysis of B31.1 branch nozzles

International Nuclear Information System (INIS)

Nitzel, M.E.; Ware, A.G.; Morton, D.K.

1996-01-01

Fatigue analyses wre conducted on two reactor coolant system branch nozzles in an operating PWR designed to the B31.1 Code, for which no explicit fatigue analysis was required by the licensing basis. These analyses were performed as part of resolving issues connected with NRC's Fatigue Action Plan to determine if the cumulative usage factor (CUF) for these nozzles, using the 1992 ASME Code and representative PWR transients, were comparable to nozzles designed and analyzed to the ASME Code. Both NB-3200 and NB-3600 ASME Code methods were used. NB-3200 analyses included the development of finite element models for each nozzle. Although detailed thermal transients were not available for the plant analyzed, representative transients from similar PWRs were applied in each method. CUFs calculated using NB-3200 methods were significantly less than using NB-3600. The paper points out differences in analysis methods and highlights difficulties and unknowns in performing more detailed analyses to reduce conservative assumptions

Full scale seismic simulation of a nuclear reactor with parallel finite element analysis code for assembled structure

International Nuclear Information System (INIS)

Yamada, Tomonori

2010-01-01

The safety requirement of nuclear power plant attracts much attention nowadays. With the growing computing power, numerical simulation is one of key technologies to meet this safety requirement. Center for Computational Science and e-Systems of Japan Atomic Energy Agency has been developing a finite element analysis code for assembled structure to accurately evaluate the structural integrity of nuclear power plant in its entirety under seismic events. Because nuclear power plant is very huge assembled structure with tens of millions of mechanical components, the finite element model of each component is assembled into one structure and non-conforming meshes of mechanical components are bonded together inside the code. The main technique to bond these mechanical components is triple sparse matrix multiplication with multiple point constrains and global stiffness matrix. In our code, this procedure is conducted in a component by component manner, so that the working memory size and computing time for this multiplication are available on the current computing environment. As an illustrative example, seismic simulation of a real nuclear reactor of High Temperature engineering Test Reactor, which is located at the O-arai research and development center of JAEA, with 80 major mechanical components was conducted. Consequently, our code successfully simulated detailed elasto-plastic deformation of nuclear reactor and its computational performance was investigated. (author)

New quantum codes constructed from quaternary BCH codes

Science.gov (United States)

Xu, Gen; Li, Ruihu; Guo, Luobin; Ma, Yuena

2016-10-01

In this paper, we firstly study construction of new quantum error-correcting codes (QECCs) from three classes of quaternary imprimitive BCH codes. As a result, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing quaternary BCH codes are determined to be much larger than the result given according to Aly et al. (IEEE Trans Inf Theory 53:1183-1188, 2007) for each different code length. Thus, families of new QECCs are newly obtained, and the constructed QECCs have larger distance than those in the previous literature. Secondly, we apply a combinatorial construction to the imprimitive BCH codes with their corresponding primitive counterpart and construct many new linear quantum codes with good parameters, some of which have parameters exceeding the finite Gilbert-Varshamov bound for linear quantum codes.

Finite Element Simulation of Sheet Metal Forming Process Using Local Interpolation for Tool Surfaces

International Nuclear Information System (INIS)

Hama, Takayuki; Takuda, Hirohiko; Takamura, Masato; Makinouchi, Akitake; Teodosiu, Cristian

2005-01-01

Treatment of contact between a sheet and tools is one of the most difficult problems to deal with in finite-element simulations of sheet forming processes. In order to obtain more accurate tool models without increasing the number of elements, this paper describes a new formulation for contact problems using interpolation proposed by Nagata for tool surfaces. A contact search algorithm between sheet nodes and the interpolated tool surfaces was developed and was introduced into the static-explicit elastoplastic finite-element method code STAMP3D. Simulations of a square cup deep drawing process with a very coarsely discretized punch model were carried out. The simulated results showed that the proposed algorithm gave the proper drawn shape, demonstrating the validity of the proposed algorithm

Finite Mathematics and Discrete Mathematics: Is There a Difference?

Science.gov (United States)

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…

ANIMAL code

International Nuclear Information System (INIS)

Lindemuth, I.R.

1979-01-01

This report describes ANIMAL, a two-dimensional Eulerian magnetohydrodynamic computer code. ANIMAL's physical model also appears. Formulated are temporal and spatial finite-difference equations in a manner that facilitates implementation of the algorithm. Outlined are the functions of the algorithm's FORTRAN subroutines and variables

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng

2015-02-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

A unified form of exact-MSR codes via product-matrix frameworks

KAUST Repository

Lin, Sian Jheng; Chung, Weiho; Han, Yunghsiangsam; Al-Naffouri, Tareq Y.

2015-01-01

Regenerating codes represent a class of block codes applicable for distributed storage systems. The [n, k, d] regenerating code has data recovery capability while possessing arbitrary k out of n code fragments, and supports the capability for code fragment regeneration through the use of other arbitrary d fragments, for k ≤ d ≤ n - 1. Minimum storage regenerating (MSR) codes are a subset of regenerating codes containing the minimal size of each code fragment. The first explicit construction of MSR codes that can perform exact regeneration (named exact-MSR codes) for d ≥ 2k - 2 has been presented via a product-matrix framework. This paper addresses some of the practical issues on the construction of exact-MSR codes. The major contributions of this paper include as follows. A new product-matrix framework is proposed to directly include all feasible exact-MSR codes for d ≥ 2k - 2. The mechanism for a systematic version of exact-MSR code is proposed to minimize the computational complexities for the process of message-symbol remapping. Two practical forms of encoding matrices are presented to reduce the size of the finite field.

Entanglement negativity and sudden death in the toric code at finite temperature

Science.gov (United States)

Hart, O.; Castelnovo, C.

2018-04-01

We study the fate of quantum correlations at finite temperature in the two-dimensional toric code using the logarithmic entanglement negativity. We are able to obtain exact results that give us insight into how thermal excitations affect quantum entanglement. The toric code has two types of elementary excitations (defects) costing different energies. We show that an O (1 ) density of the lower energy defect is required to degrade the zero-temperature entanglement between two subsystems in contact with one another. However, one type of excitation alone is not sufficient to kill all quantum correlations, and an O (1 ) density of the higher energy defect is required to cause the so-called sudden death of the negativity. Interestingly, if the energy cost of one of the excitations is taken to infinity, quantum correlations survive up to arbitrarily high temperatures, a feature that is likely shared with other quantum spin liquids and frustrated systems in general, when projected down to their low-energy states. We demonstrate this behavior both for small subsystems, where we can prove that the negativity is a necessary and sufficient condition for separability, as well as for extended subsystems, where it is only a necessary condition. We further observe that the negativity per boundary degree of freedom at a given temperature increases (parametrically) with the size of the boundary, and that quantum correlations between subsystems with extended boundaries are more robust to thermal fluctuations.

Software requirements, design, and verification and validation for the FEHM application - a finite-element heat- and mass-transfer code

International Nuclear Information System (INIS)

Dash, Z.V.; Robinson, B.A.; Zyvoloski, G.A.

1997-07-01

The requirements, design, and verification and validation of the software used in the FEHM application, a finite-element heat- and mass-transfer computer code that can simulate nonisothermal multiphase multicomponent flow in porous media, are described. The test of the DOE Code Comparison Project, Problem Five, Case A, which verifies that FEHM has correctly implemented heat and mass transfer and phase partitioning, is also covered

Does a code make a difference – assessing the English code of practice on international recruitment

Directory of Open Access Journals (Sweden)

Mensah Kwadwo

2009-04-01

Full Text Available Abstract Background This paper draws from research completed in 2007 to assess the effect of the Department of Health, England, Code of Practice for the international recruitment of health professionals. The Department of Health in England introduced a Code of Practice for international recruitment for National Health Service employers in 2001. The Code required National Health Service employers not to actively recruit from low-income countries, unless there was government-to-government agreement. The Code was updated in 2004. Methods The paper examines trends in inflow of health professionals to the United Kingdom from other countries, using professional registration data and data on applications for work permits. The paper also provides more detailed information from two country case studies in Ghana and Kenya. Results Available data show a considerable reduction in inflow of health professionals, from the peak years up to 2002 (for nurses and 2004 (for doctors. There are multiple causes for this decline, including declining demand in the United Kingdom. In Ghana and Kenya it was found that active recruitment was perceived to have reduced significantly from the United Kingdom, but it is not clear the extent to which the Code was influential in this, or whether other factors such as a lack of vacancies in the United Kingdom explains it. Conclusion Active international recruitment of health professionals was an explicit policy intervention by the Department of Health in England, as one key element in achieving rapid staffing growth, particularly in the period 2000 to 2005, but the level of international recruitment has dropped significantly since early 2006. Regulatory and education changes in the United Kingdom in recent years have also made international entry more difficult. The potential to assess the effect of the Code in England is constrained by the limitations in available databases. This is a crucial lesson for those considering a

User's Manual for the FEHM Application-A Finite-Element Heat- and Mass-Transfer Code

Energy Technology Data Exchange (ETDEWEB)

George A. Zyvoloski; Bruce A. Robinson; Zora V. Dash; Lynn L. Trease

1997-07-07

This document is a manual for the use of the FEHM application, a finite-element heat- and mass-transfer computer code that can simulate nonisothermal multiphase multicomponent flow in porous media. The use of this code is applicable to natural-state studies of geothermal systems and groundwater flow. A primary use of the FEHM application will be to assist in the understanding of flow fields and mass transport in the saturated and unsaturated zones below the proposed Yucca Mountain nuclear waste repository in Nevada. The equations of heat and mass transfer for multiphase flow in porous and permeable media are solved in the FEHM application by using the finite-element method. The permeability and porosity of the medium are allowed to depend on pressure and temperature. The code also has provisions for movable air and water phases and noncoupled tracers; that is, tracer solutions that do not affect the heat- and mass-transfer solutions. The tracers can be passive or reactive. The code can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. In fact, FEHM is capable of describing flow that is dominated in many areas by fracture and fault flow, including the inherently three-dimensional flow that results from permeation to and from faults and fractures. The code can handle coupled heat and mass-transfer effects, such as boiling, dryout, and condensation that can occur in the near-field region surrounding the potential repository and the natural convection that occurs through Yucca Mountain due to seasonal temperature changes. The code is also capable of incorporating the various adsorption mechanisms, ranging from simple linear relations to nonlinear isotherms, needed to describe the very complex transport processes at Yucca Mountain. This report outlines the uses and capabilities of the FEHM application, initialization of code variables, restart procedures, and error processing. The report describes all the data files, the input data

On finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1984-01-01

The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)

Staggered-grid finite-difference acoustic modeling with the Time-Domain Atmospheric Acoustic Propagation Suite (TDAAPS).

Energy Technology Data Exchange (ETDEWEB)

Aldridge, David Franklin; Collier, Sandra L. (U.S. Army Research Laboratory); Marlin, David H. (U.S. Army Research Laboratory); Ostashev, Vladimir E. (NOAA/Environmental Technology Laboratory); Symons, Neill Phillip; Wilson, D. Keith (U.S. Army Cold Regions Research Engineering Lab.)

2005-05-01

This document is intended to serve as a users guide for the time-domain atmospheric acoustic propagation suite (TDAAPS) program developed as part of the Department of Defense High-Performance Modernization Office (HPCMP) Common High-Performance Computing Scalable Software Initiative (CHSSI). TDAAPS performs staggered-grid finite-difference modeling of the acoustic velocity-pressure system with the incorporation of spatially inhomogeneous winds. Wherever practical the control structure of the codes are written in C++ using an object oriented design. Sections of code where a large number of calculations are required are written in C or F77 in order to enable better compiler optimization of these sections. The TDAAPS program conforms to a UNIX style calling interface. Most of the actions of the codes are controlled by adding flags to the invoking command line. This document presents a large number of examples and provides new users with the necessary background to perform acoustic modeling with TDAAPS.

Children exhibit different performance patterns in explicit and implicit theory of mind tasks.

Science.gov (United States)

Oktay-Gür, Nese; Schulz, Alexandra; Rakoczy, Hannes

2018-04-01

Three studies tested scope and limits of children's implicit and explicit theory of mind. In Studies 1 and 2, three- to six-year-olds (N = 84) were presented with closely matched explicit false belief tasks that differed in whether or not they required an understanding of aspectuality. Results revealed that children performed equally well in the different tasks, and performance was strongly correlated. Study 3 tested two-year-olds (N = 81) in implicit interactive versions of these tasks and found evidence for dis-unity: children performed competently only in those tasks that did not require an understanding of aspectuality. Taken together, the present findings suggest that early implicit and later explicit theory of mind tasks may tap different forms of cognitive capacities. Copyright © 2018 Elsevier B.V. All rights reserved.

Rn3D: A finite element code for simulating gas flow and radon transport in variably saturated, nonisothermal porous media

International Nuclear Information System (INIS)

Holford, D.J.

1994-01-01

This document is a user's manual for the Rn3D finite element code. Rn3D was developed to simulate gas flow and radon transport in variably saturated, nonisothermal porous media. The Rn3D model is applicable to a wide range of problems involving radon transport in soil because it can simulate either steady-state or transient flow and transport in one-, two- or three-dimensions (including radially symmetric two-dimensional problems). The porous materials may be heterogeneous and anisotropic. This manual describes all pertinent mathematics related to the governing, boundary, and constitutive equations of the model, as well as the development of the finite element equations used in the code. Instructions are given for constructing Rn3D input files and executing the code, as well as a description of all output files generated by the code. Five verification problems are given that test various aspects of code operation, complete with example input files, FORTRAN programs for the respective analytical solutions, and plots of model results. An example simulation is presented to illustrate the type of problem Rn3D is designed to solve. Finally, instructions are given on how to convert Rn3D to simulate systems other than radon, air, and water

A novel construction method of QC-LDPC codes based on the subgroup of the finite field multiplicative group for optical transmission systems

Science.gov (United States)

Yuan, Jian-guo; Zhou, Guang-xiang; Gao, Wen-chun; Wang, Yong; Lin, Jin-zhao; Pang, Yu

2016-01-01

According to the requirements of the increasing development for optical transmission systems, a novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on the subgroup of the finite field multiplicative group is proposed. Furthermore, this construction method can effectively avoid the girth-4 phenomena and has the advantages such as simpler construction, easier implementation, lower encoding/decoding complexity, better girth properties and more flexible adjustment for the code length and code rate. The simulation results show that the error correction performance of the QC-LDPC(3 780,3 540) code with the code rate of 93.7% constructed by this proposed method is excellent, its net coding gain is respectively 0.3 dB, 0.55 dB, 1.4 dB and 1.98 dB higher than those of the QC-LDPC(5 334,4 962) code constructed by the method based on the inverse element characteristics in the finite field multiplicative group, the SCG-LDPC(3 969,3 720) code constructed by the systematically constructed Gallager (SCG) random construction method, the LDPC(32 640,30 592) code in ITU-T G.975.1 and the classic RS(255,239) code which is widely used in optical transmission systems in ITU-T G.975 at the bit error rate ( BER) of 10-7. Therefore, the constructed QC-LDPC(3 780,3 540) code is more suitable for optical transmission systems.

A 3D spectral anelastic hydrodynamic code for shearing, stratified flows

Science.gov (United States)

Barranco, Joseph A.; Marcus, Philip S.

2006-11-01

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g., the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to a finite one with a cotangent mapping, and using cosine and sine expansions in the mapped coordinate. The nonlinear advection terms are time-integrated explicitly, the pressure/enthalpy terms are integrated semi-implicitly, and the Coriolis force and buoyancy terms are treated semi-analytically. We show that internal gravity waves can be damped by adding new terms to the Euler equations. The code exhibits excellent parallel performance with the message passing interface (MPI). As a demonstration of the code, we simulate the merger of two 3D vortices in the midplane of a protoplanetary disk.

Finite difference time domain analysis of a chiro plasma

International Nuclear Information System (INIS)

Torres-Silva, H.; Obligado, A.; Reggiani, N.; Sakanaka, P.H.

1995-01-01

The finite difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetics. Using FDTD, Maxwell's equations are solved directly in the time domain via finite differences and time stepping. The basic approach is relatively easy to understand and is an alternative to the more usual frequency-domain approaches. (author). 5 refs

Implementation of thermo-viscoplastic constitutive equations into the finite element code ABAQUS

International Nuclear Information System (INIS)

Youn, Sam Son; Lee, Soon Bok; Kim, Jong Bum; Lee, Hyeong Yeon; Yoo, Bong

1998-01-01

Sophisticated viscoplatic constitutive laws describing material behavior at high temperature have been implemented in the general-purpose finite element code ABAQUS to predict the viscoplastic response of structures to cyclic loading. Because of the complexity of viscoplastic constitutive equation, the general implementation methods are developed. The solution of the non-linear system of algebraic equations arising from time discretization is determined using line-search and back-tracking in combination with Newton method. The time integration method of the constitutive equations is based on semi-implicit method with efficient time step control. For numerical examples, the viscoplastic model proposed by Chaboche is implemented and several applications are illustrated

Higher-order harmonics coupling in different free-electron laser codes

Science.gov (United States)

Giannessi, L.; Freund, H. P.; Musumeci, P.; Reiche, S.

2008-08-01

The capability for simulation of the dynamics of a free-electron laser including the higher-order harmonics in linear undulators exists in several existing codes as MEDUSA [H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J. Quantum Electron. 27 (2000) 243; H.P. Freund, Phys. Rev. ST-AB 8 (2005) 110701] and PERSEO [L. Giannessi, Overview of Perseo, a system for simulating FEL dynamics in Mathcad, , in: Proceedings of FEL 2006 Conference, BESSY, Berlin, Germany, 2006, p. 91], and has been recently implemented in GENESIS 1.3 [See ]. MEDUSA and GENESIS also include the dynamics of even harmonics induced by the coupling through the betatron motion. In addition MEDUSA, which is based on a non-wiggler averaged model, is capable of simulating the generation of even harmonics in the transversally cold beam regime, i.e. when the even harmonic coupling arises from non-linear effects associated with longitudinal particle dynamics and not to a finite beam emittance. In this paper a comparison between the predictions of the codes in different conditions is given.

Sensitivity analyses on natural convection in an 8:1 tall enclosure using finite-volume methods

International Nuclear Information System (INIS)

Ambrosini, Walter; Forgione, N.; Ferreri, Juan C.

2004-01-01

Full text: The results herein presented are an extension of those obtained in previous work by the Authors in a benchmark problem dealing with flow driven by buoyancy in an 8:1 tall enclosure. A simple finite-volume model purposely set up for this application has provided the preliminary results reported. The adopted modeling technique was a direct extension of the one previously adopted by the Authors to deal with single-phase natural convection and boiling channel instabilities. This extension to two-dimensional flow is based on a finite-volume scheme using first order approximation in time and space. Despite its simplicity, results were reasonably good and detected the flow instabilities due to proper selection of cell Courant number and a semi-implicit solution algorithm. In this paper, results using the same code with different discretisations are presented in a more detailed way and are further discussed. They show proper capture of all the main characteristics of the flow, also reported by other authors and considered as 'converged' solutions. Results show that, as expected, first order explicit or semi-implicit methods can be considered reliable tools when dealing with stability problems, if properly used. Some initial results obtained using a second order upwind method are also presented for the purpose of comparison. Additionally, results obtained using a commercial code (FLUENT) are also reported. (author)

The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion

International Nuclear Information System (INIS)

Moczo, P.; Kristek, J.; Pazak, P.; Balazovjech, M.; Moczo, P.; Kristek, J.; Galis, M.

2007-01-01

Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite difference (FD), finite-element (FE), and hybrid FD-FE methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. We present alternative formulations of equation of motion for a smooth elastic continuum. We then develop alternative formulations for a canonical problem with a welded material interface and free surface. We continue with a model of an earthquake source. We complete the general theoretical introduction by a chapter on the constitutive laws for elastic and viscoelastic media, and brief review of strong formulations of the equation of motion. What follows is a block of chapters on the finite-difference and finite-element methods. We develop FD targets for the free surface and welded material interface. We then present various FD schemes for a smooth continuum, free surface, and welded interface. We focus on the staggered-grid and mainly optimally-accurate FD schemes. We also present alternative formulations of the FE method. We include the FD and FE implementations of the traction-at-split-nodes method for simulation of dynamic rupture propagation. The FD modeling is applied to the model of the deep sedimentary Grenoble basin, France. The FD and FE methods are combined in the hybrid FD-FE method. The hybrid

The computer code EURDYN - 1 M (release 1) for transient dynamic fluid-structure interaction. Pt.1: governing equations and finite element modelling

International Nuclear Information System (INIS)

Donea, J.; Fasoli-Stella, P.; Giuliani, S.; Halleux, J.P.; Jones, A.V.

1980-01-01

This report describes the governing equations and the finite element modelling used in the computer code EURDYN - 1 M. The code is a non-linear transient dynamic program for the analysis of coupled fluid-structure systems; It is designed for safety studies on LMFBR components (primary containment and fuel subassemblies)

Non-linear heat transfer computer code by finite element method

International Nuclear Information System (INIS)

Nagato, Kotaro; Takikawa, Noboru

1977-01-01

The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)

ELLIPT2D: A Flexible Finite Element Code Written Python

International Nuclear Information System (INIS)

Pletzer, A.; Mollis, J.C.

2001-01-01

The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research

Eulerian finite-difference calculations of explosions in partially water-filled overstrong cylindrical containment vessels

International Nuclear Information System (INIS)

Thompson, S.L.; Herrmann, W.

1977-01-01

Calculations, using the two-dimensional Eulerian finite-difference code CSQ, were performed for the problem of a small spherical high-explosive charge detonated in a closed heavy-walled cylindrical container partially filled with water. Data from corresponding experiments, specifically performed to validate codes used for hypothetical core disruptive accidents of liquid metal fast breeder reactors, are available in the literature. The calculations were performed specifically to test whether Eulerian methods could handle this type of problem, to determine whether water cavitation, which plays a large role in the loadings on the roof of the containment vessel, could be described adequately by an equilibrium liquid-vapor mixed phase model, and to investigate the trade-off between accuracy and cost of the calculations by using different sizes of computational meshes. Comparison of the experimental and computational data shows that the Eulerian method can handle the problem with ease, giving good predictions of wall and floor loadings. While roof loadings are qualitatively correct, peak impulse appears to be affected by numerical resolution and is underestimated somewhat

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

Subshifts of finite type and self-similar sets

Science.gov (United States)

Jiang, Kan; Dajani, Karma

2017-02-01

Let K\\subset {R} be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that K can be identified with a subshift of finite type. With this identification, we can calculate the Hausdorff dimension of K as well as the set of elements in K with unique codings using the machinery of Mauldin and Williams (1988 Trans. Am. Math. Soc. 309 811-29). We give three different applications of our main result. Firstly, we calculate the Hausdorff dimension of the set of points of K with multiple codings. Secondly, in the setting of β-expansions, when the set of all the unique codings is not a subshift of finite type, we can calculate in some cases the Hausdorff dimension of the univoque set. Motivated by this application, we prove that the set of all the unique codings is a subshift of finite type if and only if it is a sofic shift. This equivalent condition was not mentioned by de Vries and Komornik (2009 Adv. Math. 221 390-427, theorem 1.8). Thirdly, for the doubling map with asymmetrical holes, we give a sufficient condition such that the survivor set can be identified with a subshift of finite type. The third application partially answers a problem posed by Alcaraz Barrera (2014 PhD Thesis University of Manchester).

ABAQUS/EPGEN - a general purpose finite element code with emphasis on nonlinear applications

International Nuclear Information System (INIS)

Hibbitt, H.D.

1984-01-01

The article contains a summary description of ABAQUS, a finite element program designed for general use in nonlinear as well as linear structural problems, in the context of its application to nuclear structural integrity analysis. The article begins with a discussion of the design criteria and methods upon which the code development has been based. The engineering modelling capabilities, currently implemented in the program - elements, constitutive models and analysis procedures - are then described. Finally, a few demonstration examples are presented, to illustrate some of the program's features that are of interest in structural integrity analysis associated with nuclear power plants. (orig.)

Performance and scalability of finite-difference and finite-element wave-propagation modeling on Intel's Xeon Phi

NARCIS (Netherlands)

Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.

2013-01-01

With the rapid developments in parallel compute architectures, algorithms for seismic modeling and imaging need to be reconsidered in terms of parallelization. The aim of this paper is to compare scalability of seismic modeling algorithms: finite differences, continuous mass-lumped finite elements

VISCOT: a two-dimensional and axisymmetric nonlinear transient thermoviscoelastic and thermoviscoplastic finite-element code for modeling time-dependent viscous mechanical behavior of a rock mass

International Nuclear Information System (INIS)

1983-04-01

VISCOT is a non-linear, transient, thermal-stress finite-element code designed to determine the viscoelastic, fiscoplastic, or elastoplastic deformation of a rock mass due to mechanical and thermal loading. The numerical solution of the nonlinear incremental equilibrium equations within VISCOT is performed by using an explicit Euler time-stepping scheme. The rock mass may be modeled as a viscoplastic or viscoelastic material. The viscoplastic material model can be described by a Tresca, von Mises, Drucker-Prager or Mohr-Coulomb yield criteria (with or without strain hardening) with an associated flow rule which can be a power or an exponential law. The viscoelastic material model within VISCOT is a temperature- and stress-dependent law which has been developed specifically for salt rock masses by Pfeifle, Mellegard and Senseny in ONWI-314 topical report (1981). Site specific parameters for this creep law at the Richton, Permian, Paradox and Vacherie salt sites have been calculated and are given in ONWI-314 topical report (1981). A major application of VISCOT (in conjunction with a SCEPTER heat transfer code such as DOT) is the thermomechanical analysis of a rock mass such as salt in which significant time-dependent nonlinear deformations are expected to occur. Such problems include room- and canister-scale studies during the excavation, operation, and long-term post-closure stages in a salt repository. In Section 1.5 of this document the code custodianship and control is described along with the status of verification, validation and peer review of this report

Different radiation impedance models for finite porous materials

DEFF Research Database (Denmark)

Nolan, Melanie; Jeong, Cheol-Ho; Brunskog, Jonas

2015-01-01

The Sabine absorption coefficients of finite absorbers are measured in a reverberation chamber according to the international standard ISO 354. They vary with the specimen size essentially due to diffraction at the specimen edges, which can be seen as the radiation impedance differing from...... the infinite case. Thus, in order to predict the Sabine absorption coefficients of finite porous samples, one can incorporate models of the radiation impedance. In this study, different radiation impedance models are compared with two experimental examples. Thomasson’s model is compared to Rhazi’s method when...

Numerical experiments in finite element analysis of thermoelastoplastic behaviour of materials. Further developments of the PLASTEF code

International Nuclear Information System (INIS)

Basombrio, F.G.; Sarmiento, G.S.

1980-01-01

In a previous paper the finite element code PLASTEF for the numerical simulation of thermoelastoplastic behaviour of materials was presented in its general outline. This code employs an initial stress incremental procedure for given histories of loads and temperature. It has been formulated for medium sized computers. The present work is an extension of the previous paper to consider additional aspects of the variable temperature case. Non-trivial tests of this type of situation are described. Finally, details are given of some concrete applications to the prediction of thermoelastoplastic collapse of nuclear fuel element cladding. (author)

Convergence studies of deterministic methods for LWR explicit reflector methodology

International Nuclear Information System (INIS)

Canepa, S.; Hursin, M.; Ferroukhi, H.; Pautz, A.

2013-01-01

The standard approach in modem 3-D core simulators, employed either for steady-state or transient simulations, is to use Albedo coefficients or explicit reflectors at the core axial and radial boundaries. In the latter approach, few-group homogenized nuclear data are a priori produced with lattice transport codes using 2-D reflector models. Recently, the explicit reflector methodology of the deterministic CASMO-4/SIMULATE-3 code system was identified to potentially constitute one of the main sources of errors for core analyses of the Swiss operating LWRs, which are all belonging to GII design. Considering that some of the new GIII designs will rely on very different reflector concepts, a review and assessment of the reflector methodology for various LWR designs appeared as relevant. Therefore, the purpose of this paper is to first recall the concepts of the explicit reflector modelling approach as employed by CASMO/SIMULATE. Then, for selected reflector configurations representative of both GII and GUI designs, a benchmarking of the few-group nuclear data produced with the deterministic lattice code CASMO-4 and its successor CASMO-5, is conducted. On this basis, a convergence study with regards to geometrical requirements when using deterministic methods with 2-D homogenous models is conducted and the effect on the downstream 3-D core analysis accuracy is evaluated for a typical GII deflector design in order to assess the results against available plant measurements. (authors)

On the spectral properties of random finite difference operators

International Nuclear Information System (INIS)

Kunz, H.; Souillard, B.

1980-01-01

We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)

Analysis of lower head failure with simplified models and a finite element code

Energy Technology Data Exchange (ETDEWEB)

Koundy, V. [CEA-IPSN-DPEA-SEAC, Service d' Etudes des Accidents, Fontenay-aux-Roses (France); Nicolas, L. [CEA-DEN-DM2S-SEMT, Service d' Etudes Mecaniques et Thermiques, Gif-sur-Yvette (France); Combescure, A. [INSA-Lyon, Lab. Mecanique des Solides, Villeurbanne (France)

2001-07-01

The objective of the OLHF (OECD lower head failure) experiments is to characterize the timing, mode and size of lower head failure under high temperature loading and reactor coolant system pressure due to a postulated core melt scenario. Four tests have been performed at Sandia National Laboratories (USA), in the frame of an OECD project. The experimental results have been used to develop and validate predictive analysis models. Within the framework of this project, several finite element calculations were performed. In parallel, two simplified semi-analytical methods were developed in order to get a better understanding of the role of various parameters on the creep phenomenon, e.g. the behaviour of the lower head material and its geometrical characteristics on the timing, mode and location of failure. Three-dimensional modelling of crack opening and crack propagation has also been carried out using the finite element code Castem 2000. The aim of this paper is to present the two simplified semi-analytical approaches and to report the status of the 3D crack propagation calculations. (authors)

Tests of a 3D Self Magnetic Field Solver in the Finite Element Gun Code MICHELLE

CERN Document Server

Nelson, Eric M

2005-01-01

We have recently implemented a prototype 3d self magnetic field solver in the finite-element gun code MICHELLE. The new solver computes the magnetic vector potential on unstructured grids. The solver employs edge basis functions in the curl-curl formulation of the finite-element method. A novel current accumulation algorithm takes advantage of the unstructured grid particle tracker to produce a compatible source vector, for which the singular matrix equation is easily solved by the conjugate gradient method. We will present some test cases demonstrating the capabilities of the prototype 3d self magnetic field solver. One test case is self magnetic field in a square drift tube. Another is a relativistic axisymmetric beam freely expanding in a round pipe.

Hybrid finite difference/finite element immersed boundary method.

Science.gov (United States)

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

A non-linear, finite element, heat conduction code to calculate temperatures in solids of arbitrary geometry

International Nuclear Information System (INIS)

Tayal, M.

1987-01-01

Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated

Implementation of second moment closure turbulence model for incompressible flows in the industrial finite element code N3S

International Nuclear Information System (INIS)

Pot, G.; Laurence, D.; Rharif, N.E.; Leal de Sousa, L.; Compe, C.

1995-12-01

This paper deals with the introduction of a second moment closure turbulence model (Reynolds Stress Model) in an industrial finite element code, N3S, developed at Electricite de France.The numerical implementation of the model in N3S will be detailed in 2D and 3D. Some details are given concerning finite element computations and solvers. Then, some results will be given, including a comparison between standard k-ε model, R.S.M. model and experimental data for some test case. (authors). 22 refs., 3 figs

Finite-Difference Frequency-Domain Method in Nanophotonics

DEFF Research Database (Denmark)

Ivinskaya, Aliaksandra

Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...

Extrapolated stabilized explicit Runge-Kutta methods

Science.gov (United States)

Martín-Vaquero, J.; Kleefeld, B.

2016-12-01

Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve multi-dimensional nonlinear partial differential equations (PDEs). In such methods it is necessary to evaluate the function nt times per step, but the stability region is O (nt2). Hence, the computational cost is O (nt) times lower than for a traditional explicit algorithm. In that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used. Therefore, they are especially well-suited for the method of lines (MOL) discretizations of parabolic nonlinear multi-dimensional PDEs. In this work, first s-stages first-order methods with extended stability along the negative real axis are obtained. They have slightly shorter stability regions than other traditional first-order stabilized explicit Runge-Kutta algorithms (also called Runge-Kutta-Chebyshev codes). Later, they are used to derive nt-stages second- and fourth-order schemes using Richardson extrapolation. The stability regions of these fourth-order codes include the interval [ - 0.01nt2, 0 ] (nt being the number of total functions evaluations), which are shorter than stability regions of ROCK4 methods, for example. However, the new algorithms neither suffer from propagation of errors (as other Runge-Kutta-Chebyshev codes as ROCK4 or DUMKA) nor internal instabilities. Additionally, many other types of higher-order (and also lower-order) methods can be obtained easily in a similar way. These methods also allow adaptation of the length step with no extra cost. Hence, the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way, i.e., with minimal number of additional stages. We compare the new techniques with other well-known algorithms with good results in very stiff diffusion or reaction-diffusion multi-dimensional nonlinear equations.

NRC model simulations in support of the hydrologic code intercomparison study (HYDROCOIN): Level 1-code verification

International Nuclear Information System (INIS)

1988-03-01

HYDROCOIN is an international study for examining ground-water flow modeling strategies and their influence on safety assessments of geologic repositories for nuclear waste. This report summarizes only the combined NRC project temas' simulation efforts on the computer code bench-marking problems. The codes used to simulate thesee seven problems were SWIFT II, FEMWATER, UNSAT2M USGS-3D, AND TOUGH. In general, linear problems involving scalars such as hydraulic head were accurately simulated by both finite-difference and finite-element solution algorithms. Both types of codes produced accurate results even for complex geometrics such as intersecting fractures. Difficulties were encountered in solving problems that invovled nonlinear effects such as density-driven flow and unsaturated flow. In order to fully evaluate the accuracy of these codes, post-processing of results using paricle tracking algorithms and calculating fluxes were examined. This proved very valuable by uncovering disagreements among code results even through the hydraulic-head solutions had been in agreement. 9 refs., 111 figs., 6 tabs

Finite element formulation for fluid-structure interaction in three-dimensional space

International Nuclear Information System (INIS)

Kulak, R.F.

1979-01-01

A development is presented for a three-dimension hexahedral hydrodynamic finite-element. Using trilinear shape functions and assuming a constant pressure field in each element, simple relations were obtained for internal nodal forces. Because the formulation was based upon a rate approach it was applicable to problems involving large displacements. This element was incorporated into an existing plate-shell finite element code. Diagonal mass matrices were used and the resulting discrete equations of motion were solved using explicit temporal integrator. Results for several problems were presented which compare numerical predictions to closed form analytical solutions. In addition, the fluid-structure interaction problem of a fluid-filled, cylindrical vessel containing internal cylinders was studied. The internal cylinders were cantilever supported from the top cover of the vessel and were periodically located circumferentially at a fixed radius. A pressurized cylindrical cavity located at the bottom of the vessel at its centerline provided the loading

Real depletion in nodal diffusion codes

International Nuclear Information System (INIS)

Petkov, P.T.

2002-01-01

The fuel depletion is described by more than one hundred fuel isotopes in the advanced lattice codes like HELIOS, but only a few fuel isotopes are accounted for even in the advanced steady-state diffusion codes. The general assumption that the number densities of the majority of the fuel isotopes depend only on the fuel burnup is seriously in error if high burnup is considered. The real depletion conditions in the reactor core differ from the asymptotic ones at the stage of lattice depletion calculations. This study reveals which fuel isotopes should be explicitly accounted for in the diffusion codes in order to predict adequately the real depletion effects in the core. A somewhat strange conclusion is that if the real number densities of the main fissionable isotopes are not explicitly accounted for in the diffusion code, then Sm-149 should not be accounted for either, because the net error in k-inf is smaller (Authors)

The Laguerre finite difference one-way equation solver

Science.gov (United States)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

Coupled heat conduction and thermal stress formulation using explicit integration

International Nuclear Information System (INIS)

Marchertas, A.H.; Kulak, R.F.

1982-06-01

The formulation needed for the conductance of heat by means of explicit integration is presented. The implementation of these expressions into a transient structural code, which is also based on explicit temporal integration, is described. Comparisons of theoretical results with code predictions are given both for one-dimensional and two-dimensional problems. The coupled thermal and structural solution of a concrete crucible, when subjected to a sudden temperature increase, shows the history of cracking. The extent of cracking is compared with experimental data

DCOMP Award Lecture (Metropolis): A 3D Spectral Anelastic Hydrodynamic Code for Shearing, Stratified Flows

Science.gov (United States)

Barranco, Joseph

2006-03-01

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (eg, the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier-Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to a finite one with a cotangent mapping, and using cosine and sine expansions in the mapped coordinate. The nonlinear advection terms are time integrated explicitly, whereas the Coriolis force, buoyancy terms, and pressure/enthalpy gradient are integrated semi- implicitly. We show that internal gravity waves can be damped by adding new terms to the Euler equations. The code exhibits excellent parallel performance with the Message Passing Interface (MPI). As a demonstration of the code, we simulate vortex dynamics in protoplanetary disks and the Kelvin-Helmholtz instability in the dusty midplanes of protoplanetary disks.

Transport theory and codes

International Nuclear Information System (INIS)

Clancy, B.E.

1986-01-01

This chapter begins with a neutron transport equation which includes the one dimensional plane geometry problems, the one dimensional spherical geometry problems, and numerical solutions. The section on the ANISN code and its look-alikes covers problems which can be solved; eigenvalue problems; outer iteration loop; inner iteration loop; and finite difference solution procedures. The input and output data for ANISN is also discussed. Two dimensional problems such as the DOT code are given. Finally, an overview of the Monte-Carlo methods and codes are elaborated on

Validation of favor code linear elastic fracture solutions for finite-length flaw geometries

International Nuclear Information System (INIS)

Dickson, T.L.; Keeney, J.A.; Bryson, J.W.

1995-01-01

One of the current tasks within the US Nuclear Regulatory Commission (NRC)-funded Heavy Section Steel Technology Program (HSST) at Oak Ridge National Laboratory (ORNL) is the continuing development of the FAVOR (Fracture, analysis of Vessels: Oak Ridge) computer code. FAVOR performs structural integrity analyses of embrittled nuclear reactor pressure vessels (RPVs) with stainless steel cladding, to evaluate compliance with the applicable regulatory criteria. Since the initial release of FAVOR, the HSST program has continued to enhance the capabilities of the FAVOR code. ABAQUS, a nuclear quality assurance certified (NQA-1) general multidimensional finite element code with fracture mechanics capabilities, was used to generate a database of stress-intensity-factor influence coefficients (SIFICs) for a range of axially and circumferentially oriented semielliptical inner-surface flaw geometries applicable to RPVs with an internal radius (Ri) to wall thickness (w) ratio of 10. This database of SIRCs has been incorporated into a development version of FAVOR, providing it with the capability to perform deterministic and probabilistic fracture analyses of RPVs subjected to transients, such as pressurized thermal shock (PTS), for various flaw geometries. This paper discusses the SIFIC database, comparisons with other investigators, and some of the benchmark verification problem specifications and solutions

Development Of A Navier-Stokes Computer Code

Science.gov (United States)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Development of neutronics and thermal hydraulics coupled code – SAC-RIT for plate type fuel and its application to reactivity initiated transient analysis

International Nuclear Information System (INIS)

Singh, Tej; Kumar, Jainendra; Mazumdar, Tanay; Raina, V.K.

2013-01-01

Highlights: • A point reactor kinetics code coupled with thermal hydraulics of plate type fuel is developed. • This code is applicable for two phase flow of coolant. • Safety analysis of IAEA benchmark reactor core is carried out. • Results agree well with the results available in literature. - Abstract: A point reactor kinetics code SAC-RIT, acronym of Safety Analysis Code for Reactivity Initiated Transient, coupled with thermal hydraulics of two phase coolant flow for plate type fuel, is developed to calculate reactivity initiated transient analysis of nuclear research and test reactors. Point kinetics equations are solved by fourth order Runge Kutta method. Reactivity feedback effect is included into the code. Solution of kinetics equations gives neutronic power and it is then fed into a thermal hydraulic code where mass, momentum and thermal energy conservation equations are solved by explicit finite difference method to find out fuel, clad and coolant temperatures during transients. In this code, all possible flow regimes including laminar flow, transient flow and turbulent flow have been covered. Various heat transfer coefficients suitable for single liquid, sub-cooled boiling, saturation boiling, film boiling and single vapor phases are incorporated in the thermal hydraulic code

Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions

Directory of Open Access Journals (Sweden)

Armando Martínez-Pérez

2017-10-01

Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.

Finite-Difference Solution for Laminar or Turbulent Boundary Layer Flow over Axisymmetric Bodies with Ideal Gas, CF4, or Equilibrium Air Chemistry

Science.gov (United States)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-01-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Extrusion Process by Finite Volume Method Using OpenFoam Software

International Nuclear Information System (INIS)

Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose; Ivankovic, Alojz

2011-01-01

The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

2011-01-01

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

International Nuclear Information System (INIS)

Chernyshenko, Dmitri; Fangohr, Hans

2015-01-01

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges

An explicit method in non-linear soil-structure interaction

International Nuclear Information System (INIS)

Kunar, R.R.

1981-01-01

The explicit method of analysis in the time domain is ideally suited for the solution of transient dynamic non-linear problems. Though the method is not new, its application to seismic soil-structure interaction is relatively new and deserving of public discussion. This paper describes the principles of the explicit approach in soil-structure interaction and it presents a simple algorithm that can be used in the development of explicit computer codes. The paper also discusses some of the practical considerations like non-reflecting boundaries and time steps. The practicality of the method is demonstrated using a computer code, PRESS, which is used to compare the treatment of strain-dependent properties using average strain levels over the whole time history (the equivalent linear method) and using the actual strain levels at every time step to modify the soil properties (non-linear method). (orig.)

Chebyshev Finite Difference Method for Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

Boundary

2015-09-01

Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

How and Why Do Number-Space Associations Co-Vary in Implicit and Explicit Magnitude Processing Tasks?

Directory of Open Access Journals (Sweden)

Carrie Georges

2017-12-01

Full Text Available Evidence for number-space associations in implicit and explicit magnitude processing tasks comes from the parity and magnitude SNARC effect respectively. Different spatial accounts were suggested to underlie these spatial-numerical associations (SNAs with some inconsistencies in the literature. To determine whether the parity and magnitude SNAs arise from a single predominant account or task-dependent coding mechanisms, we adopted an individual differences approach to study their correlation and the extent of their association with arithmetic performance, spatial visualization ability and visualization profile. Additionally, we performed moderation analyses to determine whether the relation between these SNAs depended on individual differences in those cognitive factors. The parity and magnitude SNAs did not correlate and were differentially predicted by arithmetic performance and visualization profile respectively. These variables, however, also moderated the relation between the SNAs. While positive correlations were observed in object-visualizers with lower arithmetic performances, correlations were negative in spatial-visualizers with higher arithmetic performances. This suggests the predominance of a single account for both implicit and explicit SNAs in the two types of visualizers. However, the spatial nature of the account differs between object- and spatial-visualizers. No relation occurred in mixed-visualizers, indicating the activation of task-dependent coding mechanisms. Individual differences in arithmetic performance and visualization profile thus determined whether SNAs in implicit and explicit tasks co-varied and supposedly relied on similar or unrelated spatial coding mechanisms. This explains some inconsistencies in the literature regarding SNAs and highlights the usefulness of moderation analyses for understanding how the relation between different numerical concepts varies between individuals.

Parallel Finite Element Particle-In-Cell Code for Simulations of Space-charge Dominated Beam-Cavity Interactions

International Nuclear Information System (INIS)

Candel, A.; Kabel, A.; Ko, K.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Prudencio, E.; Schussman, G.; Uplenchwar, R.

2007-01-01

Over the past years, SLAC's Advanced Computations Department (ACD) has developed the parallel finite element (FE) particle-in-cell code Pic3P (Pic2P) for simulations of beam-cavity interactions dominated by space-charge effects. As opposed to standard space-charge dominated beam transport codes, which are based on the electrostatic approximation, Pic3P (Pic2P) includes space-charge, retardation and boundary effects as it self-consistently solves the complete set of Maxwell-Lorentz equations using higher-order FE methods on conformal meshes. Use of efficient, large-scale parallel processing allows for the modeling of photoinjectors with unprecedented accuracy, aiding the design and operation of the next-generation of accelerator facilities. Applications to the Linac Coherent Light Source (LCLS) RF gun are presented

Civil engineering: calculations of pre-stressed concrete structures using CodeAster

International Nuclear Information System (INIS)

Gerard, B.; Ulm, F.

1997-11-01

This document presents an analysis of the different calculation methods for pre-stressed concrete structure which can be performed by using finite element methods. Two methods of calculating the pre-stressing of concrete structures with finite elements have been determined. The equivalent method which consists of replacing the action of pre-stressing the concrete by equivalent forces. These method is well suited to dimensioning and studying the overall stability of a structure. It is not an easy matter to take into account the coupled or time-varying phenomena. This approach ignores the evolution of the interaction between the pre-stressing and the concrete. The explicit method which consists of including the mechanical resolution of the pre-stressed cables in that of a concrete structure. Not only does this allow a local study of the pre-stressed to be made, it also allows the coupling which developed over time to be determined, e.g. slip, deferred deformation and coupling between the steel and concrete behaviours. This method enables non-linear phenomena with varying degrees of complexity, such as fracture or yielding of the steels, drying out of the concrete, creep, etc to be described. The two methods are complementary. This document presents the mathematical and computer developments relating to each of this method. In the case of the explicit method, certain of the Code-Aster functions already make it possible to meet several EDF application requirements. Several couplings can be taken into account, such as thermomechanical, shrinkage in drying, creep, relaxation and injection of the cables. Three immediate developments of Code-Aster are proposed for the following applications: - a procedure for calculating the pre-stress losses along the pre-stressing cables; - a command to allocate these forces in the form of an initial force field in the bar elements associated with the cables; - a procedure for linking elements whose nodes do not coincide with each other

Finite element code FENIA verification and application for 3D modelling of thermal state of radioactive waste deep geological repository

Science.gov (United States)

Butov, R. A.; Drobyshevsky, N. I.; Moiseenko, E. V.; Tokarev, U. N.

2017-11-01

The verification of the FENIA finite element code on some problems and an example of its application are presented in the paper. The code is being developing for 3D modelling of thermal, mechanical and hydrodynamical (THM) problems related to the functioning of deep geological repositories. Verification of the code for two analytical problems has been performed. The first one is point heat source with exponential heat decrease, the second one - linear heat source with similar behavior. Analytical solutions have been obtained by the authors. The problems have been chosen because they reflect the processes influencing the thermal state of deep geological repository of radioactive waste. Verification was performed for several meshes with different resolution. Good convergence between analytical and numerical solutions was achieved. The application of the FENIA code is illustrated by 3D modelling of thermal state of a prototypic deep geological repository of radioactive waste. The repository is designed for disposal of radioactive waste in a rock at depth of several hundred meters with no intention of later retrieval. Vitrified radioactive waste is placed in the containers, which are placed in vertical boreholes. The residual decay heat of radioactive waste leads to containers, engineered safety barriers and host rock heating. Maximum temperatures and corresponding times of their establishment have been determined.

Introduction of polycrystal constitutive laws in a finite element code with applications to zirconium forming

International Nuclear Information System (INIS)

Maudlin, P.J.; Tome, C.N.; Kaschner, G.C.; Gray, G.T. III

1998-01-01

In this work the authors simulate the compressive deformation of heavily textured zirconium sheet using a finite element code with the constitutive response given by a polycrystal self-consistent model. They show that the strong anisotropy of the response can be explained in terms of the texture and the relative activity of prismatic (easy) and pyramidal (hard) slip modes. The simulations capture the yield anisotropy observed for so-called through-thickness and in-plane compression tests in terMs of the loading curves and final specimen geometries

Large Eddy Simulation of turbulent flows in compound channels with a finite element code

International Nuclear Information System (INIS)

Xavier, C.M.; Petry, A.P.; Moeller, S.V.

2011-01-01

This paper presents the numerical investigation of the developing flow in a compound channel formed by a rectangular main channel and a gap in one of the sidewalls. A three dimensional Large Eddy Simulation computational code with the classic Smagorinsky model is introduced, where the transient flow is modeled through the conservation equations of mass and momentum of a quasi-incompressible, isothermal continuous medium. Finite Element Method, Taylor-Galerkin scheme and linear hexahedrical elements are applied. Numerical results of velocity profile show the development of a shear layer in agreement with experimental results obtained with Pitot tube and hot wires. (author)

The computer code SEURBNUK/EURDYN (Release 1). Input and output specification

International Nuclear Information System (INIS)

Broadhouse, B.J.; Yerkess, A.

1986-05-01

SEURBNUK/EURODYN is an extension of SEURBNUK-2, a two dimensional, axisymmetric, Eulerian, finite element containment code in which the finite difference thin shell treatment is replaced by a finite element calculation for both thin and thick structures. These codes are designed to model the hydrodynamic development in time of a hypothetical core disruptive accident (HCDA) in a fast breeder reactor. This manual describes the input data specifications needed for the execution of SEURBNUK/EURDYN calculations, with information on output facilities, and aid to users to avoid some common difficulties. (UK)

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

Science.gov (United States)

Palmer, Grant

1988-01-01

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

A General Finite Element Scheme for Limit State Analysis and Optimization

DEFF Research Database (Denmark)

Damkilde, Lars

1999-01-01

Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...

Finite difference computing with PDEs a modern software approach

CERN Document Server

Langtangen, Hans Petter

2017-01-01

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Explicit TE/TM scheme for particle beam simulations

International Nuclear Information System (INIS)

Dohlus, M.; Zagorodnov, I.

2008-10-01

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version. It does not have dispersion in the longitudinal direction and the dispersion properties in the transversal plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee's explicit method used in the most popular electrodynamics codes. (orig.)

A Navier-Strokes Chimera Code on the Connection Machine CM-5: Design and Performance

Science.gov (United States)

Jespersen, Dennis C.; Levit, Creon; Kwak, Dochan (Technical Monitor)

1994-01-01

We have implemented a three-dimensional compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the 'chimera' approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. A parallel machine like the CM-5 is well-suited for finite-difference methods on structured grids. The regular pattern of connections of a structured mesh maps well onto the architecture of the machine. So the first design choice, finite differences on a structured mesh, is natural. We use centered differences in space, with added artificial dissipation terms. When numerically solving the Navier-Stokes equations, there are liable to be some mesh cells near a solid body that are small in at least one direction. This mesh cell geometry can impose a very severe CFL (Courant-Friedrichs-Lewy) condition on the time step for explicit time-stepping methods. Thus, though explicit time-stepping is well-suited to the architecture of the machine, we have adopted implicit time-stepping. We have further taken the approximate factorization approach. This creates the need to solve large banded linear systems and creates the first possible barrier to an efficient algorithm. To overcome this first possible barrier we have considered two options. The first is just to solve the banded linear systems with data spread over the whole machine, using whatever fast method is available. This option is adequate for solving scalar tridiagonal systems, but for scalar pentadiagonal or block tridiagonal systems it is somewhat slower than desired. The second option is to 'transpose' the flow and geometry variables as part of the time-stepping process: Start with x-lines of data in-processor. Form explicit terms in x, then transpose so y-lines of data are

High-Fidelity RF Gun Simulations with the Parallel 3D Finite Element Particle-In-Cell Code Pic3P

Energy Technology Data Exchange (ETDEWEB)

Candel, A; Kabel, A.; Lee, L.; Li, Z.; Limborg, C.; Ng, C.; Schussman, G.; Ko, K.; /SLAC

2009-06-19

SLAC's Advanced Computations Department (ACD) has developed the first parallel Finite Element 3D Particle-In-Cell (PIC) code, Pic3P, for simulations of RF guns and other space-charge dominated beam-cavity interactions. Pic3P solves the complete set of Maxwell-Lorentz equations and thus includes space charge, retardation and wakefield effects from first principles. Pic3P uses higher-order Finite Elementmethods on unstructured conformal meshes. A novel scheme for causal adaptive refinement and dynamic load balancing enable unprecedented simulation accuracy, aiding the design and operation of the next generation of accelerator facilities. Application to the Linac Coherent Light Source (LCLS) RF gun is presented.

Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model

Directory of Open Access Journals (Sweden)

Oluwaseun Egbelowo

2017-05-01

Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.

The computer code SEURBNUK/EURDYN. Pt. 2

International Nuclear Information System (INIS)

Yerkess, A.; Broadhouse, B.J.; Smith, B.L.

1987-01-01

SEURBNUK-2 is a two-dimensional, axisymmetric, Eulerian, finite difference containment code. The numerical procedure adopted in SEURBNUK to solve the hydrodynamic equations is based on the semi-implicit ICE method which itself is an extension of the MAC algorithm. SEURBNUK has a finite difference thin shell treatment for vessels and internal structures of arbitrary shape and includes the effects of the compressibility of the fluid. Fluid flow through porous media and porous structures can also be accommodated. SEURBNUK/EURDYN is an extension of SEURBNUK-2 in which the finite difference thin shell treatment is replaced by a finite element calculation for both thin or thick structures. This has been achieved by coupling the shell elements and axisymmetric triangular elements. Within the code, the equations of motion for the structures are solved quite separately from those for the fluid, and the timestep for the fluid can be an integer multiple of that for the structures. The interaction of the structures with the fluid is then considered as a modification to the coefficients in the pressure equations, the modifications naturally depending on the behaviour of the structures within the fluid cell. The code is limited to dealing with a single fluid, the coolant, and the bubble and the cover gas are treated as cavities of uniform pressure calculated via appropriate pressure-volume-energy relationships. This manual describes the input data specifications needed for the execution of SEURBNUK/EURDYN calculations. After explaining the output facilities information is included to aid users to avoid some common pit-falls

SYN3D: a single-channel, spatial flux synthesis code for diffusion theory calculations

Energy Technology Data Exchange (ETDEWEB)

Adams, C. H.

1976-07-01

This report is a user's manual for SYN3D, a computer code which uses single-channel, spatial flux synthesis to calculate approximate solutions to two- and three-dimensional, finite-difference, multigroup neutron diffusion theory equations. SYN3D is designed to run in conjunction with any one of several one- and two-dimensional, finite-difference codes (required to generate the synthesis expansion functions) currently being used in the fast reactor community. The report describes the theory and equations, the use of the code, and the implementation on the IBM 370/195 and CDC 7600 of the version of SYN3D available through the Argonne Code Center.

SYN3D: a single-channel, spatial flux synthesis code for diffusion theory calculations

International Nuclear Information System (INIS)

Adams, C.H.

1976-07-01

This report is a user's manual for SYN3D, a computer code which uses single-channel, spatial flux synthesis to calculate approximate solutions to two- and three-dimensional, finite-difference, multigroup neutron diffusion theory equations. SYN3D is designed to run in conjunction with any one of several one- and two-dimensional, finite-difference codes (required to generate the synthesis expansion functions) currently being used in the fast reactor community. The report describes the theory and equations, the use of the code, and the implementation on the IBM 370/195 and CDC 7600 of the version of SYN3D available through the Argonne Code Center

User's manual for the FEHM application - A finite-element heat- and mass-transfer code

International Nuclear Information System (INIS)

Zyvoloski, G.A.; Robinson, B.A.; Dash, Z.V.; Trease, L.L.

1997-07-01

The use of this code is applicable to natural-state studies of geothermal systems and groundwater flow. A primary use of the FEHM application will be to assist in the understanding of flow fields and mass transport in the saturated and unsaturated zones below the proposed Yucca Mountain nuclear waste repository in Nevada. The equations of heat and mass transfer for multiphase flow in porous and permeable media are solved in the FEHM application by using the finite-element method. The permeability and porosity of the medium are allowed to depend on pressure and temperature. The code also has provisions for movable air and water phases and noncoupled tracers; that is, tracer solutions that do not affect the heat- and mass-transfer solutions. The tracers can be passive or reactive. The code can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. In fact, FEHM is capable of describing flow that is dominated in many areas by fracture and fault flow, including the inherently three-dimensional flow that results from permeation to and from faults and fractures. The code can handle coupled heat and mass-transfer effects, such as boiling, dryout, and condensation that can occur in the near-field region surrounding the potential repository and the natural convection that occurs through Yucca Mountain due to seasonal temperature changes. This report outlines the uses and capabilities of the FEHM application, initialization of code variables, restart procedures, and error processing. The report describes all the data files, the input data, including individual input records or parameters, and the various output files. The system interface is described, including the software environment and installation instructions

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

Science.gov (United States)

Qiao, Shan; Jackson, Edward; Coussios, Constantin-C.; Cleveland, Robin

2015-10-01

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important.

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

Energy Technology Data Exchange (ETDEWEB)

Qiao, Shan, E-mail: shan.qiao@eng.ox.ac.uk; Jackson, Edward; Coussios, Constantin-C; Cleveland, Robin [Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford (United Kingdom)

2015-10-28

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important.

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

International Nuclear Information System (INIS)

Qiao, Shan; Jackson, Edward; Coussios, Constantin-C; Cleveland, Robin

2015-01-01

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important

Application of finite-element method to three-dimensional nuclear reactor analysis

International Nuclear Information System (INIS)

Cheung, K.Y.

1985-01-01

The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired

GAPCON-THERMAL-3 code description

International Nuclear Information System (INIS)

Lanning, D.D.; Mohr, C.L.; Panisko, F.E.; Stewart, K.B.

1978-01-01

GAPCON-3 is a computer program that predicts the thermal and mechanical behavior of an operating fuel rod during its normal lifetime. The code calculates temperatures, dimensions, stresses, and strains for the fuel and the cladding in both the radial and axial directions for each step of the user specified power history. The method of weighted residuals is for the steady state temperature calculation, and is combined with a finite difference approximation of the time derivative for transient conditions. The stress strain analysis employs an iterative axisymmetric finite element procedure that includes plasticity and creep for normal and pellet-clad mechanical interaction loads. GAPCON-3 can solve steady state and operational transient problems. Comparisons of GAPCON-3 predictions to both closed form analytical solutions and actual inpile instrumented fuel rod data have demonstrated the ability of the code to calculate fuel rod behavior. GAPCON-3 features a restart capability and an associated plot package unavailable in previous GAPCON series codes

GAPCON-THERMAL-3 code description

Energy Technology Data Exchange (ETDEWEB)

Lanning, D.D.; Mohr, C.L.; Panisko, F.E.; Stewart, K.B.

1978-01-01

GAPCON-3 is a computer program that predicts the thermal and mechanical behavior of an operating fuel rod during its normal lifetime. The code calculates temperatures, dimensions, stresses, and strains for the fuel and the cladding in both the radial and axial directions for each step of the user specified power history. The method of weighted residuals is for the steady state temperature calculation, and is combined with a finite difference approximation of the time derivative for transient conditions. The stress strain analysis employs an iterative axisymmetric finite element procedure that includes plasticity and creep for normal and pellet-clad mechanical interaction loads. GAPCON-3 can solve steady state and operational transient problems. Comparisons of GAPCON-3 predictions to both closed form analytical solutions and actual inpile instrumented fuel rod data have demonstrated the ability of the code to calculate fuel rod behavior. GAPCON-3 features a restart capability and an associated plot package unavailable in previous GAPCON series codes.

A Finite Axiomatization of G-Dependence

OpenAIRE

Paolini, Gianluca

2015-01-01

We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.

Linear tree codes and the problem of explicit constructions

Czech Academy of Sciences Publication Activity Database

Pudlák, Pavel

2016-01-01

Roč. 490, February 1 (2016), s. 124-144 ISSN 0024-3795 R&D Projects: GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : tree code * error correcting code * triangular totally nonsingular matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S002437951500645X

Explicit control of adaptive automation under different levels of environmental stress.

Science.gov (United States)

Sauer, Jürgen; Kao, Chung-Shan; Wastell, David; Nickel, Peter

2011-08-01

This article examines the effectiveness of three different forms of explicit control of adaptive automation under low- and high-stress conditions, operationalised by different levels of noise. In total, 60 participants were assigned to one of three types of automation design (free, prompted and forced choice). They were trained for 4 h on a highly automated simulation of a process control environment, called AutoCAMS. This was followed by a 4-h testing session under noise exposure and quiet conditions. Measures of performance, psychophysiology and subjective reactions were taken. The results showed that all three modes of explicit control of adaptive automation modes were able to attenuate the negative effects of noise. This was partly due to the fact that operators opted for higher levels of automation under noise. It also emerged that forced choice showed marginal advantages over the two other automation modes. Statement of Relevance: This work is relevant to the design of adaptive automation since it emphasises the need to consider the impact of work-related stressors during task completion. During the presence of stressors, different forms of operator support through automation may be required than under more favourable working conditions.

Application of viscoplastic constitutive equations in finite element programs

International Nuclear Information System (INIS)

Hornberger, K.; Stamm, H.

1987-04-01

The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de

Conversion and comparison of the mathematical, three-dimensional, finite-difference, ground-water flow model to the modular, three-dimensional, finite-difference, ground-water flow model for the Tesuque aquifer system in northern New Mexico

Science.gov (United States)

Umari, A.M.; Szeliga, T.L.

1989-01-01

The three-dimensional finite-difference groundwater model (using a mathematical groundwater flow code) of the Tesuque aquifer system in northern New Mexico was converted to run using the U.S. Geological Survey 's modular groundwater flow code. Results from the final versions of the predevelopment and 1947 to 2080 transient simulations of the two models are compared. A correlation coefficient of 0.9905 was obtained for the match in block-by-block head-dependent fluxes for predevelopment conditions. There are, however, significant differences in at least two specific cases. In the first case, a difference is associated with the net loss from the Pojoaque River and its tributaries to the aquifer. The net loss by the river is given as 1.134 cu ft/sec using the original groundwater model, which is 38.1% less than the net loss by the river of 1.8319 cu ft/sec computed in this study. In the second case, the large difference is computed for the transient decline in the hydraulic head of a model block near Tesuque Pueblo. The hydraulic-head decline by 2080 is, using the original model, 249 ft, which is 14.7% less than the hydraulic head of 292 ft computed by this study. In general, the differences between the two sets of results are not large enough to lead to different conclusions regarding the behavior of the system at steady state or when pumped. (USGS)

Elementary introduction to finite difference equations

International Nuclear Information System (INIS)

White, J.W.

1976-01-01

An elementary description is given of the basic vocabulary and concepts associated with finite difference modeling. The material discussed is biased toward the types of large computer programs used at the Lawrence Livermore Laboratory. Particular attention is focused on truncation error and how it can be affected by zoning patterns. The principle of convergence is discussed, and convergence as a tool for improving calculational accuracy and efficiency is emphasized

PRONTO3D users` instructions: A transient dynamic code for nonlinear structural analysis

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Mello, F.J.; Heinstein, M.W.; Swegle, J.W.; Ratner, J.A. [Sandia National Labs., Albuquerque, NM (United States); Zadoks, R.I. [Univ. of Texas, El Paso, TX (United States)

1998-06-01

This report provides an updated set of users` instructions for PRONTO3D. PRONTO3D is a three-dimensional, transient, solid dynamics code for analyzing large deformations of highly nonlinear materials subjected to extremely high strain rates. This Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion. Eight-node, uniform strain, hexahedral elements and four-node, quadrilateral, uniform strain shells are used in the finite element formulation. An adaptive time step control algorithm is used to improve stability and performance in plasticity problems. Hourglass distortions can be eliminated without disturbing the finite element solution using either the Flanagan-Belytschko hourglass control scheme or an assumed strain hourglass control scheme. All constitutive models in PRONTO3D are cast in an unrotated configuration defined using the rotation determined from the polar decomposition of the deformation gradient. A robust contact algorithm allows for the impact and interaction of deforming contact surfaces of quite general geometry. The Smooth Particle Hydrodynamics method has been embedded into PRONTO3D using the contact algorithm to couple it with the finite element method.

a class of finite fields, for odd primes l

Indian Academy of Sciences (India)

We see that the Fermat curves correspond precisely to those curves among each class (for = , 2), that are maximal or minimal over F q . We observe that each Fermat prime gives rise to explicit maximal and minimal curves over finite fields of characteristic 2. For = 2, we explicitly determine the -function(s) for this ...

The mimetic finite difference method for elliptic problems

CERN Document Server

Veiga, Lourenço Beirão; Manzini, Gianmarco

2014-01-01

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

NCEL: two dimensional finite element code for steady-state temperature distribution in seven rod-bundle

International Nuclear Information System (INIS)

Hrehor, M.

1979-01-01

The paper deals with an application of the finite element method to the heat transfer study in seven-pin models of LMFBR fuel subassembly. The developed code NCEL solves two-dimensional steady state heat conduction equation in the whole subassembly model cross-section and enebles to perform the analysis of thermal behaviour in both normal and accidental operational conditions as eccentricity of the central rod or full or partial (porous) blockage of some part of the cross-flow area. The heat removal is simulated by heat sinks in coolant under conditions of subchannels slug flow approximation

Finite-difference numerical simulations of underground explosion cavity decoupling

Science.gov (United States)

Aldridge, D. F.; Preston, L. A.; Jensen, R. P.

2012-12-01

Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion

Analysis of the KUCA MEU experiments using the ANL code system

Energy Technology Data Exchange (ETDEWEB)

Shiroya, S.; Hayashi, M.; Kanda, K.; Shibata, T.; Woodruff, W.L.; Matos, J.E.

1982-01-01

This paper provides some preliminary results on the analysis of the KUCA critical experiments using the ANL code system. Since this system was employed in the earlier neutronics calculations for the KUHFR, it is important to assess its capabilities for the KUHFR. The KUHFR has a unique core configuration which is difficult to model precisely with current diffusion theory codes. This paper also provides some results from a finite-element diffusion code (2D-FEM-KUR), which was developed in a cooperative research program between KURRI and JAERI. This code provides the capability for mockup of a complex core configuration as the KUHFR. Using the same group constants generated by the EPRI-CELL code, the results of the 2D-FEM-KUR code are compared with the finite difference diffusion code (DIF3D(2D) which is mainly employed in this analysis.

Analysis of the KUCA MEU experiments using the ANL code system

International Nuclear Information System (INIS)

Shiroya, S.; Hayashi, M.; Kanda, K.; Shibata, T.; Woodruff, W.L.; Matos, J.E.

1982-01-01

This paper provides some preliminary results on the analysis of the KUCA critical experiments using the ANL code system. Since this system was employed in the earlier neutronics calculations for the KUHFR, it is important to assess its capabilities for the KUHFR. The KUHFR has a unique core configuration which is difficult to model precisely with current diffusion theory codes. This paper also provides some results from a finite-element diffusion code (2D-FEM-KUR), which was developed in a cooperative research program between KURRI and JAERI. This code provides the capability for mockup of a complex core configuration as the KUHFR. Using the same group constants generated by the EPRI-CELL code, the results of the 2D-FEM-KUR code are compared with the finite difference diffusion code (DIF3D(2D) which is mainly employed in this analysis

Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.

OpenAIRE

Buttler, Hans-Jurg

1995-01-01

The purpose of this paper is to evaluate numerically the semi-American callable bond by means of finite difference methods. This study implies three results. First, the numerical error is greater for the callable bond price than for the straight bond price, and too large for real applications Secondly, the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points. Thi...

Solution of 2D and 3D hexagonal geometry benchmark problems by using the finite element diffusion code DIFGEN

International Nuclear Information System (INIS)

Gado, J.

1986-02-01

The four group, 2D and 3D hexagonal geometry HTGR benchmark problems and a 2D hexagonal geometry PWR (WWER) benchmark problem have been solved by using the finite element diffusion code DIFGEN. The hexagons (or hexagonal prisms) were subdivided into first order or second order triangles or quadrilaterals (or triangular or quadrilateral prisms). In the 2D HTGR case of the number of the inserted absorber rods was also varied (7, 6, 0 or 37 rods). The calculational results are in a good agreement with the results of other calculations. The larger systematic series of DIFGEN calculations have given a quantitative picture on the convergence properties of various finite element modellings of hexagonal grids in DIFGEN. (orig.)

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

International Nuclear Information System (INIS)

Meyers, M.D.; Huang, C.-K.; Zeng, Y.; Yi, S.A.; Albright, B.J.

2015-01-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

Science.gov (United States)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

Statistical mechanics of error-correcting codes

Science.gov (United States)

Kabashima, Y.; Saad, D.

1999-01-01

We investigate the performance of error-correcting codes, where the code word comprises products of K bits selected from the original message and decoding is carried out utilizing a connectivity tensor with C connections per index. Shannon's bound for the channel capacity is recovered for large K and zero temperature when the code rate K/C is finite. Close to optimal error-correcting capability is obtained for finite K and C. We examine the finite-temperature case to assess the use of simulated annealing for decoding and extend the analysis to accommodate other types of noisy channels.

Modification of the finite element heat and mass transfer code (FEHMN) to model multicomponent reactive transport

International Nuclear Information System (INIS)

Viswanathan, H.S.

1995-01-01

The finite element code FEHMN is a three-dimensional finite element heat and mass transport simulator that can handle complex stratigraphy and nonlinear processes such as vadose zone flow, heat flow and solute transport. Scientists at LANL have been developed hydrologic flow and transport models of the Yucca Mountain site using FEHMN. Previous FEHMN simulations have used an equivalent K d model to model solute transport. In this thesis, FEHMN is modified making it possible to simulate the transport of a species with a rigorous chemical model. Including the rigorous chemical equations into FEHMN simulations should provide for more representative transport models for highly reactive chemical species. A fully kinetic formulation is chosen for the FEHMN reactive transport model. Several methods are available to computationally implement a fully kinetic formulation. Different numerical algorithms are investigated in order to optimize computational efficiency and memory requirements of the reactive transport model. The best algorithm of those investigated is then incorporated into FEHMN. The algorithm chosen requires for the user to place strongly coupled species into groups which are then solved for simultaneously using FEHMN. The complete reactive transport model is verified over a wide variety of problems and is shown to be working properly. The simulations demonstrate that gas flow and carbonate chemistry can significantly affect 14 C transport at Yucca Mountain. The simulations also provide that the new capabilities of FEHMN can be used to refine and buttress already existing Yucca Mountain radionuclide transport studies

A 2D benchmark for the verification of the PEBBED code

International Nuclear Information System (INIS)

Ganapol, Barry D.; Gougar, Hans D.; Ougouag, Abderrafi M.

2008-01-01

A new benchmarking concept is presented for verifying the PEBBED 3D multigroup finite difference/nodal diffusion code with application to pebble bed modular reactors (PBMRs). The key idea is to perform convergence acceleration, also called extrapolation to zero discretization, of a basic finite difference numerical algorithm to give extremely high accuracy. The method is first demonstrated on a 1D cylindrical shell and then on an r,Θ wedge where the order of the second order finite difference scheme is confirmed to four places. (authors)

Ward identities at finite temperature

International Nuclear Information System (INIS)

DOlivo, J.C.; Torres, M.; Tututi, E.

1996-01-01

The Ward identities for QED at finite temperature are derived using the functional real-time formalism. They are verified by an explicit one-loop calculation. An effective causal vertex is constructed which satisfy the Ward identity with the associated retarded self-energy. copyright 1996 American Institute of Physics

A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

International Nuclear Information System (INIS)

Marxen, Olaf; Magin, Thierry E.; Shaqfeh, Eric S.G.; Iaccarino, Gianluca

2013-01-01

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as well as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium

The finite-temperature Gaussian effective potential from a variational principle

International Nuclear Information System (INIS)

Haugerud, H.; Ravndal, F.

1990-08-01

Writing the partition function for a scalar quantum field theory as a functional integral, it follows that the finite-temperature Gaussian effective potential is an upper limit to the free energy of the system. Explicit results are given for the anharmonic oscillator at finite temperature. 5 refs., 2 figs

Novel quadrilateral elements based on explicit Hermite polynomials for bending of Kirchhoff-Love plates

Science.gov (United States)

Beheshti, Alireza

2018-03-01

The contribution addresses the finite element analysis of bending of plates given the Kirchhoff-Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.

Code conforming determination of cumulative usage factors for general elastic-plastic finite element analyses

International Nuclear Information System (INIS)

Rudolph, Juergen; Goetz, Andreas; Hilpert, Roland

2012-01-01

The procedures of fatigue analyses of several relevant nuclear and conventional design codes (ASME, KTA, EN, AD) for power plant components differentiate between an elastic, simplified elastic-plastic and elastic-plastic fatigue check. As a rule, operational load levels will exclude the purely elastic fatigue check. The application of the code procedure of the simplified elastic-plastic fatigue check is common practice. Nevertheless, resulting cumulative usage factors may be overly conservative mainly due to high code based plastification penalty factors Ke. As a consequence, the more complex and still code conforming general elastic-plastic fatigue analysis methodology based on non-linear finite element analysis (FEA) is applied for fatigue design as an alternative. The requirements of the FEA and the material law to be applied have to be clarified in a first step. Current design codes only give rough guidelines on these relevant items. While the procedure for the simplified elastic-plastic fatigue analysis and the associated code passages are based on stress related cycle counting and the determination of pseudo elastic equivalent stress ranges, an adaptation to elastic-plastic strains and strain ranges is required for the elastic-plastic fatigue check. The associated requirements are explained in detail in the paper. If the established and implemented evaluation mechanism (cycle counting according to the peak and valley respectively the rainflow method, calculation of stress ranges from arbitrary load-time histories and determination of cumulative usage factors based on all load events) is to be retained, a conversion of elastic-plastic strains and strain ranges into pseudo elastic stress ranges is required. The algorithm to be applied is described in the paper. It has to be implemented in the sense of an extended post processing operation of FEA e.g. by APDL scripts in ANSYS registered . Variations of principal stress (strain) directions during the loading

Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

Science.gov (United States)

Arntsen, B.

2017-12-01

The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.

Explicit isospectral flows associated to the AKNS operator on the unit interval. II

Science.gov (United States)

Amour, Laurent

2012-10-01

Explicit flows associated to any tangent vector fields on any isospectral manifold for the AKNS operator acting in L2 × L2 on the unit interval are written down. The manifolds are of infinite dimension (and infinite codimension). The flows are called isospectral and also are Hamiltonian flows. It is proven that they may be explicitly expressed in terms of regularized determinants of infinite matrix-valued functions with entries depending only on the spectral data at the starting point of the flow. The tangent vector fields are decomposed as ∑ξkTk where ξ ∈ ℓ2 and the Tk ∈ L2 × L2 form a particular basis of the tangent vector spaces of the infinite dimensional manifold. The paper here is a continuation of Amour ["Explicit isospectral flows for the AKNS operator on the unit interval," Inverse Probl. 25, 095008 (2009)], 10.1088/0266-5611/25/9/095008 where, except for a finite number, all the components of the sequence ξ are zero in order to obtain an explicit expression for the isospectral flows. The regularized determinants induce counter-terms allowing for the consideration of finite quantities when the sequences ξ run all over ℓ2.

Adolescents' explicit and implicit evaluations of hypothetical and actual peers with different bullying participant roles.

Science.gov (United States)

Pouwels, J Loes; Lansu, Tessa A M; Cillessen, Antonius H N

2017-07-01

This study examined how adolescents evaluate bullying at three levels of specificity: (a) the general concept of bullying, (b) hypothetical peers in different bullying participant roles, and (c) actual peers in different bullying participant roles. Participants were 163 predominantly ethnic majority adolescents in The Netherlands (58% girls; M age =16.34years, SD=0.79). For the hypothetical peers, we examined adolescents' explicit evaluations as well as their implicit evaluations. Adolescents evaluated the general concept of bullying negatively. Adolescents' explicit evaluations of hypothetical and actual peers in the bullying roles depended on their own role, but adolescents' implicit evaluations of hypothetical peers did not. Adolescents' explicit evaluations of hypothetical peers and actual peers were different. Hypothetical bullies were evaluated negatively by all classmates, whereas hypothetical victims were evaluated relatively positively compared with the other roles. However, when adolescents evaluated their actual classmates, the differences between bullies and the other roles were smaller, whereas victims were evaluated the most negatively of all roles. Further research should take into account that adolescents' evaluations of hypothetical peers differ from their evaluations of actual peers. Copyright © 2017 Elsevier Inc. All rights reserved.

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

Science.gov (United States)

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Finite difference order doubling in two dimensions

International Nuclear Information System (INIS)

Killingbeck, John P; Jolicard, Georges

2008-01-01

An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process

EVALUATION OF THE POUNDING FORCES DURING EARTHQUAKE USING EXPLICIT DYNAMIC TIME INTEGRATION METHOD

Directory of Open Access Journals (Sweden)

Nica George Bogdan

2017-09-01

Full Text Available Pounding effects during earthquake is a subject of high significance for structural engineers performing in the urban areas. In this paper, two ways to account for structural pounding are used in a MATLAB code, namely classical stereomechanics approach and nonlinear viscoelastic impact element. The numerical study is performed on SDOF structures acted by ELCentro recording. While most of the studies available in the literature are related to Newmark implicit time integration method, in this study the equations of motion are numerical integrated using central finite difference method, an explicit method, having the main advantage that in the displacement at the ith+1 step is calculated based on the loads from the ith step. Thus, the collision is checked and the pounding forces are taken into account into the equation of motion in an easier manner than in an implicit integration method. First, a comparison is done using available data in the literature. Both linear and nonlinear behavior of the structures during earthquake is further investigated. Several layout scenarios are also investigated, in which one or more weak buildings are adjacent to a stiffer building. One of the main findings in this paper is related to the behavior of a weak structure located between two stiff structures.

A new 3-D integral code for computation of accelerator magnets

International Nuclear Information System (INIS)

Turner, L.R.; Kettunen, L.

1991-01-01

For computing accelerator magnets, integral codes have several advantages over finite element codes; far-field boundaries are treated automatically, and computed field in the bore region satisfy Maxwell's equations exactly. A new integral code employing edge elements rather than nodal elements has overcome the difficulties associated with earlier integral codes. By the use of field integrals (potential differences) as solution variables, the number of unknowns is reduced to one less than the number of nodes. Two examples, a hollow iron sphere and the dipole magnet of Advanced Photon Source injector synchrotron, show the capability of the code. The CPU time requirements are comparable to those of three-dimensional (3-D) finite-element codes. Experiments show that in practice it can realize much of the potential CPU time saving that parallel processing makes possible. 8 refs., 4 figs., 1 tab

A multigrid solution method for mixed hybrid finite elements

Energy Technology Data Exchange (ETDEWEB)

Schmid, W. [Universitaet Augsburg (Germany)

1996-12-31

We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal

Science.gov (United States)

Zamudio, Gabriel S.; José, Marco V.

2018-03-01

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-01-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax

Validation of finite element code DELFIN by means of the zero power experiences at the nuclear power plant of Atucha I

International Nuclear Information System (INIS)

Grant, C.R.

1996-01-01

Code DELFIN, developed in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and currents among elements and a more realistic representation of the hexagonal lattice of the reactor. It can be used for fuel management calculation, Xenon oscillation and spatial kinetics. Using the HUEMUL code for cell calculation (which uses a generalized two dimensional collision probability theory and has the WIMS library incorporated in a data base), the zero power experiences performed in 1974 were calculated. (author). 8 refs., 9 figs., 3 tabs

New nonbinary quantum codes with larger distance constructed from BCH codes over 𝔽q2

Science.gov (United States)

Xu, Gen; Li, Ruihu; Fu, Qiang; Ma, Yuena; Guo, Luobin

2017-03-01

This paper concentrates on construction of new nonbinary quantum error-correcting codes (QECCs) from three classes of narrow-sense imprimitive BCH codes over finite field 𝔽q2 (q ≥ 3 is an odd prime power). By a careful analysis on properties of cyclotomic cosets in defining set T of these BCH codes, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing BCH codes is determined to be much larger than the result given according to Aly et al. [S. A. Aly, A. Klappenecker and P. K. Sarvepalli, IEEE Trans. Inf. Theory 53, 1183 (2007)] for each different code length. Thus families of new nonbinary QECCs are constructed, and the newly obtained QECCs have larger distance than those in previous literature.

Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

KAUST Repository

Bonito, Andrea; Guermond, Jean-Luc; Popov, Bojan

2013-01-01

We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method

SLIC: an interactive mesh generator for finite element and finite difference application programs

International Nuclear Information System (INIS)

Gerhard, M.A.; Greenlaw, R.C.

1979-01-01

Computers with extended memory, such as the CDC STAR 100 and the CRAY 1 with mega-word capacities, are greatly enlarging the size of finite element problems which can be solved. The cost of developing and testing large meshes can be prohibitive unless one uses a computer program for mesh generation and plotting. SLIC is an interactive mesh program which builds and plots 2- and 3-D continuum meshes from interactive terminal or disc input. The user inputs coordinates for certain key points and enters commands which complete the description of the geometry. Entire surfaces and volumes are then generated from the geometric skeleton. SLIC allows the user to correct input errors and saves the corrected command list for later reuse. The mesh can be plotted on a video display at any stage of development to evaluate the work in progress. Output is in the form of an input file to a user-selected computer code. Among the available output types are ADINA, SAP4, and NIKE2D. 11 figures

User`s manual for the FEHM application -- A finite-element heat- and mass-transfer code

Energy Technology Data Exchange (ETDEWEB)

Zyvoloski, G.A.; Robinson, B.A.; Dash, Z.V.; Trease, L.L.

1997-07-01

The use of this code is applicable to natural-state studies of geothermal systems and groundwater flow. A primary use of the FEHM application will be to assist in the understanding of flow fields and mass transport in the saturated and unsaturated zones below the proposed Yucca Mountain nuclear waste repository in Nevada. The equations of heat and mass transfer for multiphase flow in porous and permeable media are solved in the FEHM application by using the finite-element method. The permeability and porosity of the medium are allowed to depend on pressure and temperature. The code also has provisions for movable air and water phases and noncoupled tracers; that is, tracer solutions that do not affect the heat- and mass-transfer solutions. The tracers can be passive or reactive. The code can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. In fact, FEHM is capable of describing flow that is dominated in many areas by fracture and fault flow, including the inherently three-dimensional flow that results from permeation to and from faults and fractures. The code can handle coupled heat and mass-transfer effects, such as boiling, dryout, and condensation that can occur in the near-field region surrounding the potential repository and the natural convection that occurs through Yucca Mountain due to seasonal temperature changes. This report outlines the uses and capabilities of the FEHM application, initialization of code variables, restart procedures, and error processing. The report describes all the data files, the input data, including individual input records or parameters, and the various output files. The system interface is described, including the software environment and installation instructions.

Do vision and haptics share common representations? Implicit and explicit memory within and between modalities.

Science.gov (United States)

Easton, R D; Srinivas, K; Greene, A J

1997-01-01

Previous assessments of verbal cross-modal priming have typically been conducted with the visual and auditory modalities. Within-modal priming is always found to be substantially larger than cross-modal priming, a finding that could reflect modality modularity, or alternatively, differences between the coding of visual and auditory verbal information (i.e., geometric vs. phonological). The present experiments assessed implicit and explicit memory within and between vision and haptics, where verbal information could be coded in geometric terms. Because haptic perception of words is sequential or letter-by-letter, experiments were also conducted to isolate the effects of simultaneous versus sequential processing from the manipulation of modality. Together, the results reveal no effects of modality change on implicit or explicit tests. The authors discuss representational similarities between vision and haptics as well as image mediation as possible explanations for the results.

Leading relativistic corrections for atomic P states calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions

Science.gov (United States)

Stanke, Monika; Bralin, Amir; Bubin, Sergiy; Adamowicz, Ludwik

2018-01-01

In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the L =1 total orbital angular momentum (P states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest 1P states of the helium atom and the four lowest 1P states of the beryllium atom.

Finite Difference Schemes as Algebraic Correspondences between Layers

Science.gov (United States)

Malykh, Mikhail; Sevastianov, Leonid

2018-02-01

For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

Parallel implementations of 2D explicit Euler solvers

International Nuclear Information System (INIS)

Giraud, L.; Manzini, G.

1996-01-01

In this work we present a subdomain partitioning strategy applied to an explicit high-resolution Euler solver. We describe the design of a portable parallel multi-domain code suitable for parallel environments. We present several implementations on a representative range of MlMD computers that include shared memory multiprocessors, distributed virtual shared memory computers, as well as networks of workstations. Computational results are given to illustrate the efficiency, the scalability, and the limitations of the different approaches. We discuss also the effect of the communication protocol on the optimal domain partitioning strategy for the distributed memory computers

The computer code SEURBNUK/EURDYN (release 1). Input and output specifications

International Nuclear Information System (INIS)

Smith, B.L.; Broadhouse, B.J.; Yerkess, A.

1986-05-01

SEURBNUK-2 is a two-dimensional, axisymmetric, Eulerian, finite difference containment code developed initially by AWRE Aldermaston, AEE Winfrith and JRC-Ispra, and more recently by AEEW, JRC and EIR Wuerenlingen. The numerical procedure adopted in SEURBNUK to solve the hydrodynamic equations is based on the semi-implicit ICE method which itself is an extension of the MAC algorithm. SEURBNUK has a finite difference thin shell treatment for vessels and internal structures of arbitrary shape and includes the effects of the compressibility of the fluid. Fluid flow through porous media and porous structures can also be accommodated. SEURBNUK/EURDYN is an extension of SEURBNUK-2 in which the finite difference thin shell treatment is replaced by a finite element calculation for both thin or thick structures. This has been achieved by coupling the finite element code EURDYN with SEURBNUK-2, allowing the use of conical shell elements and axisymmetric triangular elements. Within the code, the equations of motion for the structures are solved quite separately from those for the fluid, and the timestep for the fluid can be an integer multiple of that for the structures. The interaction of the structures with the fluid is then considered as a modification to the coefficients in the pressure equations, the modifications naturally depending on the behaviour of the structures within the fluid cell. The code is limited to dealing with a single fluid, the coolant, and the bubble and the cover gas are treated as cavities of uniform pressure calculated via appropriate pressure-volume-energy relationships. This manual describes the input data specifications needed for the execution of SEURBNUK/EURDYN calculations. After explaining the output facilities information is included to aid users to avoid some common pit-falls. (author)

FDiff3: a finite-difference solver for facilitating understanding of heat conduction and numerical analysis

Energy Technology Data Exchange (ETDEWEB)

Russell, M.B. [University of Hertfordshire, Hatfield (United Kingdom). Department of Aerospace, Automotive and Design Engineering; Probert, S.D. [Cranfield University, Bedfordshire (United Kingdom). School of Engineering

2004-12-01

The growing requirement for energy thrift and hence the increasing emphasis on 'low-purchased-energy' designs are stimulating the need for more accurate insights into the thermal behaviours of buildings and their components. This better understanding is preferably achieved, rather than by using 'closed software' or teaching the relevant mathematics outside heat-transfer lessons, but from embedding the pertinent tutoring while dealing with heat-transfer problems using an open-source code approach. Hence a finite-difference software program (FDiff3) has been composed to show the principles of numerical analysis as well as improve the undergraduates' perception of transient conduction. The pedagogic approach behind the development, its present capabilities and applications to sample test-cases are discussed. (author)

Yucca Mountain Project thermal and mechanical codes first benchmark exercise: Part 3, Jointed rock mass analysis

International Nuclear Information System (INIS)

Costin, L.S.; Bauer, S.J.

1991-10-01

Thermal and mechanical models for intact and jointed rock mass behavior are being developed, verified, and validated at Sandia National Laboratories for the Yucca Mountain Site Characterization Project. Benchmarking is an essential part of this effort and is one of the tools used to demonstrate verification of engineering software used to solve thermomechanical problems. This report presents the results of the third (and final) phase of the first thermomechanical benchmark exercise. In the first phase of this exercise, nonlinear heat conduction code were used to solve the thermal portion of the benchmark problem. The results from the thermal analysis were then used as input to the second and third phases of the exercise, which consisted of solving the structural portion of the benchmark problem. In the second phase of the exercise, a linear elastic rock mass model was used. In the third phase of the exercise, two different nonlinear jointed rock mass models were used to solve the thermostructural problem. Both models, the Sandia compliant joint model and the RE/SPEC joint empirical model, explicitly incorporate the effect of the joints on the response of the continuum. Three different structural codes, JAC, SANCHO, and SPECTROM-31, were used with the above models in the third phase of the study. Each model was implemented in two different codes so that direct comparisons of results from each model could be made. The results submitted by the participants showed that the finite element solutions using each model were in reasonable agreement. Some consistent differences between the solutions using the two different models were noted but are not considered important to verification of the codes. 9 refs., 18 figs., 8 tabs

The finite Fourier transform of classical polynomials

OpenAIRE

Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

2014-01-01

The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

Feedback equivalence of convolutional codes over finite rings

Directory of Open Access Journals (Sweden)

DeCastro-García Noemí

2017-12-01

Full Text Available The approach to convolutional codes from the linear systems point of view provides us with effective tools in order to construct convolutional codes with adequate properties that let us use them in many applications. In this work, we have generalized feedback equivalence between families of convolutional codes and linear systems over certain rings, and we show that every locally Brunovsky linear system may be considered as a representation of a code under feedback convolutional equivalence.

Method for calculating internal radiation and ventilation with the ADINAT heat-flow code

International Nuclear Information System (INIS)

Butkovich, T.R.; Montan, D.N.

1980-01-01

One objective of the spent fuel test in Climax Stock granite (SFTC) is to correctly model the thermal transport, and the changes in the stress field and accompanying displacements from the application of the thermal loads. We have chosen the ADINA and ADINAT finite element codes to do these calculations. ADINAT is a heat transfer code compatible to the ADINA displacement and stress analysis code. The heat flow problem encountered at SFTC requires a code with conduction, radiation, and ventilation capabilities, which the present version of ADINAT does not have. We have devised a method for calculating internal radiation and ventilation with the ADINAT code. This method effectively reproduces the results from the TRUMP multi-dimensional finite difference code, which correctly models radiative heat transport between drift surfaces, conductive and convective thermal transport to and through air in the drifts, and mass flow of air in the drifts. The temperature histories for each node in the finite element mesh calculated with ADINAT using this method can be used directly in the ADINA thermal-mechanical calculation

The Hellman-Feynman theorem at finite temperature

International Nuclear Information System (INIS)

Cabrera, A.; Calles, A.

1990-01-01

The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)

The development of fluid codes for the laser compression of plasma

International Nuclear Information System (INIS)

Nicholas, D.J.

1982-08-01

Notes are given on the construction and use of simulation codes in plasma physics requiring only a limited background knowledge in numerical analysis and finite-difference techniques. The development of a 1-D Eulerian codes to source form is followed as an example. (U.K.)

The Aster code; Code Aster

Energy Technology Data Exchange (ETDEWEB)

Delbecq, J.M

1999-07-01

The Aster code is a 2D or 3D finite-element calculation code for structures developed by the R and D direction of Electricite de France (EdF). This dossier presents a complete overview of the characteristics and uses of the Aster code: introduction of version 4; the context of Aster (organisation of the code development, versions, systems and interfaces, development tools, quality assurance, independent validation); static mechanics (linear thermo-elasticity, Euler buckling, cables, Zarka-Casier method); non-linear mechanics (materials behaviour, big deformations, specific loads, unloading and loss of load proportionality indicators, global algorithm, contact and friction); rupture mechanics (G energy restitution level, restitution level in thermo-elasto-plasticity, 3D local energy restitution level, KI and KII stress intensity factors, calculation of limit loads for structures), specific treatments (fatigue, rupture, wear, error estimation); meshes and models (mesh generation, modeling, loads and boundary conditions, links between different modeling processes, resolution of linear systems, display of results etc..); vibration mechanics (modal and harmonic analysis, dynamics with shocks, direct transient dynamics, seismic analysis and aleatory dynamics, non-linear dynamics, dynamical sub-structuring); fluid-structure interactions (internal acoustics, mass, rigidity and damping); linear and non-linear thermal analysis; steels and metal industry (structure transformations); coupled problems (internal chaining, internal thermo-hydro-mechanical coupling, chaining with other codes); products and services. (J.S.)

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

Science.gov (United States)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Gender Differences in Implicit and Explicit Memory for Affective Passages

Science.gov (United States)

Burton, Leslie A.; Rabin, Laura; Vardy, Susan Bernstein.; Frohlich, Jonathan; Wyatt, Gwinne; Dimitri, Diana; Constante, Shimon; Guterman, Elan

2004-01-01

Thirty-two participants were administered 4 verbal tasks, an Implicit Affective Task, an Implicit Neutral Task, an Explicit Affective Task, and an Explicit Neutral Task. For the Implicit Tasks, participants were timed while reading passages aloud as quickly as possible, but not so quickly that they did not understand. A target verbal passage was…

Propel: A Discontinuous-Galerkin Finite Element Code for Solving the Reacting Navier-Stokes Equations

Science.gov (United States)

Johnson, Ryan; Kercher, Andrew; Schwer, Douglas; Corrigan, Andrew; Kailasanath, Kazhikathra

2017-11-01

This presentation focuses on the development of a Discontinuous Galerkin (DG) method for application to chemically reacting flows. The in-house code, called Propel, was developed by the Laboratory of Computational Physics and Fluid Dynamics at the Naval Research Laboratory. It was designed specifically for developing advanced multi-dimensional algorithms to run efficiently on new and innovative architectures such as GPUs. For these results, Propel solves for convection and diffusion simultaneously with detailed transport and thermodynamics. Chemistry is currently solved in a time-split approach using Strang-splitting with finite element DG time integration of chemical source terms. Results presented here show canonical unsteady reacting flow cases, such as co-flow and splitter plate, and we report performance for higher order DG on CPU and GPUs.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

Science.gov (United States)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Development of a computer code for thermohydraulic analysis of a heated channel in transients

International Nuclear Information System (INIS)

Jafari, J.; Kazeminejad, H.; Davilu, H.

2004-01-01

This paper discusses the thermohydraulic analysis of a heated channel of a nuclear reactor in transients by a computer code that has been developed by the writer. The considered geometry is a channel of a nuclear reactor with cylindrical or planar fuel rods. The coolant is water and flows from the outer surface of the fuel rod. To model the heat transfer in the fuel rod, two dimensional time dependent conduction equations has been solved by combination of numerical methods, O rthogonal Collocation Method in radial direction and finite difference method in axial direction . For coolant modelling the single phase time dependent energy equation has been used and solved by finite difference method . The combination of the first module that solves the conduction in the fuel rod and a second one that solved the energy balance in the coolant region constitute the computer code (Thyc-1) to analysis thermohydraulic of a heated channel in transients. The Orthogonal collocation method maintains the accuracy and computing time of conventional finite difference methods, while the computer storage is reduced by a factor of two. The same problem has been modelled by RELAP5/M3 system code to asses the validity of the Thyc-1 code. The good agreement of the results qualifies the developed code

Automated Testing Infrastructure and Result Comparison for Geodynamics Codes

Science.gov (United States)

Heien, E. M.; Kellogg, L. H.

2013-12-01

The geodynamics community uses a wide variety of codes on a wide variety of both software and hardware platforms to simulate geophysical phenomenon. These codes are generally variants of finite difference or finite element calculations involving Stokes flow or wave propagation. A significant problem is that codes of even low complexity will return different results depending on the platform due to slight differences in hardware, software, compiler, and libraries. Furthermore, changes to the codes during development may affect solutions in unexpected ways such that previously validated results are altered. The Computational Infrastructure for Geodynamics (CIG) is funded by the NSF to enhance the capabilities of the geodynamics community through software development. CIG has recently done extensive work in setting up an automated testing and result validation system based on the BaTLab system developed at the University of Wisconsin, Madison. This system uses 16 variants of Linux and Mac platforms on both 32 and 64-bit processors to test several CIG codes, and has also recently been extended to support testing on the XSEDE TACC (Texas Advanced Computing Center) Stampede cluster. In this work we overview the system design and demonstrate how automated testing and validation occurs and results are reported. We also examine several results from the system from different codes and discuss how changes in compilers and libraries affect the results. Finally we detail some result comparison tools for different types of output (scalar fields, velocity fields, seismogram data), and discuss within what margins different results can be considered equivalent.

Preconditioned finite-difference frequency-domain for modelling periodic dielectric structures - comparisons with FDTD

NARCIS (Netherlands)

Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.

2008-01-01

Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling

Preconditioned finite-difference frequency-domain for modelling periodic dielectric structures : comparisons with FDTD

NARCIS (Netherlands)

Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.

2008-01-01

Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling

Modelling the attenuation in the ATHENA finite elements code for the ultrasonic testing of austenitic stainless steel welds.

Science.gov (United States)

Chassignole, B; Duwig, V; Ploix, M-A; Guy, P; El Guerjouma, R

2009-12-01

Multipass welds made in austenitic stainless steel, in the primary circuit of nuclear power plants with pressurized water reactors, are characterized by an anisotropic and heterogeneous structure that disturbs the ultrasonic propagation and makes ultrasonic non-destructive testing difficult. The ATHENA 2D finite element simulation code was developed to help understand the various physical phenomena at play. In this paper, we shall describe the attenuation model implemented in this code to give an account of wave scattering phenomenon through polycrystalline materials. This model is in particular based on the optimization of two tensors that characterize this material on the basis of experimental values of ultrasonic velocities attenuation coefficients. Three experimental configurations, two of which are representative of the industrial welds assessment case, are studied in view of validating the model through comparison with the simulation results. We shall thus provide a quantitative proof that taking into account the attenuation in the ATHENA code dramatically improves the results in terms of the amplitude of the echoes. The association of the code and detailed characterization of a weld's structure constitutes a remarkable breakthrough in the interpretation of the ultrasonic testing on this type of component.

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

International Nuclear Information System (INIS)

Adelman, H.M.; Haftka, R.T.; Robinson, J.C.

1982-08-01

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame test article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

Science.gov (United States)

Adelman, H. M.; Haftka, R. T.; Robinson, J. C.

1982-01-01

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Heterogeneous redox reactions in groundwater flow systems - Investigation and application of two different coupled codes

Energy Technology Data Exchange (ETDEWEB)

Pfingsten, W.; Carnahan, C.L. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

1995-05-01

Two simulators of reactive chemical transport are applied to a set of problems involving heterogeneous reactions of uranium species. The simulators use similar algorithms to compute the heterogeneous chemical equilibria, but they use different approaches to the computation of solute transport and to the coupling of transport with chemical reactions. One simulator (MCOTAC) sequentially couples calculations of static chemical equilibria to a random-walk simulation of solute advection and dispersion. The other simulator (THCC) directly couples mass action relations for chemical equilibria to finite-difference representations of the solute transport equations. The aim of the comparison was to demonstrate the applicability of the newly developed code MCOTAC to redox problems, and to identify and investigate general differences between the two types of codes within these applications. The chosen heterogeneous redox systems are hypothetically generate systems which provide numerical difficulties within the coupled code calculation. Uranium, an important component of heterogeneous redox systems consisting of uraniferous solids and natural groundwaters, was chosen as a main component in the example redox systems because of practical interest for performance assessment of geological repositories for nuclear wastes. The calculations show reasonable agreement, in general, between the two computational approaches. Specific areas of disagreement arise from numerical difficulties to each approach. Such `benchmarking` can enhance confidence in the overall performance of individual simulators while identifying aspects that may require further investigations and possible modifications. (author) figs., tabs., 7 refs.

Generalized concatenated quantum codes

International Nuclear Information System (INIS)

Grassl, Markus; Shor, Peter; Smith, Graeme; Smolin, John; Zeng Bei

2009-01-01

We discuss the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we construct families of single-error-correcting nonadditive quantum codes, in both binary and nonbinary cases, which not only outperform any stabilizer codes for finite block length but also asymptotically meet the quantum Hamming bound for large block length.

Integral equations with difference kernels on finite intervals

CERN Document Server

Sakhnovich, Lev A

2015-01-01

This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful...

STEALTH: a Lagrange explicit finite difference code for solids, structural, and thermohydraulic analysis. Volume 2: sample and verification problems. Computer code manual

International Nuclear Information System (INIS)

Hofmann, R.

1982-08-01

STEALTH sample and verification problems are presented to help users become familiar with STEALTH capabilities, input, and output. Problems are grouped into articles which are completely self-contained. The pagination in each article is A.n, where A is a unique alphabetic-character article identifier and n is a sequential page number which starts from 1 on the first page of text for each article. Articles concerning new capabilities will be added as they become available. STEALTH sample and verification calculations are divided into the following general categories: transient mechanical calculations dealing with solids; transient mechanical calculations dealing with fluids; transient thermal calculations dealing with solids; transient thermal calculations dealing with fluids; static and quasi-static calculations; and complex boundary interaction calculations

Computer Simulation and Experimental Study of Deformation in a Radial Tire under Different Static Loads Using Finite Element Method

Directory of Open Access Journals (Sweden)

Mir Hamid Reza Ghoreishy

2014-10-01

Full Text Available This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC.MARC code, installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models, namely Marlow and Yeoh, and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts, respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts, polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial, tangential, lateral and torsional loads. Different finite element models were developed, in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement data, the tire stiffness under radial, tangential, lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However, due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites, modeled with rebar layer methodology, the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed.

An Explicit Consistent Geometric Stiffness Matrix for the DKT Element

Directory of Open Access Journals (Sweden)

Eliseu Lucena Neto

Full Text Available Abstract A large number of references dealing with the geometric stiffness matrix of the DKT finite element exist in the literature, where nearly all of them adopt an inconsistent form. While such a matrix may be part of the element to treat nonlinear problems in general, it is of crucial importance for linearized buckling analysis. The present work seems to be the first to obtain an explicit expression for this matrix in a consistent way. Numerical results on linear buckling of plates assess the element performance either with the proposed explicit consistent matrix, or with the most commonly used inconsistent matrix.

Formulation of coarse mesh finite difference to calculate mathematical adjoint flux

International Nuclear Information System (INIS)

Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations. [with applications to Burger equation and stream function-vorticity problem

Science.gov (United States)

Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.

1978-01-01

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

SPORTS - a simple non-linear thermalhydraulic stability code

International Nuclear Information System (INIS)

Chatoorgoon, V.

1986-01-01

A simple code, called SPORTS, has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers. (orig.)

Validation of High Displacement Piezoelectric Actuator Finite Element Models

Science.gov (United States)

Taleghani, B. K.

2000-01-01

The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.

A first course in finite elements

CERN Document Server

Fish, Jacob

2007-01-01

Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations.  Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts

Finite element concept to derive isostatic residual maps ...

Indian Academy of Sciences (India)

A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the ... not require explicit assumptions on isostatic models. Besides .... This information is implicit in the Bouguer ...

Finite element calculation of the interaction energy of shape memory alloy

International Nuclear Information System (INIS)

Yang, Seung Yong

2004-01-01

Strain energy due to the mechanical interaction between self-accommodation groups of martensitic phase transformation is called interaction energy. Evaluation of the interaction energy should be accurate since the energy appears in constitutive models for predicting the mechanical behavior of shape memory alloy. In this paper, the interaction energy is evaluated in terms of theoretical formulation and explicit finite element calculation. A simple example with two habit plane variants was considered. It was shown that the theoretical formulation assuming elastic interaction between the self-accommodation group and matrix gives larger interaction energy than explicit finite element calculation in which transformation softening is accounted for

Sample test cases using the environmental computer code NECTAR

International Nuclear Information System (INIS)

Ponting, A.C.

1984-06-01

This note demonstrates a few of the many different ways in which the environmental computer code NECTAR may be used. Four sample test cases are presented and described to show how NECTAR input data are structured. Edited output is also presented to illustrate the format of the results. Two test cases demonstrate how NECTAR may be used to study radio-isotopes not explicitly included in the code. (U.K.)

Development of a finite element code to solve thermo-hydro-mechanical coupling and simulate induced seismicity.

Science.gov (United States)

María Gómez Castro, Berta; De Simone, Silvia; Rossi, Riccardo; Larese De Tetto, Antonia; Carrera Ramírez, Jesús

2015-04-01

Coupled thermo-hydro-mechanical modeling is essential for CO2 storage because of (1) large amounts of CO2 will be injected, which will cause large pressure buildups and might compromise the mechanical stability of the caprock seal, (2) the most efficient technique to inject CO2 is the cold injection, which induces thermal stress changes in the reservoir and seal. These stress variations can cause mechanical failure in the caprock and can also trigger induced earthquakes. To properly assess these effects, numerical models that take into account the short and long-term thermo-hydro-mechanical coupling are an important tool. For this purpose, there is a growing need of codes that couple these processes efficiently and accurately. This work involves the development of an open-source, finite element code written in C ++ for correctly modeling the effects of thermo-hydro-mechanical coupling in the field of CO2 storage and in others fields related to these processes (geothermal energy systems, fracking, nuclear waste disposal, etc.), and capable to simulate induced seismicity. In order to be able to simulate earthquakes, a new lower dimensional interface element will be implemented in the code to represent preexisting fractures, where pressure continuity will be imposed across the fractures.

Network Coding Over The 232

DEFF Research Database (Denmark)

Pedersen, Morten Videbæk; Heide, Janus; Vingelmann, Peter

2013-01-01

Creating efficient finite field implementations has been an active research topic for several decades. Many appli- cations in areas such as cryptography, signal processing, erasure coding and now also network coding depend on this research to deliver satisfactory performance. In this paper we...... from a benchmark application written in C++. These results are finally compared to different binary and binary extension field implementations. The results show that the prime field implementation offers a large field size while maintaining a very good performance. We believe that using prime fields...

Quality-assurance study of the special-purpose finite-element program SPECTROM: II. Plasticity problems

International Nuclear Information System (INIS)

Callahan, G.D.; Fossum, A.F.

1982-11-01

General plasticity theory and solution techniques as are currently employed in RE/SPEC's finite element plasticity code SPECTROM-II are presented. Various yield functions are discussed and their differences are illustrated using example problems. Comparison of the results of SPECTROM-II with analytical solutions, numerical solutions, and the general purpose finite element program MARC-CDC show excellent agreement

Open problems in CEM: Porting an explicit time-domain volume-integral- equation solver on GPUs with OpenACC

KAUST Repository

Ergül, Özgür

2014-04-01

Graphics processing units (GPUs) are gradually becoming mainstream in high-performance computing, as their capabilities for enhancing performance of a large spectrum of scientific applications to many fold when compared to multi-core CPUs have been clearly identified and proven. In this paper, implementation and performance-tuning details for porting an explicit marching-on-in-time (MOT)-based time-domain volume-integral-equation (TDVIE) solver onto GPUs are described in detail. To this end, a high-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs, is annotated with compiler directives to port it to GPUs in a fashion similar to how OpenMP targets multi-core CPUs. In contrast to CUDA and OpenCL, where significant modifications to CPU-based codes are required, this high-level approach therefore requires minimal changes to the codes. In this work, we make use of two available OpenACC compilers, CAPS and PGI. Our experience reveals that different annotations of the code are required for each of the compilers, due to different interpretations of the fairly new standard by the compiler developers. Both versions of the OpenACC accelerated code achieved significant performance improvements, with up to 30× speedup against the sequential CPU code using recent hardware technology. Moreover, we demonstrated that the GPU-accelerated fully explicit MOT-TDVIE solver leveraged energy-consumption gains of the order of 3× against its CPU counterpart. © 2014 IEEE.

Explicit expression for effective moment of inertia of RC beams

Directory of Open Access Journals (Sweden)

K.A. Patel

Full Text Available AbstractDeflection is an important design parameter for structures subjected to service load. This paper provides an explicit expression for effective moment of inertia considering cracking, for uniformly distributed loaded reinforced concrete (RC beams. The proposed explicit expression can be used for rapid prediction of short-term deflection at service load. The explicit expression has been obtained from the trained neural network considering concrete cracking, tension stiffening and entire practical range of reinforcement. Three significant structural parameters have been identified that govern the change in effective moment of inertia and therefore deflection. These three parameters are chosen as inputs to train neural network. The training data sets for neural network are generated using finite element software ABAQUS. The explicit expression has been validated for a number of simply supported and continuous beams and it is shown that the predicted deflections have reasonable accuracy for practical purpose. A sensitivity analysis has been performed, which indicates substantial dependence of effective moment of inertia on the selected input parameters.

Different Stimuli, Different Spatial Codes: A Visual Map and an Auditory Rate Code for Oculomotor Space in the Primate Superior Colliculus

Science.gov (United States)

Lee, Jungah; Groh, Jennifer M.

2014-01-01

Maps are a mainstay of visual, somatosensory, and motor coding in many species. However, auditory maps of space have not been reported in the primate brain. Instead, recent studies have suggested that sound location may be encoded via broadly responsive neurons whose firing rates vary roughly proportionately with sound azimuth. Within frontal space, maps and such rate codes involve different response patterns at the level of individual neurons. Maps consist of neurons exhibiting circumscribed receptive fields, whereas rate codes involve open-ended response patterns that peak in the periphery. This coding format discrepancy therefore poses a potential problem for brain regions responsible for representing both visual and auditory information. Here, we investigated the coding of auditory space in the primate superior colliculus(SC), a structure known to contain visual and oculomotor maps for guiding saccades. We report that, for visual stimuli, neurons showed circumscribed receptive fields consistent with a map, but for auditory stimuli, they had open-ended response patterns consistent with a rate or level-of-activity code for location. The discrepant response patterns were not segregated into different neural populations but occurred in the same neurons. We show that a read-out algorithm in which the site and level of SC activity both contribute to the computation of stimulus location is successful at evaluating the discrepant visual and auditory codes, and can account for subtle but systematic differences in the accuracy of auditory compared to visual saccades. This suggests that a given population of neurons can use different codes to support appropriate multimodal behavior. PMID:24454779

Finite element analysis of thermal stress distribution in different ...

African Journals Online (AJOL)

Nigerian Journal of Clinical Practice • Jan-Feb 2016 • Vol 19 • Issue 1. Abstract ... Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ... applications for force analysis and assessment of different.

Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

Directory of Open Access Journals (Sweden)

Shouquan Pang

2016-01-01

Full Text Available Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.

Developmental differences in explicit and implicit conceptual memory tests: a processing view account.

Science.gov (United States)

Sauzéon, Hélène; Déjos, Marie; Lestage, Philippe; Arvind Pala, Prashant; N'kaoua, Bernard

2012-01-01

The present study addressed contradictory results in childhood literature about conceptual priming. Based on the processing view, two forms of conceptual priming were investigated across two experiments in children aged from 7 to 16: associative priming (using the free-association test) and relational (categorical) priming (using the categorical exemplar generation test) as well as their explicit memory measure counterparts (the associative-cued recall and the category-cued recall). Experiment 1 compared age differences in associative and relational (categorical) priming. Experiment 2 focused on relational (categorical) priming with manipulations of blocked/unblocked words per category. The results showed that (a) associative priming was unchanged in children aged from 7 to 16, whereas relational (categorical) priming improved from 7-9 to 13-16 years old, and (b) age differences in relational (categorical) priming still occurred under unblocked conditions and blocked condition, while age differences in explicit measures were reduced under blocked conditions. These findings were discussed in line with the debate between the system and processing view and in terms of knowledge and automaticity development.

High-order finite-difference methods for Poisson's equation

NARCIS (Netherlands)

van Linde, Hendrik Jan

1971-01-01

In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator

Development of a computer code 'CRACK' for elastic and elastoplastic fracture mechanics analysis of 2-D structures by finite element technique

International Nuclear Information System (INIS)

Dutta, B.K.; Kakodkar, A.; Maiti, S.K.

1986-01-01

The fracture mechanics analysis of nuclear components is required to ensure prevention of sudden failure due to dynamic loadings. The linear elastic analysis near to a crack tip shows presence of stress singularity at the crack tip. The simulation of this singularity in numerical methods enhance covergence capability. In finite element technique this can be achieved by placing mid nodes of 8 noded or 6 noded isoparametric elements, at one fourth ditance from crack tip. Present report details this characteristic of finite element, implementation of this element in a code 'CRACK', implementation of J-integral to compute stress intensity factor and solution of number of cases for elastic and elastoplastic fracture mechanics analysis. 6 refs., 6 figures. (author)

Elements of algebraic coding systems

CERN Document Server

Cardoso da Rocha, Jr, Valdemar

2014-01-01

Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...

Contaminant transport in fracture networks with heterogeneous rock matrices. The Picnic code

International Nuclear Information System (INIS)

Barten, Werner; Robinson, Peter C.

2001-02-01

In the context of safety assessment of radioactive waste repositories, complex radionuclide transport models covering key safety-relevant processes play a major role. In recent Swiss safety assessments, such as Kristallin-I, an important drawback was the limitation in geosphere modelling capability to account for geosphere heterogeneities. In marked contrast to this limitation in modelling capabilities, great effort has been put into investigating the heterogeneity of the geosphere as it impacts on hydrology. Structural geological methods have been used to look at the geometry of the flow paths on a small scale and the diffusion and sorption properties of different rock materials have been investigated. This huge amount of information could however be only partially applied in geosphere transport modelling. To make use of these investigations the 'PICNIC project' was established as a joint cooperation of PSI/Nagra and QuantiSci to provide a new geosphere transport model for Swiss safety assessment of radioactive waste repositories. The new transport code, PICNIC, can treat all processes considered in the older geosphere model RANCH MD generally used in the Kristallin-I study and, in addition, explicitly accounts for the heterogeneity of the geosphere on different spatial scales. The effects and transport phenomena that can be accounted for by PICNIC are a combination of (advective) macro-dispersion due to transport in a network of conduits (legs), micro-dispersion in single legs, one-dimensional or two-dimensional matrix diffusion into a wide range of homogeneous and heterogeneous rock matrix geometries, linear sorption of nuclides in the flow path and the rock matrix and radioactive decay and ingrowth in the case of nuclide chains. Analytical and numerical Laplace transformation methods are integrated in a newly developed hierarchical linear response concept to efficiently account for the transport mechanisms considered which typically act on extremely different

Contaminant transport in fracture networks with heterogeneous rock matrices. The Picnic code

Energy Technology Data Exchange (ETDEWEB)

Barten, Werner [Paul Scherrer Inst., CH-5232 Villigen PSI (Switzerland); Robinson, Peter C. [QuantiSci Limited, Henley-on-Thames (United Kingdom)

2001-02-01

In the context of safety assessment of radioactive waste repositories, complex radionuclide transport models covering key safety-relevant processes play a major role. In recent Swiss safety assessments, such as Kristallin-I, an important drawback was the limitation in geosphere modelling capability to account for geosphere heterogeneities. In marked contrast to this limitation in modelling capabilities, great effort has been put into investigating the heterogeneity of the geosphere as it impacts on hydrology. Structural geological methods have been used to look at the geometry of the flow paths on a small scale and the diffusion and sorption properties of different rock materials have been investigated. This huge amount of information could however be only partially applied in geosphere transport modelling. To make use of these investigations the 'PICNIC project' was established as a joint cooperation of PSI/Nagra and QuantiSci to provide a new geosphere transport model for Swiss safety assessment of radioactive waste repositories. The new transport code, PICNIC, can treat all processes considered in the older geosphere model RANCH MD generally used in the Kristallin-I study and, in addition, explicitly accounts for the heterogeneity of the geosphere on different spatial scales. The effects and transport phenomena that can be accounted for by PICNIC are a combination of (advective) macro-dispersion due to transport in a network of conduits (legs), micro-dispersion in single legs, one-dimensional or two-dimensional matrix diffusion into a wide range of homogeneous and heterogeneous rock matrix geometries, linear sorption of nuclides in the flow path and the rock matrix and radioactive decay and ingrowth in the case of nuclide chains. Analytical and numerical Laplace transformation methods are integrated in a newly developed hierarchical linear response concept to efficiently account for the transport mechanisms considered which typically act on extremely

EFLOD code for reflood heat transfer

International Nuclear Information System (INIS)

Gay, R.R.

1979-01-01

A computer code called EFLOD has been developed for simulation of the heat transfer and hydrodynamics of a nuclear power reactor during the reflood phase of a loss-of-coolant accident. EFLOD models the downcomer, lower plenum, core, and upper plenum of a nuclear reactor vessel using seven control volumes assuming either homogeneous or unequal-velocity, unequal-temperature (UVUT) models of two-phase flow, depending on location within the vessel. The moving control volume concept in which a single control volume models the quench region in the core and moves with the core liquid level was developed and implemented in EFLOD so that three control volumes suffice to model the core region. A simplified UVUT model that assumes saturated liquid above the quench front was developed to handle the nonhomogeneous flow situation above the quench region. An explicit finite difference routine is used to model conduction heat transfer in the fuel, gap, and cladding regions of the fuel rod. In simulation of a selected FLECHT-SET experimental run, EFLOD successfully predicted the midplane maximum temperature and turnaround time as well as the time-dependent advance of the core liquid level. However, the rate of advancement of the quench level and the ensuing liquid entrainment were overpredicted during the early part of the transient

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

CERN Document Server

Gedney, Stephen

2011-01-01

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p

Locality-preserving logical operators in topological stabilizer codes

Science.gov (United States)

Webster, Paul; Bartlett, Stephen D.

2018-01-01

Locality-preserving logical operators in topological codes are naturally fault tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure for finding all locality-preserving logical operators admitted by a large and important class of topological stabilizer codes. In particular, we focus on those equivalent to a stack of a finite number of surface codes of any spatial dimension, where our procedure fully specifies the group of locality-preserving logical operators. We also present examples of how our procedure applies to codes with different boundary conditions, including color codes and toric codes, as well as more general codes such as Abelian quantum double models and codes with fermionic excitations in more than two dimensions.

Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

Energy Technology Data Exchange (ETDEWEB)

Dolbow, John [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Ziyu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Jiang, Wen [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2015-09-01

Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside of the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.

Optimization of Finite-Differencing Kernels for Numerical Relativity Applications

Directory of Open Access Journals (Sweden)

Roberto Alfieri

2018-05-01

Full Text Available A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes. Our proposed method provides substantial speedup in computations involving tensor contractions and 3D stencil calculations on different processor microarchitectures, including Intel Knight Landing.

Finite element modelling of different CANDU fuel bundle types in various refuelling conditions

International Nuclear Information System (INIS)

Roman, M. R.; Ionescu, D. V.; Olteanu, G.; Florea, S.; Radut, A. C.

2016-01-01

The objective of this paper is to develop a finite element model for static strength analysis of the CANDU standard with 37 elements fuel bundle and the SEU43 with 43 elements fuel bundle design for various refuelling conditions. The computer code, ANSYS7.1, is used to simulate the axial compression in CANDU type fuel bundles subject to hydraulic drag loads, deflection of fuel elements, stresses and displacements in the end plates. Two possible situations for the fuelling machine side stops are considered in our analyses, as follows: the last fuel bundle is supported by the two side stops and a side stop can be blocked therefore, the last fuel bundle is supported by only one side stop. The results of the analyses performed are briefly presented and also illustrated in a graphical form. The finite element model developed in present study is verified against test results for endplate displacement and element bowing obtained from strength tests with fuel bundle string and fuelling machine side-stop simulators. Comparison of ANSYS model predictions with these experimental results led to a very good agreement. Despite the difference in hydraulic load between SEU43 and CANDU standard fuel bundles strings, the maximum stress in the SEU43 endplate is about the same with the maximum stress in the CANDU standard endplate. The comparative assessment reveals that SEU43 fuel bundle is able to withstand high flow rate without showing a significant geometric instability. (authors)

Explicit and implicit springback simulation in sheet metal forming using fully coupled ductile damage and distortional hardening model

Science.gov (United States)

Yetna n'jock, M.; Houssem, B.; Labergere, C.; Saanouni, K.; Zhenming, Y.

2018-05-01

The springback is an important phenomenon which accompanies the forming of metallic sheets especially for high strength materials. A quantitative prediction of springback becomes very important for newly developed material with high mechanical characteristics. In this work, a numerical methodology is developed to quantify this undesirable phenomenon. This methodoly is based on the use of both explicit and implicit finite element solvers of Abaqus®. The most important ingredient of this methodology consists on the use of highly predictive mechanical model. A thermodynamically-consistent, non-associative and fully anisotropic elastoplastic constitutive model strongly coupled with isotropic ductile damage and accounting for distortional hardening is then used. An algorithm for local integration of the complete set of the constitutive equations is developed. This algorithm considers the rotated frame formulation (RFF) to ensure the incremental objectivity of the model in the framework of finite strains. This algorithm is implemented in both explicit (Abaqus/Explicit®) and implicit (Abaqus/Standard®) solvers of Abaqus® through the users routine VUMAT and UMAT respectively. The implicit solver of Abaqus® has been used to study spingback as it is generally a quasi-static unloading. In order to compare the methods `efficiency, the explicit method (Dynamic Relaxation Method) proposed by Rayleigh has been also used for springback prediction. The results obtained within U draw/bending benchmark are studied, discussed and compared with experimental results as reference. Finally, the purpose of this work is to evaluate the reliability of different methods predict efficiently springback in sheet metal forming.

Structural evaluation method for class 1 vessels by using elastic-plastic finite element analysis in code case of JSME rules on design and construction

International Nuclear Information System (INIS)

Asada, Seiji; Hirano, Takashi; Nagata, Tetsuya; Kasahara, Naoto

2008-01-01

A structural evaluation method by using elastic-plastic finite element analysis has been developed and published as a code case of Rules on Design and Construction for Nuclear Power Plants (The First Part: Light Water Reactor Structural Design Standard) in the JSME Codes for Nuclear Power Generation Facilities. Its title is 'Alternative Structural Evaluation Criteria for Class 1 Vessels Based on Elastic-Plastic Finite Element Analysis' (NC-CC-005). This code case applies elastic-plastic analysis to evaluation of such failure modes as plastic collapse, thermal ratchet, fatigue and so on. Advantage of this evaluation method is free from stress classification, consistently use of Mises stress and applicability to complex 3-dimensional structures which are hard to be treated by the conventional stress classification method. The evaluation method for plastic collapse has such variation as the Lower Bound Approach Method, Twice-Elastic-Slope Method and Elastic Compensation Method. Cyclic Yield Area (CYA) based on elastic analysis is applied to screening evaluation of thermal ratchet instead of secondary stress evaluation, and elastic-plastic analysis is performed when the CYA screening criteria is not satisfied. Strain concentration factors can be directly calculated based on elastic-plastic analysis. (author)

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

KAUST Repository

Gao, Longfei

2018-02-22

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

KAUST Repository

Gao, Longfei; Keyes, David E.

2018-01-01

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

Accuracy of finite-difference harmonic frequencies in density functional theory.

Science.gov (United States)

Liu, Kuan-Yu; Liu, Jie; Herbert, John M

2017-07-15

Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors numbers. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Automation of finite element methods

CERN Document Server

Korelc, Jože

2016-01-01

New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

Energy Technology Data Exchange (ETDEWEB)

Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others

2016-09-15

Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

International Nuclear Information System (INIS)

Nakra Mohajer, Soukaina; El Harouny, El Hassan; Ibral, Asmaa; El Khamkhami, Jamal

2016-01-01

Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.

The computation of pressure waves in shock tubes by a finite difference procedure

International Nuclear Information System (INIS)

Barbaro, M.

1988-09-01

A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)

Solution of the diffusion equations for several groups by the finite elements method

International Nuclear Information System (INIS)

Arredondo S, C.

1975-01-01

The code DELFIN has been implemented for the solution of the neutrons diffusion equations in two dimensions obtained by applying the approximation of several groups of energy. The code works with any number of groups and regions, and can be applied to thermal reactors as well as fast reactor. Providing it with the diffusion coefficients, the effective sections and the fission spectrum we obtain the results for the systems multiplying constant and the flows of each groups. The code was established using the method of finite elements, which is a form of resolution of the variational formulation of the equations applying the Ritz-Galerkin method with continuous polynomial functions by parts, in one case of the Lagrange type with rectangular geometry and up to the third grade. The obtained results and the comparison with the results in the literature, permit to reach the conclusion that it is convenient, to use the rectangular elements in all the cases where the geometry permits it, and demonstrate also that the finite elements method is better than the finite differences method. (author)

Toward finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1986-01-01

The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)

Implementation of an Euler/Navier-Stokes finite element algorithm on the Connection Machine

International Nuclear Information System (INIS)

Shapiro, R.A.

1991-01-01

Massively parallel computers such as the Connection Machine (CM-2) have the potential to reduce significantly the computational cost for large problems of interest to the aerospace community. This paper examines the applicability of the CM-2 to an explicit, time-marching finite element solution method for the Euler and Navier-Stokes equations. The CM-2 architecture and the CM FORTRAN language are introduced. The paper points out some of the pitfalls involved in putting this code on the CM-2, with emphasis on interprocessor communications issues. The use of the FastGraph communication compiler and grid renumbering to reduce communication costs is discussed. Performance comparisons which indicate the approximate equivalence of a uniprocessor Cray and 1/8 of a CM-2 (8192 processors) for some typical problems are presented. 8 refs

Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term

International Nuclear Information System (INIS)

Johnston, Hans; Liu Jianguo

2004-01-01

We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C 0 elements to implement

An object-oriented decomposition of the adaptive-hp finite element method

Energy Technology Data Exchange (ETDEWEB)

Wiley, J.C.

1994-12-13

Adaptive-hp methods are those which use a refinement control strategy driven by a local error estimate to locally modify the element size, h, and polynomial order, p. The result is an unstructured mesh in which each node may be associated with a different polynomial order and which generally require complex data structures to implement. Object-oriented design strategies and languages which support them, e.g., C++, help control the complexity of these methods. Here an overview of the major classes and class structure of an adaptive-hp finite element code is described. The essential finite element structure is described in terms of four areas of computation each with its own dynamic characteristics. Implications of converting the code for a distributed-memory parallel environment are also discussed.

Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

KAUST Repository

Parsani, Matteo

2013-04-10

Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

KAUST Repository

Parsani, Matteo; Ketcheson, David I.; Deconinck, W.

2013-01-01

Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

Reference manual for the POISSON/SUPERFISH Group of Codes

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

The POISSON/SUPERFISH Group codes were set up to solve two separate problems: the design of magnets and the design of rf cavities in a two-dimensional geometry. The first stage of either problem is to describe the layout of the magnet or cavity in a way that can be used as input to solve the generalized Poisson equation for magnets or the Helmholtz equations for cavities. The computer codes require that the problems be discretized by replacing the differentials (dx,dy) by finite differences ({delta}X,{delta}Y). Instead of defining the function everywhere in a plane, the function is defined only at a finite number of points on a mesh in the plane.

FEMSYN - a code system to solve multigroup diffusion theory equations using a variety of solution techniques. Part 1 : Description of code system - input and sample problems

International Nuclear Information System (INIS)

Jagannathan, V.

1985-01-01

A modular computer code system called FEMSYN has been developed to solve the multigroup diffusion theory equations. The various methods that are incorporated in FEMSYN are (i) finite difference method (FDM) (ii) finite element method (FEM) and (iii) single channel flux synthesis method (SCFS). These methods are described in detail in parts II, III and IV of the present report. In this report, a comparison of the accuracy and the speed of different methods of solution for some benchmark problems are reported. The input preparation and listing of sample input and output are included in the Appendices. The code FEMSYN has been used to solve a wide variety of reactor core problems. It can be used for both LWR and PHWR applications. (author)

Reduced equations for finite beta tearing modes in tokamaks

International Nuclear Information System (INIS)

Izzo, R.; Monticello, D.A.; DeLucia, J.; Park, W.; Ryu, C.M.

1984-10-01

The equations of resistive magnetohydrodynamics (MHD) are recast in a form that is useful for studying the evolution of those toroidal systems where the fast magnetosonic wave plays no important role. The equations are exact and have nabla vector.B vector = O satisfied explicitly. From this set of equations it is a simple matter to derive the equations of reduced MHD to any order in the inverse aspect ratio epsilon of the torus, and for β approx. epsilon or smaller. We demonstrate this by deriving a reduced set of MHD equations that are correct to 5th order in epsilon. These equations contain the exact equilibrium relation and as such can be used to find 3-D stellarator equilibria. In addition, if a subsidiary ordering in eta, the resistivity, is made, the equations of Glasser, Greene, and Johnson are recovered. This set of reduced equations has been coded by extending the initial value code, HILO. Results obtained, for both ideal and resistive linear stability, from the reduced equations are compared with those obtained by solving the full set of MHD equations in a cylinder. The agreement is shown to be excellent for both zero and finite beta calculations. Comparisons are also made with analytic theory illuminating the present limitations of the latter

Optimal variable-grid finite-difference modeling for porous media

International Nuclear Information System (INIS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-01-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)

CONVEC: a computer program for transient incompressible fluid flow based on quadratic finite elements. Part 1: theoretical aspects

International Nuclear Information System (INIS)

Laval, H.

1981-01-01

This report describes the theoretical and numerical aspects of the finite element computer code CONVEC designed for the transient analysis of two-dimensional plane or three-dimensional axisymmetric incompressible flows including the effects of heat transfer. The governing equations for the above class of problems are the time-dependent incompressible Navier-Stokes equations and the thermal energy equation. The general class of flow problems analysed by CONVEC is discussed and the equations for the initial-boundary value problem are represented. A brief description of the finite element method and the weighted residual formulation is presented. The numerical solution of the incompressible equations is achieved by using a fractional step method. The mass lumping process associated with an explicit time integration scheme is described. The time integration is analysed and the stability conditions are derived. Numerical applications are presented. Standard problems of natural and forced convection are solved and the solutions obtained are compared with other numerical solutions published in the literature

Decoding Hermitian Codes with Sudan's Algorithm

DEFF Research Database (Denmark)

Høholdt, Tom; Nielsen, Rasmus Refslund

1999-01-01

We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q-polynomial, and a reduct......We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q...

Analysis of equilibrium in a tokamak by the finite-difference method

International Nuclear Information System (INIS)

Kim, K.E.; Jeun, G.D.

1983-01-01

Ideal magnetohydrodynamic equilibrium in a Tokamak having a small radius with an elongated rectangular cross section is studied by applying the finite-difference method to the Grad-Shafranov equation to determine possible limitations for *b=8*pPsup(2)/Bsup(2). The coupled first-order differential equations resulting from the finite-difference Grad-Shafranov equation is solved by the numarical method:1)We concluded that equilibrium consideration alone gives no limitation even for *b approx.1. 2)We have obtained the equilibrium magnetic field configuration charcterized by a set of three parameters;the aspect ratio, *b,and the safety factor. (Author)

The Dirac Equation in the algebraic approximation. VII. A comparison of molecular finite difference and finite basis set calculations using distributed Gaussian basis sets

NARCIS (Netherlands)

Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E

2001-01-01

A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and

A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

International Nuclear Information System (INIS)

Ansanay-Alex, G.

2009-01-01

The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

Storm Water Infiltration and Focused Groundwater Recharge in a Rain Garden: Finite Volume Model and Numerical Simulations for Different Configurations and Climates

Science.gov (United States)

Aravena, J.; Dussaillant, A. R.

2006-12-01

Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).

Rapid installation of numerical models in multiple parent codes

Energy Technology Data Exchange (ETDEWEB)

Brannon, R.M.; Wong, M.K.

1996-10-01

A set of``model interface guidelines``, called MIG, is offered as a means to more rapidly install numerical models (such as stress-strain laws) into any parent code (hydrocode, finite element code, etc.) without having to modify the model subroutines. The model developer (who creates the model package in compliance with the guidelines) specifies the model`s input and storage requirements in a standardized way. For portability, database management (such as saving user inputs and field variables) is handled by the parent code. To date, NUG has proved viable in beta installations of several diverse models in vectorized and parallel codes written in different computer languages. A NUG-compliant model can be installed in different codes without modifying the model`s subroutines. By maintaining one model for many codes, MIG facilitates code-to-code comparisons and reduces duplication of effort potentially reducing the cost of installing and sharing models.

Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

Science.gov (United States)

Syed, S. A.; Chiappetta, L. M.

1985-01-01

A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

Finite element analysis of a finite-strain plasticity problem

International Nuclear Information System (INIS)

Crose, J.G.; Fong, H.H.

1984-01-01

A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme. (orig.)

Mimetic finite difference method

Science.gov (United States)

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.

Paracantor: A two group, two region reactor code

Energy Technology Data Exchange (ETDEWEB)

Stone, Stuart

1956-07-01

Paracantor I a two energy group, two region, time independent reactor code, which obtains a closed solution for a critical reactor assembly. The code deals with cylindrical reactors of finite length and with a radial reflector of finite thickness. It is programmed for the 1.B.M: Magnetic Drum Data-Processing Machine, Type 650. The limited memory space available does not permit a flux solution to be included in the basic Paracantor code. A supplementary code, Paracantor 11, has been programmed which computes fluxes, .including adjoint fluxes, from the .output of Paracamtor I.

Composite Extension Finite Fields for Low Overhead Network Coding

DEFF Research Database (Denmark)

Heide, Janus; Roetter, Daniel Enrique Lucani

2015-01-01

Although Network Coding (NC) has been proven to increase throughput and reliability in communication networks, its adoption is typically hindered by the additional complexity it introduces at various nodes in the network and the overhead to signal the coding coefficients associated with each code...

Symbolic computation with finite biquandles

OpenAIRE

Creel, Conrad; Nelson, Sam

2007-01-01

A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Z_p from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang-Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.

LAPU2: a laser pulse propagation code with diffraction

International Nuclear Information System (INIS)

Goldstein, J.C.; Dickman, D.O.

1978-03-01

Complete descriptions of the mathematical models and numerical methods used in the code LAPU2 are presented. This code can be used to study the propagation with diffraction of a temporally finite pulse through a sequence of resonant media and simple optical components. The treatment assumes cylindrical symmetry and allows nonlinear refractive indices. An unlimited number of different media can be distributed along the propagation path of the pulse. A complete users guide to input data is given as well as a FORTRAN listing of the code

Recent uses of the finite element method in design/analysis of CANDU fuel

International Nuclear Information System (INIS)

Tayal, M.; Lim, D.

1985-06-01

Finite element codes FEAST and ELESTRES have been used to show: that initial pellet density can have a significant effect on the probability of fuel defect near end cap welds; that sheath stresses/strains are highly multiaxial near circumferential ridges; and that the multiaxiality affects sheath integrity significantly. The finite element thermal code FEAT was used to redesign bearing pads to obtain lower temperture; this eliminated crevice corrosion. FEAT was also used to assess the influences of braze voids and of end flux peaking. These analyses involved complex geometries. By using finite elements, we could obtain accurate assessments economically and rapidly. Finite element codes are also being developed for bowing, diffusion, flow patterns, and stress corrosion cracking

Finite fields and applications

CERN Document Server

Mullen, Gary L

2007-01-01

This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...

Implementation of compact finite-difference method to parabolized Navier-Stokes equations

International Nuclear Information System (INIS)

Esfahanian, V.; Hejranfar, K.; Darian, H.M.

2005-01-01

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

Explicit Dynamic Finite Element Method for Predicting Implosion/Explosion Induced Failure of Shell Structures

Directory of Open Access Journals (Sweden)

Jeong-Hoon Song

2013-01-01

Full Text Available A simplified implementation of the conventional extended finite element method (XFEM for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.

The Finite Heisenberg-Weyl Groups in Radar and Communications

Directory of Open Access Journals (Sweden)

Calderbank AR

2006-01-01

Full Text Available We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error-correcting codes, that the finite Heisenberg-Weyl groups provide a unified basis for the construction of useful waveforms/sequences for radar, communications, and the theory of error-correcting codes.

Alternative conceptual models and codes for unsaturated flow in fractured tuff: Preliminary assessments for GWTT-95

International Nuclear Information System (INIS)

Ho, C.K.; Altman, S.J.; Arnold, B.W.

1995-09-01

Groundwater travel time (GWTT) calculations will play an important role in addressing site-suitability criteria for the potential high-level nuclear waste repository at Yucca Mountain,Nevada. In support of these calculations, Preliminary assessments of the candidate codes and models are presented in this report. A series of benchmark studies have been designed to address important aspects of modeling flow through fractured media representative of flow at Yucca Mountain. Three codes (DUAL, FEHMN, and TOUGH 2) are compared in these benchmark studies. DUAL is a single-phase, isothermal, two-dimensional flow simulator based on the dual mixed finite element method. FEHMN is a nonisothermal, multiphase, multidimensional simulator based primarily on the finite element method. TOUGH2 is anon isothermal, multiphase, multidimensional simulator based on the integral finite difference method. Alternative conceptual models of fracture flow consisting of the equivalent continuum model (ECM) and the dual permeability (DK) model are used in the different codes

Network coding at different layers in wireless networks

CERN Document Server

2016-01-01

This book focuses on how to apply network coding at different layers in wireless networks – including MAC, routing, and TCP – with special focus on cognitive radio networks. It discusses how to select parameters in network coding (e.g., coding field, number of packets involved, and redundant information ration) in order to be suitable for the varying wireless environments. The book explores how to deploy network coding in MAC to improve network performance and examines joint network coding with opportunistic routing to improve the successful rate of routing. In regards to TCP and network coding, the text considers transport layer protocol working with network coding to overcome the transmission error rate, particularly with how to use the ACK feedback of TCP to enhance the efficiency of network coding. The book pertains to researchers and postgraduate students, especially whose interests are in opportunistic routing and TCP in cognitive radio networks.

Explicit Oral Narrative Intervention for Students with Williams Syndrome

Directory of Open Access Journals (Sweden)

Eliseo Diez-Itza

2018-01-01

Full Text Available Narrative skills play a crucial role in organizing experience, facilitating social interaction and building academic discourse and literacy. They are at the interface of cognitive, social, and linguistic abilities related to school engagement. Despite their relative strengths in social and grammatical skills, students with Williams syndrome (WS do not show parallel cognitive and pragmatic performance in narrative generation tasks. The aim of the present study was to assess retelling of a TV cartoon tale and the effect of an individualized explicit instruction of the narrative structure. Participants included eight students with WS who attended different special education levels. Narratives were elicited in two sessions (pre and post intervention, and were transcribed, coded and analyzed using the tools of the CHILDES Project. Narratives were coded for productivity and complexity at the microstructure and macrostructure levels. Microstructure productivity (i.e., length of narratives included number of utterances, clauses, and tokens. Microstructure complexity included mean length of utterances, lexical diversity and use of discourse markers as cohesive devices. Narrative macrostructure was assessed for textual coherence through the Pragmatic Evaluation Protocol for Speech Corpora (PREP-CORP. Macrostructure productivity and complexity included, respectively, the recall and sequential order of scenarios, episodes, events and characters. A total of four intervention sessions, lasting approximately 20 min, were delivered individually once a week. This brief intervention addressed explicit instruction about the narrative structure and the use of specific discourse markers to improve cohesion of story retellings. Intervention strategies included verbal scaffolding and modeling, conversational context for retelling the story and visual support with pictures printed from the cartoon. Results showed significant changes in WS students’ retelling of the

Explicit Oral Narrative Intervention for Students with Williams Syndrome

Science.gov (United States)

Diez-Itza, Eliseo; Martínez, Verónica; Pérez, Vanesa; Fernández-Urquiza, Maite

2018-01-01

Narrative skills play a crucial role in organizing experience, facilitating social interaction and building academic discourse and literacy. They are at the interface of cognitive, social, and linguistic abilities related to school engagement. Despite their relative strengths in social and grammatical skills, students with Williams syndrome (WS) do not show parallel cognitive and pragmatic performance in narrative generation tasks. The aim of the present study was to assess retelling of a TV cartoon tale and the effect of an individualized explicit instruction of the narrative structure. Participants included eight students with WS who attended different special education levels. Narratives were elicited in two sessions (pre and post intervention), and were transcribed, coded and analyzed using the tools of the CHILDES Project. Narratives were coded for productivity and complexity at the microstructure and macrostructure levels. Microstructure productivity (i.e., length of narratives) included number of utterances, clauses, and tokens. Microstructure complexity included mean length of utterances, lexical diversity and use of discourse markers as cohesive devices. Narrative macrostructure was assessed for textual coherence through the Pragmatic Evaluation Protocol for Speech Corpora (PREP-CORP). Macrostructure productivity and complexity included, respectively, the recall and sequential order of scenarios, episodes, events and characters. A total of four intervention sessions, lasting approximately 20 min, were delivered individually once a week. This brief intervention addressed explicit instruction about the narrative structure and the use of specific discourse markers to improve cohesion of story retellings. Intervention strategies included verbal scaffolding and modeling, conversational context for retelling the story and visual support with pictures printed from the cartoon. Results showed significant changes in WS students’ retelling of the story, both at

Toric Codes, Multiplicative Structure and Decoding

DEFF Research Database (Denmark)

Hansen, Johan Peder

2017-01-01

Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for \\emph{decoding}, resembling the decoding of Reed-Solomon codes and al...

A finite difference method for free boundary problems

KAUST Repository

Fornberg, Bengt

2010-04-01

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

FCG: a code generator for lazy functional languages

NARCIS (Netherlands)

Kastens, U.; Langendoen, K.G.; Hartel, Pieter H.; Pfahler, P.

1992-01-01

The FCGcode generator produces portable code that supports efficient two-space copying garbage collection. The code generator transforms the output of the FAST compiler front end into an abstract machine code. This code explicitly uses a call stack, which is accessible to the garbage collector. In

Application of compact finite-difference schemes to simulations of stably stratified fluid flows

Czech Academy of Sciences Publication Activity Database

Bodnár, Tomáš; Beneš, L.; Fraunie, P.; Kozel, Karel

2012-01-01

Roč. 219, č. 7 (2012), s. 3336-3353 ISSN 0096-3003 Institutional support: RVO:61388998 Keywords : stratification * finite- difference * finite-volume * Runge-Kutta Subject RIV: BA - General Mathematics Impact factor: 1.349, year: 2012 http://www.sciencedirect.com/science/article/pii/S0096300311010988

Modification of the finite element heat and mass transfer code (FEHM) to model multicomponent reactive transport

International Nuclear Information System (INIS)

Viswanathan, H.S.

1996-08-01

The finite element code FEHMN, developed by scientists at Los Alamos National Laboratory (LANL), is a three-dimensional finite element heat and mass transport simulator that can handle complex stratigraphy and nonlinear processes such as vadose zone flow, heat flow and solute transport. Scientists at LANL have been developing hydrologic flow and transport models of the Yucca Mountain site using FEHMN. Previous FEHMN simulations have used an equivalent Kd model to model solute transport. In this thesis, FEHMN is modified making it possible to simulate the transport of a species with a rigorous chemical model. Including the rigorous chemical equations into FEHMN simulations should provide for more representative transport models for highly reactive chemical species. A fully kinetic formulation is chosen for the FEHMN reactive transport model. Several methods are available to computationally implement a fully kinetic formulation. Different numerical algorithms are investigated in order to optimize computational efficiency and memory requirements of the reactive transport model. The best algorithm of those investigated is then incorporated into FEHMN. The algorithm chosen requires for the user to place strongly coupled species into groups which are then solved for simultaneously using FEHMN. The complete reactive transport model is verified over a wide variety of problems and is shown to be working properly. The new chemical capabilities of FEHMN are illustrated by using Los Alamos National Laboratory's site scale model of Yucca Mountain to model two-dimensional, vadose zone 14 C transport. The simulations demonstrate that gas flow and carbonate chemistry can significantly affect 14 C transport at Yucca Mountain. The simulations also prove that the new capabilities of FEHMN can be used to refine and buttress already existing Yucca Mountain radionuclide transport studies

Critical state and magnetization loss in multifilamentary superconducting wire solved through the commercial finite element code ANSYS

Science.gov (United States)

Farinon, S.; Fabbricatore, P.; Gömöry, F.

2010-11-01

The commercially available finite element code ANSYS has been adapted to solve the critical state of single strips and multifilamentary tapes. We studied a special algorithm which approaches the critical state by an iterative adjustment of the material resistivity. Then, we proved its validity by comparing the results obtained for a thin strip to the Brand theory for the transport current and magnetization cases. Also, the challenging calculation of the magnetization loss of a real multifilamentary BSCCO tape showed the usefulness of our method. Finally, we developed several methods to enhance the speed of convergence, making the proposed process quite competitive in the existing survey of ac losses simulations.

Comparison of finite-difference and variational solutions to advection-diffusion problems

International Nuclear Information System (INIS)

Lee, C.E.; Washington, K.E.

1984-01-01

Two numerical solution methods are developed for 1-D time-dependent advection-diffusion problems on infinite and finite domains. Numerical solutions are compared with analytical results for constant coefficients and various boundary conditions. A finite-difference spectrum method is solved exactly in time for periodic boundary conditions by a matrix operator method and exhibits excellent accuracy compared with other methods, especially at late times, where it is also computationally more efficient. Finite-system solutions are determined from a conservational variational principle with cubic spatial trial functions and solved in time by a matrix operator method. Comparisons of problems with few nodes show excellent agreement with analytical solutions and exhibit the necessity of implementing Lagrangian conservational constraints for physically-correct solutions. (author)

A finite element conjugate gradient FFT method for scattering

Science.gov (United States)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Finite Element Modelling of Seismic Liquefaction in Soils

NARCIS (Netherlands)

Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.

2013-01-01

Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom

A new fitted operator finite difference method to solve systems of ...

African Journals Online (AJOL)

In recent years, fitted operator finite difference methods (FOFDMs) have been developed for numerous types of singularly perturbed ordinary differential equations. The construction of most of these methods differed though the final outcome remained similar. The most crucial aspect was how the difference operator was ...

Comparison of different precondtioners for nonsymmtric finite volume element methods

Energy Technology Data Exchange (ETDEWEB)

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.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang

2010-01-01

Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo

2010-01-01

Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

On integral and finite Fourier transforms of continuous q-Hermite polynomials

International Nuclear Information System (INIS)

Atakishiyeva, M. K.; Atakishiyev, N. M.

2009-01-01

We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

Finite-difference time-domain simulation of electromagnetic bandgap and bi-anisotropic metamaterials

Science.gov (United States)

Bray, Matthew G.

The term "Metamaterial" has been introduced into the electromagnetic lexicon in recent years to describe new artificial materials with electromagnetic properties that are not found in naturally occurring materials. Metamaterials exhibit electromagnetic properties that are not observed in its constituent materials, and/or not observed in nature. This thesis will analyze two different classes of metamaterials through the use of the finite-difference time-domain (FDTD) technique. The first class of metamaterials are artificial magnetic conductors (AMC) which approximate the behavior of a perfect magnetic conductor (PMC) over a finite frequency range. The AMC metamaterials are created through the use of an electromagnetic bandgap (EBG) structure. A periodic FDTD code is used to simulate a full-wave model of the metallodielectric EBG structures. The AMCs developed with the aid of the FDTD tool are then used to create low-profile antenna systems consisting of a dipole antenna in close proximity to an AMC surface. Through the use of this FDTD tool, several original contributions were made to the electromagnetic community. These include the first dual-band independently tunable EBG AMC ground plane and the first linearly polarized single-band and dual-band tunable antenna/EBG systems. The second class of materials analyzed are bi-anisotropic metamaterials. Bi-anisotropic media are the largest class of linear media which is able to describe the macroscopic material properties of artificial dielectrics, artificial magnetics, artificial chiral materials, left-handed materials, and other composite materials. The dispersive properties of these materials can be approximated by the oscillator model. This model assumes a Lorentzian frequency profile for the permittivity and permeability and a Condon model for chirality. A new FDTD formulation is introduced which can simulate this type of bi-anisotropic media. This FDTD method incorporates the dispersive material properties through

Explicit Constructions and Bounds for Batch Codes with Restricted Size of Reconstruction Sets

OpenAIRE

Thomas, Eldho K.; Skachek, Vitaly

2017-01-01

Linear batch codes and codes for private information retrieval (PIR) with a query size $t$ and a restricted size $r$ of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of $t$ or of $r$ by providing corresponding constructions. By building on the ideas of Cadambe and Mazumdar, a new bound in a recursive form is derived for batch codes and PIR codes.

Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

Science.gov (United States)

Miyazaki, Yutaka; Tsuchiya, Takao

2012-07-01

The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

Finite Heisenberg groups and Seiberg dualities in quiver gauge theories