Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

An Improved Transformation and Optimized Sampling Scheme for the Numerical Evaluation of Singular and Near-Singular Potentials

NASA Technical Reports Server (NTRS)

Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.

2007-01-01

Simple and efficient numerical procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration scheme.

Implementing a Flipped Classroom Approach in a University Numerical Methods Mathematics Course

ERIC Educational Resources Information Center

Johnston, Barbara M.

2017-01-01

This paper describes and analyses the implementation of a "flipped classroom" approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an…

Numerical simulation of the hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor

NASA Astrophysics Data System (ADS)

Fortova, S. V.; Shepelev, V. V.; Troshkin, O. V.; Kozlov, S. A.

2017-09-01

The paper presents the results of numerical simulation of the development of hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor encountered in experiments [1-3]. For the numerical solution used the TPS software package (Turbulence Problem Solver) that implements a generalized approach to constructing computer programs for a wide range of problems of hydrodynamics, described by the system of equations of hyperbolic type. As numerical methods are used the method of large particles and ENO-scheme of the second order with Roe solver for the approximate solution of the Riemann problem.

Free Radical Addition Polymerization Kinetics without Steady-State Approximations: A Numerical Analysis for the Polymer, Physical, or Advanced Organic Chemistry Course

ERIC Educational Resources Information Center

Iler, H. Darrell; Brown, Amber; Landis, Amanda; Schimke, Greg; Peters, George

2014-01-01

A numerical analysis of the free radical addition polymerization system is described that provides those teaching polymer, physical, or advanced organic chemistry courses the opportunity to introduce students to numerical methods in the context of a simple but mathematically stiff chemical kinetic system. Numerical analysis can lead students to an…

Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.

2015-03-01

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.

Numerical study of combustion processes in afterburners

NASA Technical Reports Server (NTRS)

Zhou, Xiaoqing; Zhang, Xiaochun

1986-01-01

Mathematical models and numerical methods are presented for computer modeling of aeroengine afterburners. A computer code GEMCHIP is described briefly. The algorithms SIMPLER, for gas flow predictions, and DROPLET, for droplet flow calculations, are incorporated in this code. The block correction technique is adopted to facilitate convergence. The method of handling irregular shapes of combustors and flameholders is described. The predicted results for a low-bypass-ratio turbofan afterburner in the cases of gaseous combustion and multiphase spray combustion are provided and analyzed, and engineering guides for afterburner optimization are presented.

A time-accurate finite volume method valid at all flow velocities

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1993-01-01

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

PubMed Central

Zhao, Lei; Yue, Xingye; Waxman, David

2013-01-01

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size. PMID:23749318

Numerical simulation of self-sustained oscillation of a voice-producing element based on Navier-Stokes equations and the finite element method.

PubMed

de Vries, Martinus P; Hamburg, Marc C; Schutte, Harm K; Verkerke, Gijsbertus J; Veldman, Arthur E P

2003-04-01

Surgical removal of the larynx results in radically reduced production of voice and speech. To improve voice quality a voice-producing element (VPE) is developed, based on the lip principle, called after the lips of a musician while playing a brass instrument. To optimize the VPE, a numerical model is developed. In this model, the finite element method is used to describe the mechanical behavior of the VPE. The flow is described by two-dimensional incompressible Navier-Stokes equations. The interaction between VPE and airflow is modeled by placing the grid of the VPE model in the grid of the aerodynamical model, and requiring continuity of forces and velocities. By applying and increasing pressure to the numerical model, pulses comparable to glottal volume velocity waveforms are obtained. By variation of geometric parameters their influence can be determined. To validate this numerical model, an in vitro test with a prototype of the VPE is performed. Experimental and numerical results show an acceptable agreement.

Zdeněk Kopal: Numerical Analyst

NASA Astrophysics Data System (ADS)

Křížek, M.

2015-07-01

We give a brief overview of Zdeněk Kopal's life, his activities in the Czech Astronomical Society, his collaboration with Vladimír Vand, and his studies at Charles University, Cambridge, Harvard, and MIT. Then we survey Kopal's professional life. He published 26 monographs and 20 conference proceedings. We will concentrate on Kopal's extensive monograph Numerical Analysis (1955, 1961) that is widely accepted to be the first comprehensive textbook on numerical methods. It describes, for instance, methods for polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations with initial or boundary conditions, and numerical solution of integral and integro-differential equations. Special emphasis will be laid on error analysis. Kopal himself applied numerical methods to celestial mechanics, in particular to the N-body problem. He also used Fourier analysis to investigate light curves of close binaries to discover their properties. This is, in fact, a problem from mathematical analysis.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

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Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-29

... TSD will describe methods and approaches for developing numeric nutrient criteria for Florida's... support document on development of numeric nutrient criteria for Florida's estuarine and coastal waters...

Numerical methods for axisymmetric and 3D nonlinear beams

NASA Astrophysics Data System (ADS)

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

Analytical and numerical analysis of the slope of von Mises planar trusses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalina, M.; Frantík, P.

2016-06-08

In the present paper, there are presented post-critical stress states which will occur at loading by vertical shift of the top joint in the direction downwards. The formation of certain stress states depends on the size of the angle formed by a straight beam of the von Mises planar truss with horizontal plane. Numerical and analytical methods and their problems with finding the angle were described. The numerical solution applies the method of searching for a minimum of potential energy.

A three-dimensional, compressible, laminar boundary-layer method for general fuselages. Volume 1: Numerical method

NASA Technical Reports Server (NTRS)

Wie, Yong-Sun

1990-01-01

A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.

High-order scheme for the source-sink term in a one-dimensional water temperature model

PubMed Central

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data. PMID:28264005

High-order scheme for the source-sink term in a one-dimensional water temperature model.

PubMed

Jing, Zheng; Kang, Ling

2017-01-01

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

PubMed

Khoram, Nafiseh; Zayane, Chadia; Djellouli, Rabia; Laleg-Kirati, Taous-Meriem

2016-03-15

The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages. We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data. Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method. We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods. We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%). Published by Elsevier B.V.

Numerical simulation of blast wave propagation in vicinity of standalone prism on flat plate

NASA Astrophysics Data System (ADS)

Valger, Svetlana; Fedorova, Natalya; Fedorov, Alexander

2018-03-01

In the paper, numerical simulation of shock wave propagation in the vicinity of a standalone prism and a prism with a cavity in front of it was carried out. The modeling was based on the solution of 3D Euler equations and Fluent software was used as a main computational tool. The algorithm for local dynamic mesh adaptation to high gradients of pressure was applied. The initial stage of the explosion of condensed explosive was described with the help of "Compressed balloon method". The research allowed describing the characteristic stages of the blast in a semi-closed space, the structure of secondary shock waves and their interaction with obstacles. The numerical approach in Fluent based on combining inviscid gas dynamics methods and "Compressed balloon method" was compared with the method which had been used by the authors earlier with the help of AUTODYN and which is based on the use of the hydrodynamic model of a material to describe state of detonation products. For the problem of shock wave propagation in the vicinity of standalone prism the comparison of the simulation results obtained using both the methods with the experimental data was performed on the dependence of static pressure and effective momentum on time for the characteristic points located on prism walls.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

Efficient numerical method for investigating diatomic molecules with single active electron subjected to intense and ultrashort laser fields

NASA Astrophysics Data System (ADS)

Kiss, Gellért Zsolt; Borbély, Sándor; Nagy, Ladislau

2017-12-01

We have presented here an efficient numerical approach for the ab initio numerical solution of the time-dependent Schrödinger Equation describing diatomic molecules, which interact with ultrafast laser pulses. During the construction of the model we have assumed a frozen nuclear configuration and a single active electron. In order to increase efficiency our system was described using prolate spheroidal coordinates, where the wave function was discretized using the finite-element discrete variable representation (FE-DVR) method. The discretized wave functions were efficiently propagated in time using the short-iterative Lanczos algorithm. As a first test we have studied here how the laser induced bound state dynamics in H2+ is influenced by the strength of the driving laser field.

Efficient Numerical Methods for Nonlinear-Facilitated Transport and Exchange in a Blood-Tissue Exchange Unit

PubMed Central

Poulain, Christophe A.; Finlayson, Bruce A.; Bassingthwaighte, James B.

2010-01-01

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data. PMID:9146808

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

Comparison of Artificial Compressibility Methods

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Housman, Jeffrey; Kwak, Dochan

2004-01-01

Various artificial compressibility methods for calculating the three-dimensional incompressible Navier-Stokes equations are compared. Each method is described and numerical solutions to test problems are conducted. A comparison based on convergence behavior, accuracy, and robustness is given.

Simplified method for numerical modeling of fiber lasers.

PubMed

Shtyrina, O V; Yarutkina, I A; Fedoruk, M P

2014-12-29

A simplified numerical approach to modeling of dissipative dispersion-managed fiber lasers is examined. We present a new numerical iteration algorithm for finding the periodic solutions of the system of nonlinear ordinary differential equations describing the intra-cavity dynamics of the dissipative soliton characteristics in dispersion-managed fiber lasers. We demonstrate that results obtained using simplified model are in good agreement with full numerical modeling based on the corresponding partial differential equations.

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1993-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.

Singularity Preserving Numerical Methods for Boundary Integral Equations

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki (Principal Investigator)

1996-01-01

In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

NASA Technical Reports Server (NTRS)

Connor, J. N. L.; Curtis, P. R.; Farrelly, D.

1984-01-01

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bogdanov, Yu. I., E-mail: bogdanov-yurii@inbox.ru; Avosopyants, G. V.; Belinskii, L. V.

We describe a new method for reconstructing the quantum state of the electromagnetic field from the results of mutually complementary optical quadrature measurements. This method is based on the root approach and displaces squeezed Fock states are used as the basis. Theoretical analysis and numerical experiments demonstrate the considerable advantage of the developed tools over those described in the literature.

Multicomponent-flow analyses by multimode method of characteristics

USGS Publications Warehouse

Lai, Chintu

1994-01-01

For unsteady open-channel flows having N interacting unknown variables, a system of N mutually independent, partial differential equations can be used to describe the flow-field. The system generally belongs to marching-type problems and permits transformation into characteristic equations that are associated with N distinct characteristics directions. Because characteristics can be considered 'wave' or 'disturbance' propagation, a fluvial system so described can be viewed as adequately definable using these N component waves. A numerical algorithm to solve the N families of characteristics can then be introduced for formulation of an N-component flow-simulation model. The multimode method of characteristics (MMOC), a new numerical scheme that has a combined capacity of several specified-time-interval (STI) schemes of the method of characteristics, makes numerical modeling of such N-component riverine flows feasible and attainable. Merging different STI schemes yields different kinds of MMOC schemes, for which two kinds are displayed herein. With the MMOC, each characteristics is dynamically treated by an appropriate numerical mode, which should lead to an effective and suitable global simulation, covering various types of unsteady flow. The scheme is always linearly stable and its numerical accuracy can be systematically analyzed. By increasing the N value, one can develop a progressively sophisticated model that addresses increasingly complex river-mechanics problems.

Analysis of the discontinuous Galerkin method applied to the European option pricing problem

NASA Astrophysics Data System (ADS)

Hozman, J.

2013-12-01

In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

Splitting algorithm for numerical simulation of Li-ion battery electrochemical processes

NASA Astrophysics Data System (ADS)

Iliev, Oleg; Nikiforova, Marina A.; Semenov, Yuri V.; Zakharov, Petr E.

2017-11-01

In this paper we present a splitting algorithm for a numerical simulation of Li-ion battery electrochemical processes. Liion battery consists of three domains: anode, cathode and electrolyte. Mathematical model of electrochemical processes is described on a microscopic scale, and contains nonlinear equations for concentration and potential in each domain. On the interface of electrodes and electrolyte there are the Lithium ions intercalation and deintercalation processes, which are described by Butler-Volmer nonlinear equation. To approximate in spatial coordinates we use finite element methods with discontinues Galerkin elements. To simplify numerical simulations we develop the splitting algorithm, which split the original problem into three independent subproblems. We investigate the numerical convergence of the algorithm on 2D model problem.

Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria

2009-07-15

We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (nonstationary) black holes. We use a parabolic heat flow to solve numerically the stationary axially symmetric Einstein equations. As a by-product of our method, we also give numerical evidences that there are no regular solutions of Einstein equations that describe two extreme, axially symmetric black holes in equilibrium.

The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories

NASA Technical Reports Server (NTRS)

Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.

1972-01-01

An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.

AI/OR computational model for integrating qualitative and quantitative design methods

NASA Technical Reports Server (NTRS)

Agogino, Alice M.; Bradley, Stephen R.; Cagan, Jonathan; Jain, Pramod; Michelena, Nestor

1990-01-01

A theoretical framework for integrating qualitative and numerical computational methods for optimally-directed design is described. The theory is presented as a computational model and features of implementations are summarized where appropriate. To demonstrate the versatility of the methodology we focus on four seemingly disparate aspects of the design process and their interaction: (1) conceptual design, (2) qualitative optimal design, (3) design innovation, and (4) numerical global optimization.

Numerical built-in method for the nonlinear JRC/JCS model in rock joint.

PubMed

Liu, Qunyi; Xing, Wanli; Li, Ying

2014-01-01

The joint surface is widely distributed in the rock, thus leading to the nonlinear characteristics of rock mass strength and limiting the effectiveness of the linear model in reflecting characteristics. The JRC/JCS model is the nonlinear failure criterion and generally believed to describe the characteristics of joints better than other models. In order to develop the numerical program for JRC/JCS model, this paper established the relationship between the parameters of the JRC/JCS and Mohr-Coulomb models. Thereafter, the numerical implement method and implementation process of the JRC/JCS model were discussed and the reliability of the numerical method was verified by the shear tests of jointed rock mass. Finally, the effect of the JRC/JCS model parameters on the shear strength of the joint was analyzed.

Allergic Contact Dermatitis to Ophthalmic Medications: Relevant Allergens and Alternative Testing Methods.

PubMed

Grey, Katherine R; Warshaw, Erin M

Allergic contact dermatitis is an important cause of periorbital dermatitis. Topical ophthalmic agents are relevant sensitizers. Contact dermatitis to ophthalmic medications can be challenging to diagnose and manage given the numerous possible offending agents, including both active and inactive ingredients. Furthermore, a substantial body of literature reports false-negative patch test results to ophthalmic agents. Subsequently, numerous alternative testing methods have been described. This review outlines the periorbital manifestations, causative agents, and alternative testing methods of allergic contact dermatitis to ophthalmic medications.

Remarks on a financial inverse problem by means of Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Di Somma, Vittorio; Sica, Federica

2017-10-01

Estimating the price of a barrier option is a typical inverse problem. In this paper we present a numerical and statistical framework for a market with risk-free interest rate and a risk asset, described by a Geometric Brownian Motion (GBM). After approximating the risk asset with a numerical method, we find the final option price by following an approach based on sequential Monte Carlo methods. All theoretical results are applied to the case of an option whose underlying is a real stock.

Modelling crystal growth: Convection in an asymmetrically heated ampoule

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.; Rosenberger, Franz; Pulicani, J. P.; Krukowski, S.; Ouazzani, Jalil

1990-01-01

The objective was to develop and implement a numerical method capable of solving the nonlinear partial differential equations governing heat, mass, and momentum transfer in a 3-D cylindrical geometry in order to examine the character of convection in an asymmetrically heated cylindrical ampoule. The details of the numerical method, including verification tests involving comparison with results obtained from other methods, are presented. The results of the study of 3-D convection in an asymmetrically heated cylinder are described.

Advanced numerical methods for three dimensional two-phase flow calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toumi, I.; Caruge, D.

1997-07-01

This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses anmore » extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.« less

Numerical Analysis of Deflections of Multi-Layered Beams

NASA Astrophysics Data System (ADS)

Biliński, Tadeusz; Socha, Tomasz

2015-03-01

The paper concerns the rheological bending problem of wooden beams reinforced with embedded composite bars. A theoretical model of the behaviour of a multi-layered beam is presented. The component materials of this beam are described with equations for the linear viscoelastic five-parameter rheological model. Two numerical analysis methods for the long-term response of wood structures are presented. The first method has been developed with SCILAB software. The second one has been developed with the finite element calculation software ABAQUS and user subroutine UMAT. Laboratory investigations were conducted on sample beams of natural dimensions in order to validate the proposed theoretical model and verify numerical simulations. Good agreement between experimental measurements and numerical results is observed.

Programmable Numerical Function Generators: Architectures and Synthesis Method

DTIC Science & Technology

2005-08-01

generates HDL (Hardware Descrip- tion Language) code from the design specification described by Scilab [14], a MATLAB-like numerical calculation soft...cad.com/Error-NFG/. [14] Scilab 3.0, INRIA-ENPC, France, http://scilabsoft.inria.fr/ [15] M. J. Schulte and J. E. Stine, “Approximating elementary functions

Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers.

PubMed

Gong, Mali; Yuan, Yanyang; Li, Chen; Yan, Ping; Zhang, Haitao; Liao, Suying

2007-03-19

A model based on propagation-rate equations with consideration of transverse gain distribution is built up to describe the transverse mode competition in strongly pumped multimode fiber lasers and amplifiers. An approximate practical numerical algorithm by multilayer method is presented. Based on the model and the numerical algorithm, the behaviors of multitransverse mode competition are demonstrated and individual transverse modes power distributions of output are simulated numerically for both fiber lasers and amplifiers under various conditions.

Evaluation of equipment and methods to map lost circulation zones in geothermal wells

DOE Office of Scientific and Technical Information (OSTI.GOV)

McDonald, W.J.; Leon, P.A.; Pittard, G.

A study and evaluation of methods to locate, characterize, and quantify lost circulation zones are described. Twenty-five methods of mapping and quantifying lost circulation zones were evaluated, including electrical, acoustical, mechanical, radioactive, and optical systems. Each tool studied is described. The structured, numerical evaluation plan, used as the basis for comparing the 25 tools, and the resulting ranking among the tools is presented.

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

PubMed

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1992-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

NASA Technical Reports Server (NTRS)

Rummel, R.; Sjoeberg, L.; Rapp, R. H.

1978-01-01

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.

Hybrid Particle-Element Simulation of Impact on Composite Orbital Debris Shields

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2004-01-01

This report describes the development of new numerical methods and new constitutive models for the simulation of hypervelocity impact effects on spacecraft. The research has included parallel implementation of the numerical methods and material models developed under the project. Validation work has included both one dimensional simulations, for comparison with exact solutions, and three dimensional simulations of published hypervelocity impact experiments. The validated formulations have been applied to simulate impact effects in a velocity and kinetic energy regime outside the capabilities of current experimental methods. The research results presented here allow for the expanded use of numerical simulation, as a complement to experimental work, in future design of spacecraft for hypervelocity impact effects.

A numerical method for the dynamics of non-spherical cavitation bubbles

NASA Technical Reports Server (NTRS)

Lucca, G.; Prosperetti, A.

1982-01-01

A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics.

PubMed

Brocchini, Maurizio

2013-12-08

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

PubMed Central

Brocchini, Maurizio

2013-01-01

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention. PMID:24353475

A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

2014-12-01

The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Numerical Characterization of Piezoceramics Using Resonance Curves

PubMed Central

Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

2016-01-01

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875

Numerical Characterization of Piezoceramics Using Resonance Curves.

PubMed

Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

2016-01-27

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

Probabilistic structural analysis methods of hot engine structures

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Hopkins, D. A.

1989-01-01

Development of probabilistic structural analysis methods for hot engine structures is a major activity at Lewis Research Center. Recent activities have focused on extending the methods to include the combined uncertainties in several factors on structural response. This paper briefly describes recent progress on composite load spectra models, probabilistic finite element structural analysis, and probabilistic strength degradation modeling. Progress is described in terms of fundamental concepts, computer code development, and representative numerical results.

Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth's satellites

NASA Astrophysics Data System (ADS)

Vashkovyaka, M. A.; Zaslavskii, G. S.

2016-09-01

We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth's satellites. We describe parameters of the motion model used for the artificial Earth's satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.

(U) Introduction to Monte Carlo Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hungerford, Aimee L.

2017-03-20

Monte Carlo methods are very valuable for representing solutions to particle transport problems. Here we describe a “cook book” approach to handling the terms in a transport equation using Monte Carlo methods. Focus is on the mechanics of a numerical Monte Carlo code, rather than the mathematical foundations of the method.

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

NASA Astrophysics Data System (ADS)

Mamehrashi, K.; Yousefi, S. A.

2017-02-01

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

Modeling of diatomic molecule using the Morse potential and the Verlet algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fidiani, Elok

Performing molecular modeling usually uses special software for Molecular Dynamics (MD) such as: GROMACS, NAMD, JMOL etc. Molecular dynamics is a computational method to calculate the time dependent behavior of a molecular system. In this work, MATLAB was used as numerical method for a simple modeling of some diatomic molecules: HCl, H{sub 2} and O{sub 2}. MATLAB is a matrix based numerical software, in order to do numerical analysis, all the functions and equations describing properties of atoms and molecules must be developed manually in MATLAB. In this work, a Morse potential was generated to describe the bond interaction betweenmore » the two atoms. In order to analyze the simultaneous motion of molecules, the Verlet Algorithm derived from Newton’s Equations of Motion (classical mechanics) was operated. Both the Morse potential and the Verlet algorithm were integrated using MATLAB to derive physical properties and the trajectory of the molecules. The data computed by MATLAB is always in the form of a matrix. To visualize it, Visualized Molecular Dynamics (VMD) was performed. Such method is useful for development and testing some types of interaction on a molecular scale. Besides, this can be very helpful for describing some basic principles of molecular interaction for educational purposes.« less

On numerical solution of the Schrödinger equation: the shooting method revisited

NASA Astrophysics Data System (ADS)

Indjin, D.; Todorović, G.; Milanović, V.; Ikonić, Z.

1995-09-01

An alternative formulation of the "shooting" method for a numerical solution of the Schrödinger equation is described for cases of general asymmetric one-dimensional potential (planar geometry), and spherically symmetric potential. The method relies on matching the asymptotic wavefunctions and the potential core region wavefunctions, in course of finding bound states energies. It is demonstrated in the examples of Morse and Kratzer potentials, where a high accuracy of the calculated eigenvalues is found, together with a considerable saving of the computation time.

40 CFR 194.24 - Waste characterization.

Code of Federal Regulations, 2010 CFR

2010-07-01

... other information and methods. (b) The Department shall submit in the compliance certification... proposed for disposal in the disposal system, WIPP complies with the numeric requirements of § 194.34 and... release. (2) Identify and describe the method(s) used to quantify the limits of waste components...

Automating FEA programming

NASA Technical Reports Server (NTRS)

Sharma, Naveen

1992-01-01

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer.

Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prinja, Anil K.

The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset aremore » amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.« less

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

2016-08-01

Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Water-waves on linear shear currents. A comparison of experimental and numerical results.

NASA Astrophysics Data System (ADS)

Simon, Bruno; Seez, William; Touboul, Julien; Rey, Vincent; Abid, Malek; Kharif, Christian

2016-04-01

Propagation of water waves can be described for uniformly sheared current conditions. Indeed, some mathematical simplifications remain applicable in the study of waves whether there is no current or a linearly sheared current. However, the widespread use of mathematical wave theories including shear has rarely been backed by experimental studies of such flows. New experimental and numerical methods were both recently developed to study wave current interactions for constant vorticity. On one hand, the numerical code can simulate, in two dimensions, arbitrary non-linear waves. On the other hand, the experimental methods can be used to generate waves with various shear conditions. Taking advantage of the simplicity of the experimental protocol and versatility of the numerical code, comparisons between experimental and numerical data are discussed and compared with linear theory for validation of the methods. ACKNOWLEDGEMENTS The DGA (Direction Générale de l'Armement, France) is acknowledged for its financial support through the ANR grant N° ANR-13-ASTR-0007.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

NASA Astrophysics Data System (ADS)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

PubMed

Lambert, B; Weynans, L; Bergmann, M

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

Analysis of supersonic combustion flow fields with embedded subsonic regions

NASA Technical Reports Server (NTRS)

Dash, S.; Delguidice, P.

1972-01-01

The viscous characteristic analysis for supersonic chemically reacting flows was extended to include provisions for analyzing embedded subsonic regions. The numerical method developed to analyze this mixed subsonic-supersonic flow fields is described. The boundary conditions are discussed related to the supersonic-subsonic and subsonic-supersonic transition, as well as a heuristic description of several other numerical schemes for analyzing this problem. An analysis of shock waves generated either by pressure mismatch between the injected fluid and surrounding flow or by chemical heat release is also described.

Numerical Simulations of Multidimensional Flows in Presence of either Strong Shocks or Strong Gravitational Fields

NASA Astrophysics Data System (ADS)

Font, J. A.; Ibanez, J. M.; Marti, J. M.

1993-04-01

Some numerical solutions via local characteristic approach have been obtained describing multidimensional flows. These solutions have been used as tests of a two- dimensional code which extends some high-resolution shock-captunng methods, designed recently to solve nonlinear hyperbolic systems of conservation laws. K words: HYDRODYNAMICS - BLACK HOLE - RELATIVITY - SHOCK WAVES

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models

NASA Astrophysics Data System (ADS)

Wang, Xiaoqiang; Ju, Lili; Du, Qiang

2016-07-01

The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Calculation of double-lunar swingby trajectories: Part 2: Numerical solutions in the restricted problem of three bodies

NASA Technical Reports Server (NTRS)

Stalos, S.

1990-01-01

The double-lunar swingby trajectory is a method for maintaining alignment of an Earth satellite's line of apsides with the Sun-Earth line. From a Keplerian point of view, successive close encounters with the Moon cause discrete, instantaneous changes in the satellite's eccentricity and semimajor axis. Numerical solutions to the planar, restricted problem of three bodies as double-lunar swingby trajectories are identified. The method of solution is described and the results compared to the Keplerian formulation.

Numerical calculation of transonic flow about slender bodies of revolution

NASA Technical Reports Server (NTRS)

Bailey, F. R.

1971-01-01

A relaxation method is described for the numerical solution of the transonic small disturbance equation for flow about a slender body of revolution. Results for parabolic arc bodies, both with and without an attached sting, are compared with wind-tunnel measurements for a free-stream Mach number range from 0.90 to 1.20. The method is also used to show the effects of wind-tunnel wall interference by including boundary conditions representing porous-wall and open-jet wind-tunnel test sections.

The use of rational functions in numerical quadrature

NASA Astrophysics Data System (ADS)

Gautschi, Walter

2001-08-01

Quadrature problems involving functions that have poles outside the interval of integration can profitably be solved by methods that are exact not only for polynomials of appropriate degree, but also for rational functions having the same (or the most important) poles as the function to be integrated. Constructive and computational tools for accomplishing this are described and illustrated in a number of quadrature contexts. The superiority of such rational/polynomial methods is shown by an analysis of the remainder term and documented by numerical examples.

Benchmark solution for the Spencer-Lewis equation of electron transport theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganapol, B.D.

As integrated circuits become smaller, the shielding of these sensitive components against penetrating electrons becomes extremely critical. Monte Carlo methods have traditionally been the method of choice in shielding evaluations primarily because they can incorporate a wide variety of relevant physical processes. Recently, however, as a result of a more accurate numerical representation of the highly forward peaked scattering process, S/sub n/ methods for one-dimensional problems have been shown to be at least as cost-effective in comparison with Monte Carlo methods. With the development of these deterministic methods for electron transport, a need has arisen to assess the accuracy ofmore » proposed numerical algorithms and to ensure their proper coding. It is the purpose of this presentation to develop a benchmark to the Spencer-Lewis equation describing the transport of energetic electrons in solids. The solution will take advantage of the correspondence between the Spencer-Lewis equation and the transport equation describing one-group time-dependent neutron transport.« less

Computational Physics.

ERIC Educational Resources Information Center

Borcherds, P. H.

1986-01-01

Describes an optional course in "computational physics" offered at the University of Birmingham. Includes an introduction to numerical methods and presents exercises involving fast-Fourier transforms, non-linear least-squares, Monte Carlo methods, and the three-body problem. Recommends adding laboratory work into the course in the…

Gram-Schmidt Orthogonalization by Gauss Elimination.

ERIC Educational Resources Information Center

Pursell, Lyle; Trimble, S. Y.

1991-01-01

Described is the hand-calculation method for the orthogonalization of a given set of vectors through the integration of Gaussian elimination with existing algorithms. Although not numerically preferable, this method adds increased precision as well as organization to the solution process. (JJK)

Tempest - Efficient Computation of Atmospheric Flows Using High-Order Local Discretization Methods

NASA Astrophysics Data System (ADS)

Ullrich, P. A.; Guerra, J. E.

2014-12-01

The Tempest Framework composes several compact numerical methods to easily facilitate intercomparison of atmospheric flow calculations on the sphere and in rectangular domains. This framework includes the implementations of Spectral Elements, Discontinuous Galerkin, Flux Reconstruction, and Hybrid Finite Element methods with the goal of achieving optimal accuracy in the solution of atmospheric problems. Several advantages of this approach are discussed such as: improved pressure gradient calculation, numerical stability by vertical/horizontal splitting, arbitrary order of accuracy, etc. The local numerical discretization allows for high performance parallel computation and efficient inclusion of parameterizations. These techniques are used in conjunction with a non-conformal, locally refined, cubed-sphere grid for global simulations and standard Cartesian grids for simulations at the mesoscale. A complete implementation of the methods described is demonstrated in a non-hydrostatic setting.

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

GCKP84-general chemical kinetics code for gas-phase flow and batch processes including heat transfer effects

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1984-01-01

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

Numerical simulation of water hammer in low pressurized pipe: comparison of SimHydraulics and Lax-Wendroff method with experiment

NASA Astrophysics Data System (ADS)

Himr, D.

2013-04-01

Article describes simulation of unsteady flow during water hammer with two programs, which use different numerical approaches to solve ordinary one dimensional differential equations describing the dynamics of hydraulic elements and pipes. First one is Matlab-Simulink-SimHydraulics, which is a commercial software developed to solve the dynamics of general hydraulic systems. It defines them with block elements. The other software is called HYDRA and it is based on the Lax-Wendrff numerical method, which serves as a tool to solve the momentum and continuity equations. This program was developed in Matlab by Brno University of Technology. Experimental measurements were performed on a simple test rig, which consists of an elastic pipe with strong damping connecting two reservoirs. Water hammer is induced with fast closing the valve. Physical properties of liquid and pipe elasticity parameters were considered in both simulations, which are in very good agreement and differences in comparison with experimental data are minimal.

Shock capturing finite difference algorithms for supersonic flow past fighter and missile type configurations

NASA Technical Reports Server (NTRS)

Osher, S.

1984-01-01

The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.

Vortex methods for separated flows

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.

1988-01-01

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity

NASA Astrophysics Data System (ADS)

Voronych, Oksana; Buraczewski, Adam; Matuszewski, Michał; Stobińska, Magdalena

2017-06-01

A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge-Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which has been used for theoretical investigation of exciton-polaritons. Catalogue identifier: AFBQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD-3 No. of lines in distributed program, including test data, etc.: 2157 No. of bytes in distributed program, including test data, etc.: 498994 Distribution format: tar.gz Programming language: C++ with OpenMP extensions (main numerical program), Python (helper scripts). Computer: Modern PC (tested on AMD and Intel processors), HP BL2x220. Operating system: Unix/Linux and Windows. Has the code been vectorized or parallelized?: Yes (OpenMP) RAM: 200 MB for single run Classification: 7, 7.7. Nature of problem: An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose-Einstein condensation of exciton-polaritons-quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross-Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons. Solution method: A Runge-Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware. Running time: 6h for 100 ps evolution, depending on the values of parameters

Exact analytic solutions of Maxwell's equations describing propagating nonparaxial electromagnetic beams.

PubMed

Garay-Avendaño, Roger L; Zamboni-Rached, Michel

2014-07-10

In this paper, we propose a method that is capable of describing in exact and analytic form the propagation of nonparaxial scalar and electromagnetic beams. The main features of the method presented here are its mathematical simplicity and the fast convergence in the cases of highly nonparaxial electromagnetic beams, enabling us to obtain high-precision results without the necessity of lengthy numerical simulations or other more complex analytical calculations. The method can be used in electromagnetism (optics, microwaves) as well as in acoustics.

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

General chemical kinetics computer program for static and flow reactions, with application to combustion and shock-tube kinetics

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1972-01-01

A general chemical kinetics program is described for complex, homogeneous ideal-gas reactions in any chemical system. Its main features are flexibility and convenience in treating many different reaction conditions. The program solves numerically the differential equations describing complex reaction in either a static system or one-dimensional inviscid flow. Applications include ignition and combustion, shock wave reactions, and general reactions in a flowing or static system. An implicit numerical solution method is used which works efficiently for the extreme conditions of a very slow or a very fast reaction. The theory is described, and the computer program and users' manual are included.

CSM Testbed Development and Large-Scale Structural Applications

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.; Gillian, R. E.; Mccleary, Susan L.; Lotts, C. G.; Poole, E. L.; Overman, A. L.; Macy, S. C.

1989-01-01

A research activity called Computational Structural Mechanics (CSM) conducted at the NASA Langley Research Center is described. This activity is developing advanced structural analysis and computational methods that exploit high-performance computers. Methods are developed in the framework of the CSM Testbed software system and applied to representative complex structural analysis problems from the aerospace industry. An overview of the CSM Testbed methods development environment is presented and some new numerical methods developed on a CRAY-2 are described. Selected application studies performed on the NAS CRAY-2 are also summarized.

Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation

NASA Astrophysics Data System (ADS)

Gallinato, Olivier; Poignard, Clair

2017-06-01

In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.

The Instructional Cost Index. A Simplified Approach to Interinstitutional Cost Comparison.

ERIC Educational Resources Information Center

Beatty, George, Jr.; And Others

The paper describes a simple, yet effective method of computing a comparative index of instructional costs. The Instructional Cost Index identifies direct cost differentials among instructional programs. Cost differentials are described in terms of differences among numerical values of variables that reflect fundamental academic and resource…

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, Robert J.; Beylkin, Gregory; Bischoff, Florian A.

2016-01-01

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

Electro-Optic Data Acquisition and Processing.

DTIC Science & Technology

Methods for the analysis of electro - optic relaxation data are discussed. Emphasis is on numerical methods using high speed computers. A data acquisition system using a minicomputer for data manipulation is described. Relationship of the results obtained here to other possible uses is given. (Author)

Transonic Flow Computations Using Nonlinear Potential Methods

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Kwak, Dochan (Technical Monitor)

2000-01-01

This presentation describes the state of transonic flow simulation using nonlinear potential methods for external aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall. nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions. Published by Elsevier Science Ltd. All rights reserved.

Some problems in applications of the linear variational method

NASA Astrophysics Data System (ADS)

Pupyshev, Vladimir I.; Montgomery, H. E.

2015-09-01

The linear variational method is a standard computational method in quantum mechanics and quantum chemistry. As taught in most classes, the general guidance is to include as many basis functions as practical in the variational wave function. However, if it is desired to study the patterns of energy change accompanying the change of system parameters such as the shape and strength of the potential energy, the problem becomes more complicated. We use one-dimensional systems with a particle in a rectangular or in a harmonic potential confined in an infinite rectangular box to illustrate situations where a variational calculation can give incorrect results. These situations result when the energy of the lowest eigenvalue is strongly dependent on the parameters that describe the shape and strength of the potential. The numerical examples described in this work are provided as cautionary notes for practitioners of numerical variational calculations.

Spatio-temporal instabilities for counterpropagating waves in periodic media.

PubMed

Haus, Joseph; Soon, Boon Yi; Scalora, Michael; Bloemer, Mark; Bowden, Charles; Sibilia, Concita; Zheltikov, Alexei

2002-01-28

Nonlinear evolution of coupled forward and backward fields in a multi-layered film is numerically investigated. We examine the role of longitudinal and transverse modulation instabilities in media of finite length with a homogeneous nonlinear susceptibility c((3)). The numerical solution of the nonlinear equations by a beam-propagation method that handles backward waves is described.

GIM code user's manual for the STAR-100 computer. [for generating numerical analogs of the conversion laws

NASA Technical Reports Server (NTRS)

Spradley, L.; Pearson, M.

1979-01-01

The General Interpolants Method (GIM), a three dimensional, time dependent, hybrid procedure for generating numerical analogs of the conversion laws, is described. The Navier-Stokes equations written for an Eulerian system are considered. The conversion of the GIM code to the STAR-100 computer, and the implementation of 'GIM-ON-STAR' is discussed.

Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer

NASA Technical Reports Server (NTRS)

Rai, Man M.; Moin, Parviz

1991-01-01

A high-order-accurate finite-difference approach to direct simulations of transition and turbulence in compressible flows is described. Attention is given to the high-free-stream disturbance case in which transition to turbulence occurs close to the leading edge. In effect, computation requirements are reduced. A method for numerically generating free-stream disturbances is presented.

Lagrangian analysis of multiscale particulate flows with the particle finite element method

NASA Astrophysics Data System (ADS)

Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy

2014-05-01

We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

On the use of attachment modes in substructure coupling for dynamic analysis

NASA Technical Reports Server (NTRS)

Craig, R. R., Jr.; Chang, C.-J.

1977-01-01

Substructure coupling or component-mode synthesis may be employed in the solution of dynamics problems for complex structures. Although numerous substructure-coupling methods have been devised, little attention has been devoted to methods employing attachment modes. In the present paper the various mode sets (normal modes, constraint modes, attachment modes) are defined. A generalized substructure-coupling procedure is described. Those substructure-coupling methods which employ attachment modes are described in detail. One of these methods is shown to lead to results (e.g., system natural frequencies) comparable to or better than those obtained by the Hurty (1965) method.

Numerical-graphical method for describing the creep of damaged highly filled polymer materials

NASA Astrophysics Data System (ADS)

Bykov, D. L.; Martynova, E. D.; Mel'nikov, V. P.

2015-09-01

A method for describing the creep behavior until fracture of a highly filled polymer material previously damaged in preliminary tests is proposed. The constitutive relations are the relations of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) [1]. The numerical-graphical method for identifying the functions occurring in NETAVEM, which was proposed in [2] for describing loading processes at a constant strain rate, is used here for the first time in creep theory. We use the results of experiments with undamaged and preliminary damaged specimens under the action of the same constant tensile loads. The creep kernel is determined in experiments with an undamaged specimen. The reduced time function contained in NETAVEM is determined from the position of points corresponding to the same values of strain on the creep curves of the damaged and undamaged specimens. An integral equation is solved to obtain the aging function, and then the viscosity function is determined. The knowledge of all functions contained in the constitutive relations permits solving the creep problem for products manufactured from a highly filled polymer material.

A Method for Calculating Fermi Energy and Carrier Concentrations in Semiconducts

ERIC Educational Resources Information Center

Gaylord, T. K.; Linxwiler, J. N., Jr.

1976-01-01

An efficient numerical method for calculating the Fermi energy, the free electron and free hole concentrations, and the ionized impurity conductors in a semiconductor material is described. The method allows freedom with respect to type of material, temperature, and amount and type of donor and acceptor impurities. (Author/CP)

Hybrid RANS-LES using high order numerical methods

NASA Astrophysics Data System (ADS)

Henry de Frahan, Marc; Yellapantula, Shashank; Vijayakumar, Ganesh; Knaus, Robert; Sprague, Michael

2017-11-01

Understanding the impact of wind turbine wake dynamics on downstream turbines is particularly important for the design of efficient wind farms. Due to their tractable computational cost, hybrid RANS/LES models are an attractive framework for simulating separation flows such as the wake dynamics behind a wind turbine. High-order numerical methods can be computationally efficient and provide increased accuracy in simulating complex flows. In the context of LES, high-order numerical methods have shown some success in predictions of turbulent flows. However, the specifics of hybrid RANS-LES models, including the transition region between both modeling frameworks, pose unique challenges for high-order numerical methods. In this work, we study the effect of increasing the order of accuracy of the numerical scheme in simulations of canonical turbulent flows using RANS, LES, and hybrid RANS-LES models. We describe the interactions between filtering, model transition, and order of accuracy and their effect on turbulence quantities such as kinetic energy spectra, boundary layer evolution, and dissipation rate. This work was funded by the U.S. Department of Energy, Exascale Computing Project, under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.

Numerical simulation of photocurrent generation in bilayer organic solar cells: Comparison of master equation and kinetic Monte Carlo approaches

NASA Astrophysics Data System (ADS)

Casalegno, Mosè; Bernardi, Andrea; Raos, Guido

2013-07-01

Numerical approaches can provide useful information about the microscopic processes underlying photocurrent generation in organic solar cells (OSCs). Among them, the Kinetic Monte Carlo (KMC) method is conceptually the simplest, but computationally the most intensive. A less demanding alternative is potentially represented by so-called Master Equation (ME) approaches, where the equations describing particle dynamics rely on the mean-field approximation and their solution is attained numerically, rather than stochastically. The description of charge separation dynamics, the treatment of electrostatic interactions and numerical stability are some of the key issues which have prevented the application of these methods to OSC modelling, despite of their successes in the study of charge transport in disordered system. Here we describe a three-dimensional ME approach to photocurrent generation in OSCs which attempts to deal with these issues. The reliability of the proposed method is tested against reference KMC simulations on bilayer heterojunction solar cells. Comparison of the current-voltage curves shows that the model well approximates the exact result for most devices. The largest deviations in current densities are mainly due to the adoption of the mean-field approximation for electrostatic interactions. The presence of deep traps, in devices characterized by strong energy disorder, may also affect result quality. Comparison of the simulation times reveals that the ME algorithm runs, on the average, one order of magnitude faster than KMC.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Numerical study on anaerobic digestion of fruit and vegetable waste: Biogas generation

NASA Astrophysics Data System (ADS)

Wardhani, Puteri Kusuma; Watanabe, Masaji

2016-02-01

The study provides experimental results and numerical results concerning anaerobic digestion of fruit and vegetable waste. Experiments were carried out by using batch floating drum type digester without mixing and temperature setting. The retention time was 30 days. Numerical results based on Monod type model with influence of temperature is introduced. Initial value problems were analyzed numerically, while kinetic parameters were analyzed by using trial error methods. The numerical results for the first five days seems appropriate in comparison with the experimental outcomes. However, numerical results shows that the model is inappropriate for 30 days of fermentation. This leads to the conclusion that Monod type model is not suitable for describe the mixture degradation of fruit and vegetable waste and horse dung.

Application of Energy Function as a Measure of Error in the Numerical Solution for Online Transient Stability Assessment

NASA Astrophysics Data System (ADS)

Sarojkumar, K.; Krishna, S.

2016-08-01

Online dynamic security assessment (DSA) is a computationally intensive task. In order to reduce the amount of computation, screening of contingencies is performed. Screening involves analyzing the contingencies with the system described by a simpler model so that computation requirement is reduced. Screening identifies those contingencies which are sure to not cause instability and hence can be eliminated from further scrutiny. The numerical method and the step size used for screening should be chosen with a compromise between speed and accuracy. This paper proposes use of energy function as a measure of error in the numerical solution used for screening contingencies. The proposed measure of error can be used to determine the most accurate numerical method satisfying the time constraint of online DSA. Case studies on 17 generator system are reported.

Low cycle fatigue numerical estimation of a high pressure turbine disc for the AL-31F jet engine

NASA Astrophysics Data System (ADS)

Spodniak, Miroslav; Klimko, Marek; Hocko, Marián; Žitek, Pavel

This article deals with the description of an approximate numerical estimation approach of a low cycle fatigue of a high pressure turbine disc for the AL-31F turbofan jet engine. The numerical estimation is based on the finite element method carried out in the SolidWorks software. The low cycle fatigue assessment of a high pressure turbine disc was carried out on the basis of dimensional, shape and material disc characteristics, which are available for the particular high pressure engine turbine. The method described here enables relatively fast setting of economically feasible low cycle fatigue of the assessed high pressure turbine disc using a commercially available software. The numerical estimation of accuracy of a low cycle fatigue depends on the accuracy of required input data for the particular investigated object.

Concept and numerical simulations of a reactive anti-fragment armour layer

NASA Astrophysics Data System (ADS)

Hušek, Martin; Kala, Jiří; Král, Petr; Hokeš, Filip

2017-07-01

The contribution describes the concept and numerical simulation of a ballistic protective layer which is able to actively resist projectiles or smaller colliding fragments flying at high speed. The principle of the layer was designed on the basis of the action/reaction system of reactive armour which is used for the protection of armoured vehicles. As the designed ballistic layer consists of steel plates simultaneously combined with explosive material - primary explosive and secondary explosive - the technique of coupling the Finite Element Method with Smoothed Particle Hydrodynamics was used for the simulations. Certain standard situations which the ballistic layer should resist were simulated. The contribution describes the principles for the successful execution of numerical simulations, their results, and an evaluation of the functionality of the ballistic layer.

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.

1973-01-01

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

Sound propagation in a duct of periodic wall structure. [numerical analysis

NASA Technical Reports Server (NTRS)

Kurze, U.

1978-01-01

A boundary condition, which accounts for the coupling in the sections behind the duct boundary, is given for the sound-absorbing duct with a periodic structure of the wall lining and using regular partition walls. The soundfield in the duct is suitably described by the method of differences. For locally active walls this renders an explicit approximate solution for the propagation constant. Coupling may be accounted for by the method of differences in a clear manner. Numerical results agree with measurements and yield information which has technical applications.

Efficient solution methodology for calibrating the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

PubMed

Zambri, Brian; Djellouli, Rabia; Laleg-Kirati, Taous-Meriem

2015-08-01

Our aim is to propose a numerical strategy for retrieving accurately and efficiently the biophysiological parameters as well as the external stimulus characteristics corresponding to the hemodynamic mathematical model that describes changes in blood flow and blood oxygenation during brain activation. The proposed method employs the TNM-CKF method developed in [1], but in a prediction/correction framework. We present numerical results using both real and synthetic functional Magnetic Resonance Imaging (fMRI) measurements to highlight the performance characteristics of this computational methodology.

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

New method of processing heat treatment experiments with numerical simulation support

NASA Astrophysics Data System (ADS)

Kik, T.; Moravec, J.; Novakova, I.

2017-08-01

In this work, benefits of combining modern software for numerical simulations of welding processes with laboratory research was described. Proposed new method of processing heat treatment experiments leading to obtaining relevant input data for numerical simulations of heat treatment of large parts was presented. It is now possible, by using experiments on small tested samples, to simulate cooling conditions comparable with cooling of bigger parts. Results from this method of testing makes current boundary conditions during real cooling process more accurate, but also can be used for improvement of software databases and optimization of a computational models. The point is to precise the computation of temperature fields for large scale hardening parts based on new method of temperature dependence determination of the heat transfer coefficient into hardening media for the particular material, defined maximal thickness of processed part and cooling conditions. In the paper we will also present an example of the comparison standard and modified (according to newly suggested methodology) heat transfer coefficient data’s and theirs influence on the simulation results. It shows how even the small changes influence mainly on distribution of temperature, metallurgical phases, hardness and stresses distribution. By this experiment it is also possible to obtain not only input data and data enabling optimization of computational model but at the same time also verification data. The greatest advantage of described method is independence of used cooling media type.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution ofmore » dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.« less

Numeric and symbolic knowledge representation of cerebral cortex anatomy: methods and preliminary results.

PubMed

Dameron, O; Gibaud, B; Morandi, X

2004-06-01

The human cerebral cortex anatomy describes the brain organization at the scale of gyri and sulci. It is used as landmarks for neurosurgery as well as localization support for functional data analysis or inter-subject data comparison. Existing models of the cortex anatomy either rely on image labeling but fail to represent variability and structural properties or rely on a conceptual model but miss the inner 3D nature and relations of anatomical structures. This study was therefore conducted to propose a model of sulco-gyral anatomy for the healthy human brain. We hypothesized that both numeric knowledge (i.e., image-based) and symbolic knowledge (i.e., concept-based) have to be represented and coordinated. In addition, the representation of this knowledge should be application-independent in order to be usable in various contexts. Therefore, we devised a symbolic model describing specialization, composition and spatial organization of cortical anatomical structures. We also collected numeric knowledge such as 3D models of shape and shape variation about cortical anatomical structures. For each numeric piece of knowledge, a companion file describes the concept it refers to and the nature of the relationship. Demonstration software performs a mapping between the numeric and the symbolic aspects for browsing the knowledge base.

Methods for describing the electromagnetic properties of silver and gold nanoparticles.

PubMed

Zhao, Jing; Pinchuk, Anatoliy O; McMahon, Jeffrey M; Li, Shuzhou; Ausman, Logan K; Atkinson, Ariel L; Schatz, George C

2008-12-01

This Account provides an overview of the methods that are currently being used to study the electromagnetics of silver and gold nanoparticles, with an emphasis on the determination of extinction and surface-enhanced Raman scattering (SERS) spectra. These methods have proven to be immensely useful in recent years for interpreting a wide range of nanoscience experiments and providing the capability to describe optical properties of particles up to several hundred nanometers in dimension, including arbitrary particle structures and complex dielectric environments (adsorbed layers of molecules, nearby metal films, and other particles). While some of the methods date back to Mie's celebrated work a century ago, others are still at the forefront of algorithm development in computational electromagnetics. This Account gives a qualitative description of the physical and mathematical basis behind the most commonly used methods, including both analytical and numerical methods, as well as representative results of applications that are relevant to current experiments. The analytical methods that we discuss are either derived from Mie theory for spheres or from the quasistatic (Gans) model as applied to spheres and spheroids. In this discussion, we describe the use of Mie theory to determine electromagnetic contributions to SERS enhancements that include for retarded dipole emission effects, and the use of the quasistatic approximation for spheroidal particles interacting with dye adsorbate layers. The numerical methods include the discrete dipole approximation (DDA), the finite difference time domain (FDTD) method, and the finite element method (FEM) based on Whitney forms. We discuss applications such as using DDA to describe the interaction of two gold disks to define electromagnetic hot spots, FDTD for light interacting with metal wires that go from particle-like plasmonic response to the film-like transmission as wire dimension is varied, and FEM studies of electromagnetic fields near cubic particles.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

DOE PAGES

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich; ...

2017-10-28

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE PAGES

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.; ...

2016-09-18

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

Numerical algebraic geometry: a new perspective on gauge and string theories

NASA Astrophysics Data System (ADS)

Mehta, Dhagash; He, Yang-Hui; Hauensteine, Jonathan D.

2012-07-01

There is a rich interplay between algebraic geometry and string and gauge theories which has been recently aided immensely by advances in computational algebra. However, symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these shortcomings. The so-called `embarrassing parallelizability' allows us to solve many problems and extract physical information which elude symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

25 Years of Self-organized Criticality: Numerical Detection Methods

NASA Astrophysics Data System (ADS)

McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna

2016-01-01

The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.

A generalized theory for the design of contraction cones and other low speed ducts

NASA Technical Reports Server (NTRS)

Barger, R. L.; Bowen, J. T.

1972-01-01

A generalization of the Tsien method of contraction cone design is described. The design velocity distribution is expressed in such a form that the required high order derivatives can be obtained by recursion rather than by numerical or analytic differentiation. The method is applicable to the design of diffusers and converging-diverging ducts as well as contraction cones. The computer program is described and a FORTRAN listing of the program is provided.

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Mathematical modeling of heat transfer problems in the permafrost

NASA Astrophysics Data System (ADS)

Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

2014-11-01

In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

DOE PAGES

Harrison, Robert J.; Beylkin, Gregory; Bischoff, Florian A.; ...

2016-01-01

We present MADNESS (multiresolution adaptive numerical environment for scientific simulation) that is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

Salt-water-freshwater transient upconing - An implicit boundary-element solution

USGS Publications Warehouse

Kemblowski, M.

1985-01-01

The boundary-element method is used to solve the set of partial differential equations describing the flow of salt water and fresh water separated by a sharp interface in the vertical plane. In order to improve the accuracy and stability of the numerical solution, a new implicit scheme was developed for calculating the motion of the interface. The performance of this scheme was tested by means of numerical simulation. The numerical results are compared to experimental results for a salt-water upconing under a drain problem. ?? 1985.

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution. [rocket nozzle and orbital plume flow fields

NASA Technical Reports Server (NTRS)

Smith, S. D.

1984-01-01

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

Optimization of the Bridgman crystal growth process

NASA Astrophysics Data System (ADS)

Margulies, M.; Witomski, P.; Duffar, T.

2004-05-01

A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid-liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.

Re-Computation of Numerical Results Contained in NACA Report No. 496

NASA Technical Reports Server (NTRS)

Perry, Boyd, III

2015-01-01

An extensive examination of NACA Report No. 496 (NACA 496), "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen, is described. The examination included checking equations and solution methods and re-computing interim quantities and all numerical examples in NACA 496. The checks revealed that NACA 496 contains computational shortcuts (time- and effort-saving devices for engineers of the time) and clever artifices (employed in its solution methods), but, unfortunately, also contains numerous tripping points (aspects of NACA 496 that have the potential to cause confusion) and some errors. The re-computations were performed employing the methods and procedures described in NACA 496, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in fair-to-very-good agreement with the re-computed results. The exceptions included what are speculated to be computational errors in the original in some instances and transcription errors in the original in others. Independent flutter calculations were performed and, in all cases, including those where the original and re-computed results differed significantly, were in excellent agreement with the re-computed results. Appendix A contains NACA 496; Appendix B contains a Matlab(Reistered) program that performs the re-computation of results; Appendix C presents three alternate solution methods, with examples, for the two-degree-of-freedom solution method of NACA 496; Appendix D contains the three-degree-of-freedom solution method (outlined in NACA 496 but never implemented), with examples.

Computing the optimal path in stochastic dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

2016-08-15

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

An Extended Lagrangian Method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1995-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

A new numerical approximation of the fractal ordinary differential equation

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

PubMed Central

Cilfone, Nicholas A.; Kirschner, Denise E.; Linderman, Jennifer J.

2015-01-01

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level. PMID:26366228

Solving PDEs with Intrepid

DOE PAGES

Bochev, P.; Edwards, H. C.; Kirby, R. C.; ...

2012-01-01

Intrepid is a Trilinos package for advanced discretizations of Partial Differential Equations (PDEs). The package provides a comprehensive set of tools for local, cell-based construction of a wide range of numerical methods for PDEs. This paper describes the mathematical ideas and software design principles incorporated in the package. We also provide representative examples showcasing the use of Intrepid both in the context of numerical PDEs and the more general context of data analysis.

Subtractive procedure for calculating the anomalous electron magnetic moment in QED and its application for numerical calculation at the three-loop level

DOE Office of Scientific and Technical Information (OSTI.GOV)

Volkov, S. A., E-mail: volkoff-sergey@mail.ru

2016-06-15

A new subtractive procedure for canceling ultraviolet and infrared divergences in the Feynman integrals described here is developed for calculating QED corrections to the electron anomalous magnetic moment. The procedure formulated in the form of a forest expression with linear operators applied to Feynman amplitudes of UV-diverging subgraphs makes it possible to represent the contribution of each Feynman graph containing only electron and photon propagators in the form of a converging integral with respect to Feynman parameters. The application of the developed method for numerical calculation of two- and threeloop contributions is described.

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1992-01-01

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Study of stability of the difference scheme for the model problem of the gaslift process

NASA Astrophysics Data System (ADS)

Temirbekov, Nurlan; Turarov, Amankeldy

2017-09-01

The paper studies a model of the gaslift process where the motion in a gas-lift well is described by partial differential equations. The system describing the studied process consists of equations of motion, continuity, equations of thermodynamic state, and hydraulic resistance. A two-layer finite-difference Lax-Vendroff scheme is constructed for the numerical solution of the problem. The stability of the difference scheme for the model problem is investigated using the method of a priori estimates, the order of approximation is investigated, the algorithm for numerical implementation of the gaslift process model is given, and the graphs are presented. The development and investigation of difference schemes for the numerical solution of systems of equations of gas dynamics makes it possible to obtain simultaneously exact and monotonic solutions.

A general numerical model for wave rotor analysis

NASA Technical Reports Server (NTRS)

Paxson, Daniel W.

1992-01-01

Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved.

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Use of CFD modelling for analysing air parameters in auditorium halls

NASA Astrophysics Data System (ADS)

Cichowicz, Robert

2017-11-01

Modelling with the use of numerical methods is currently the most popular method of solving scientific as well as engineering problems. Thanks to the use of computer methods it is possible for example to comprehensively describe the conditions in a given room and to determine thermal comfort, which is a complex issue including subjective sensations of the persons in a given room. The article presents the results of measurements and numerical computing that enabled carrying out the assessment of environment parameters, taking into consideration microclimate, temperature comfort, speeds in the zone of human presence and dustiness in auditory halls. For this purpose measurements of temperature, relative humidity and dustiness were made with the use of a digital microclimate meter and a laser dust particles counter. Thanks to the above by using the application DesignBuilder numerical computing was performed and the obtained results enabled determining PMV comfort indicator in selected rooms.

Numerical and experimental study of expiratory flow in the case of major upper airway obstructions with fluid structure interaction

NASA Astrophysics Data System (ADS)

Chouly, F.; van Hirtum, A.; Lagrée, P.-Y.; Pelorson, X.; Payan, Y.

2008-02-01

This study deals with the numerical prediction and experimental description of the flow-induced deformation in a rapidly convergent divergent geometry which stands for a simplified tongue, in interaction with an expiratory airflow. An original in vitro experimental model is proposed, which allows measurement of the deformation of the artificial tongue, in condition of major initial airway obstruction. The experimental model accounts for asymmetries in geometry and tissue properties which are two major physiological upper airway characteristics. The numerical method for prediction of the fluid structure interaction is described. The theory of linear elasticity in small deformations has been chosen to compute the mechanical behaviour of the tongue. The main features of the flow are taken into account using a boundary layer theory. The overall numerical method entails finite element solving of the solid problem and finite differences solving of the fluid problem. First, the numerical method predicts the deformation of the tongue with an overall error of the order of 20%, which can be seen as a preliminary successful validation of the theory and simulations. Moreover, expiratory flow limitation is predicted in this configuration. As a result, both the physical and numerical models could be useful to understand this phenomenon reported in heavy snorers and apneic patients during sleep.

Spreadsheets in Science Teaching.

ERIC Educational Resources Information Center

Elliot, Chris

1988-01-01

Described is the use of a spreadsheet to model dynamic phenomena using numerical iterative methods. Uses the discharge of a capacitor, simple and damped harmonic motion, and the flow of heat along a bar as examples. (Author/CW)

Numerical Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1996-01-01

A numerical method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a Lagrangian particle tracking scheme, and the inter-phase momentum exchange is described by the Particle-In-Cell scheme. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.

Meshfree and efficient modeling of swimming cells

NASA Astrophysics Data System (ADS)

Gallagher, Meurig T.; Smith, David J.

2018-05-01

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab® or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

Numerical method of lines for the relaxational dynamics of nematic liquid crystals.

PubMed

Bhattacharjee, A K; Menon, Gautam I; Adhikari, R

2008-08-01

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase, and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic-nematic interface, illustrate the anisotropic character of droplets in the nucleation regime, and validate dynamical scaling in the coarsening regime.

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

A methodology for designing aircraft to low sonic boom constraints

NASA Technical Reports Server (NTRS)

Mack, Robert J.; Needleman, Kathy E.

1991-01-01

A method for designing conceptual supersonic cruise aircraft to meet low sonic boom requirements is outlined and described. The aircraft design is guided through a systematic evolution from initial three view drawing to a final numerical model description, while the designer using the method controls the integration of low sonic boom, high supersonic aerodynamic efficiency, adequate low speed handling, and reasonable structure and materials technologies. Some experience in preliminary aircraft design and in the use of various analytical and numerical codes is required for integrating the volume and lift requirements throughout the design process.

A numerical model for simulation of bioremediation of hydrocarbons in aquifers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, J.F.; Irarrazaval, M.J.

1998-03-01

A numerical model was developed to describe the bioremediation of hydrocarbons in ground water aquifers considering aerobic degradation. The model solves the independent transport of three solutes (oxygen, hydrocarbons, and microorganisms) in ground water flow using the method of characteristics. Interactions between the three solutes, in which oxygen and hydrocarbons are consumed by microorganisms, are represented by Monod kinetics, solved using a Runge-Kutta method. Model simulations showed good correlation as compared with results of soil column experiments. The model was used to estimate the time needed to remediate the columns, which varied from one to two years.

Error behavior of multistep methods applied to unstable differential systems

NASA Technical Reports Server (NTRS)

Brown, R. L.

1977-01-01

The problem of modeling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulas. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulas and two different stepsizes to illustrate the appropriateness of the criteria.

An Laudau-Lifschitz theory based algorithm on calculating post-buckling configuration of a rod buckling in elastic media

NASA Astrophysics Data System (ADS)

Huang, Shicheng; Tan, Likun; Hu, Nan; Grover, Hannah; Chu, Kevin; Chen, Zi

This reserach introduces a new numerical approach of calculating the post-buckling configuration of a thin rod embedded in elastic media. The theoretical base is the governing ODEs describing the balance of forces and moments, the length conservation, and the physics of bending and twisting by Laudau and Lifschitz. The numerical methods applied in the calculation are continuation method and Newton's method of iteration in combination with spectrum method. To the authors' knowledge, it is the first trial of directly applying the L-L theory to numerically studying the phenomenon of rod buckling in elastic medium. This method accounts for nonlinearity of geometry, thus is capable of calculating large deformation. The stability of this method is another advantage achieved by expressing the governing equations in a set of first-order derivative form. The wave length, amplitude, and decay effect all agree with the experiment without any further assumptions. This program can be applied to different occasions with varying stiffness of the elastic medai and rigidity of the rod.

Determination of plasma density from data on the ion current to cylindrical and planar probes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Voloshin, D. G., E-mail: dvoloshin@mics.msu.su; Vasil’eva, A. N.; Kovalev, A. S.

2016-12-15

To improve probe methods of plasma diagnostics, special probe measurements were performed and numerical models describing ion transport to a probe with allowance for collisions were developed. The current–voltage characteristics of cylindrical and planar probes were measured in an RF capacitive discharge in argon at a frequency of 81 MHz and plasma densities of 10{sup 10}–10{sup 11} cm{sup –3}, typical of modern RF reactors. 1D and 2D numerical models based on the particle-in-cell method with Monte Carlo collisions for simulating ion motion and the Boltzmann equilibrium for electrons are developed to describe current collection by a probe. The models weremore » used to find the plasma density from the ion part of the current–voltage characteristic, study the effect of ion collisions, and verify simplified approaches to determining the plasma density. A 1D hydrodynamic model of the ion current to a cylindrical probe with allowance for ion collisions is proposed. For a planar probe, a method to determine the plasma density from the averaged numerical results is developed. A comparative analysis of different approaches to calculating the plasma density from the ion current to a probe is performed.« less

Calculating Resonance Positions and Widths Using the Siegert Approximation Method

ERIC Educational Resources Information Center

Rapedius, Kevin

2011-01-01

Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…

Acceleration of boundary element method for linear elasticity

NASA Astrophysics Data System (ADS)

Zapletal, Jan; Merta, Michal; Čermák, Martin

2017-07-01

In this work we describe the accelerated assembly of system matrices for the boundary element method using the Intel Xeon Phi coprocessors. We present a model problem, provide a brief overview of its discretization and acceleration of the system matrices assembly using the coprocessors, and test the accelerated version using a numerical benchmark.

Managing Stress for College Success through Self-Hypnosis.

ERIC Educational Resources Information Center

Carrese, Marie A.

1998-01-01

Addresses the problem of stress and outlines the steps for self-hypnosis as an effective method of teaching inner-city college freshmen ways of coping with the pressures of higher education. The described method can be used in numerous settings with all populations. An appendix provides the Stress Identification and Evaluation Form. (Author/MKA)

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

NASA Technical Reports Server (NTRS)

Smith, R. L.; Huang, C.

1986-01-01

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.

Optimal interpolation and the Kalman filter. [for analysis of numerical weather predictions

NASA Technical Reports Server (NTRS)

Cohn, S.; Isaacson, E.; Ghil, M.

1981-01-01

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Peng; Barajas-Solano, David A.; Constantinescu, Emil

Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

PubMed

Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-02-01

Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Modelling the cancer growth process by Stochastic Differential Equations with the effect of Chondroitin Sulfate (CS) as anticancer therapeutics

NASA Astrophysics Data System (ADS)

Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina

2017-09-01

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

Fast multilevel radiative transfer

NASA Astrophysics Data System (ADS)

Paletou, Frédéric; Léger, Ludovick

2007-01-01

The vast majority of recent advances in the field of numerical radiative transfer relies on approximate operator methods better known in astrophysics as Accelerated Lambda-Iteration (ALI). A superior class of iterative schemes, in term of rates of convergence, such as Gauss-Seidel and Successive Overrelaxation methods were therefore quite naturally introduced in the field of radiative transfer by Trujillo Bueno & Fabiani Bendicho (1995); it was thoroughly described for the non-LTE two-level atom case. We describe hereafter in details how such methods can be generalized when dealing with non-LTE unpolarised radiation transfer with multilevel atomic models, in monodimensional geometry.

The numerical solution of ordinary differential equations by the Taylor series method

NASA Technical Reports Server (NTRS)

Silver, A. H.; Sullivan, E.

1973-01-01

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Aeroelastic analysis of bridge girder section using computer modeling

DOT National Transportation Integrated Search

2001-05-01

This report describes the numerical simulation of wind flow around bridges using the Finite Element Method (FEM) and the principles of Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD). Since, the suspension bridges are p...

A Most Rare Vision: Improvisations on "A Midsummer Night's Dream."

ERIC Educational Resources Information Center

Hakaim, Charles J., Jr.

1993-01-01

Describes one teacher's methods for introducing to secondary English students the concepts of improvisation, experimentation, and innovation. Discusses numerous techniques for fostering such skills when working with William Shakespeare's "A Midsummer Night's Dream." (HB)

SDF technology in location and navigation procedures: a survey of applications

NASA Astrophysics Data System (ADS)

Kelner, Jan M.; Ziółkowski, Cezary

2017-04-01

The basis for development the Doppler location method, also called the signal Doppler frequency (SDF) method or technology is the analytical solution of the wave equation for a mobile source. This paper presents an overview of the simulations, numerical analysis and empirical studies of the possibilities and the range of SDF method applications. In the paper, the various applications from numerous publications are collected and described. They mainly focus on the use of SDF method in: emitter positioning, electronic warfare, crisis management, search and rescue, navigation. The developed method is characterized by an innovative, unique property among other location methods, because it allows the simultaneous location of the many radio emitters. Moreover, this is the first method based on the Doppler effect, which allows positioning of transmitters, using a single mobile platform. In the paper, the results of the using SDF method by the other teams are also presented.

Numerical modeling of the strain of elastic rubber elements

NASA Astrophysics Data System (ADS)

Moskvichev, E. N.; Porokhin, A. V.; Shcherbakov, I. V.

2017-11-01

A comparative analysis of the results of experimental investigation of mechanical behavior of the rubber sample during biaxial compression testing and numerical simulation results obtained by the finite element method was carried out to determine the correctness of the model applied in the engineering calculations of elastic structural elements made of the rubber. The governing equation represents the five-parameter Mooney-Rivlin model with the constants determined from experimental data. The investigation results showed that these constants reliably describe the mechanical behavior of the material under consideration. The divergence of experimental and numerical results does not exceed 15%.

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Optimization methods and silicon solar cell numerical models

NASA Technical Reports Server (NTRS)

Girardini, K.; Jacobsen, S. E.

1986-01-01

An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

An efficient and guaranteed stable numerical method for continuous modeling of infiltration and redistribution with a shallow dynamic water table

NASA Astrophysics Data System (ADS)

Lai, Wencong; Ogden, Fred L.; Steinke, Robert C.; Talbot, Cary A.

2015-03-01

We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call "GARTO" can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a near-surface water table.

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

A hybrid method combining the surface integral equation method and ray tracing for the numerical simulation of high frequency diffraction involved in ultrasonic NDT

NASA Astrophysics Data System (ADS)

Bonnet, M.; Collino, F.; Demaldent, E.; Imperiale, A.; Pesudo, L.

2018-05-01

Ultrasonic Non-Destructive Testing (US NDT) has become widely used in various fields of applications to probe media. Exploiting the surface measurements of the ultrasonic incident waves echoes after their propagation through the medium, it allows to detect potential defects (cracks and inhomogeneities) and characterize the medium. The understanding and interpretation of those experimental measurements is performed with the help of numerical modeling and simulations. However, classical numerical methods can become computationally very expensive for the simulation of wave propagation in the high frequency regime. On the other hand, asymptotic techniques are better suited to model high frequency scattering over large distances but nevertheless do not allow accurate simulation of complex diffraction phenomena. Thus, neither numerical nor asymptotic methods can individually solve high frequency diffraction problems in large media, as those involved in UNDT controls, both quickly and accurately, but their advantages and limitations are complementary. Here we propose a hybrid strategy coupling the surface integral equation method and the ray tracing method to simulate high frequency diffraction under speed and accuracy constraints. This strategy is general and applicable to simulate diffraction phenomena in acoustic or elastodynamic media. We provide its implementation and investigate its performances for the 2D acoustic diffraction problem. The main features of this hybrid method are described and results of 2D computational experiments discussed.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

A method for experimental modal separation

NASA Technical Reports Server (NTRS)

Hallauer, W. L., Jr.

1977-01-01

A method is described for the numerical simulation of multiple-shaker modal survey testing using simulated experimental data to optimize the shaker force-amplitude distribution for the purpose of isolating individual modes of vibration. Inertia, damping, stiffness, and model data are stored on magnetic disks, available by direct access to the interactive FORTRAN programs which perform all computations required by this relative force amplitude distribution method.

Imposing the free-slip condition with a continuous forcing immersed boundary method

NASA Astrophysics Data System (ADS)

Kempe, Tobias; Lennartz, Matthias; Schwarz, Stephan; Fröhlich, Jochen

2015-02-01

The numerical simulation of spherical and ellipsoidal bubbles in purified fluids requires the imposition of the free-slip boundary condition at the bubble surface. This paper describes a numerical method for the implementation of free-slip boundary conditions in the context of immersed boundary methods. In contrast to other numerical approaches for multiphase flows, the realization is not straightforward. The reason is that the immersed boundary method treats the liquid as well as the gas phase as a field of constant density and viscosity with a fictitious fluid inside the bubble. The motion of the disperse phase is computed explicitly by solving the momentum balance for each of its elements and is coupled to the continuous phase via additional source terms in the Navier-Stokes equations. The paper starts with illustrating that an ad hoc method is unsuccessful. On this basis, a new method is proposed employing appropriate direct forcing at the bubble surface. A central finding is that with common ratios between the step size of the grid and the bubble diameter, curvature terms need to be accounted for to obtain satisfactory results. The new method is first developed for spherical objects and then extended to generally curved interfaces. This is done by introducing a local coordinate system which approximates the surface in the vicinity of a Lagrangian marker with the help of the two principal curvatures of the surface at this point. The numerical scheme is then validated for spherical and ellipsoidal objects with or without prescribed constant angular velocity. It is shown that the proposed method achieves similar convergence behavior as the method for no-slip boundaries. The results are compared to analytical solutions for creeping flow around a sphere and to numerical reference data obtained on a body-fitted grid. The numerical tests confirm the excellent performance of the proposed method.

A Review of Numerical Simulation and Analytical Modeling for Medical Devices Safety in MRI

PubMed Central

Kabil, J.; Belguerras, L.; Trattnig, S.; Pasquier, C.; Missoffe, A.

2016-01-01

Summary Objectives To review past and present challenges and ongoing trends in numerical simulation for MRI (Magnetic Resonance Imaging) safety evaluation of medical devices. Methods A wide literature review on numerical and analytical simulation on simple or complex medical devices in MRI electromagnetic fields shows the evolutions through time and a growing concern for MRI safety over the years. Major issues and achievements are described, as well as current trends and perspectives in this research field. Results Numerical simulation of medical devices is constantly evolving, supported by calculation methods now well-established. Implants with simple geometry can often be simulated in a computational human model, but one issue remaining today is the experimental validation of these human models. A great concern is to assess RF heating on implants too complex to be traditionally simulated, like pacemaker leads. Thus, ongoing researches focus on alternative hybrids methods, both numerical and experimental, with for example a transfer function method. For the static field and gradient fields, analytical models can be used for dimensioning simple implants shapes, but limited for complex geometries that cannot be studied with simplifying assumptions. Conclusions Numerical simulation is an essential tool for MRI safety testing of medical devices. The main issues remain the accuracy of simulations compared to real life and the studies of complex devices; but as the research field is constantly evolving, some promising ideas are now under investigation to take up the challenges. PMID:27830244

Investigation Study on Determination of Fracture Strain and Fractuer Forming Limit Curve Using Different Experimental and Numerical Methods

NASA Astrophysics Data System (ADS)

Farahnak, P.; Urbanek, M.; Džugan, J.

2017-09-01

Forming Limit Curve (FLC) is a well-known tool for the evaluation of failure in sheet metal process. However, its experimental determination and evaluation are rather complex. From theoretical point of view, FLC describes initiation of the instability not fracture. During the last years Digital Image Correlation (DIC) techniques have been developed extensively. Throughout this paper, all the measurements were done using DIC and as it is reported in the literature, different approaches to capture necking and fracture phenomena using Cross Section Method (CSM), Time dependent Method (TDM) and Thinning Method (TM) were investigated. Each aforementioned method has some advantages and disadvantages. Moreover, a cruciform specimen was used in order to cover whole FLC in the range between uniaxial to equi-biaxial tension and as an alternative for Nakajima test. Based on above-mentioned uncertainty about the fracture strain, some advanced numerical failure models can describe necking and fracture phenomena accurately with consideration of anisotropic effects. It is noticeable that in this paper, dog-bone, notch and circular disk specimens are used to calibrate Johnson-Cook (J-C) fracture model. The results are discussed for mild steel DC01.

The Numerical Simulation of Coupling Behavior of Soil with Chemical Pollutant Effects

NASA Astrophysics Data System (ADS)

Liu, Z. J.; Li, X. K.; Tang, L. Q.

2010-05-01

The coupling behavior of clay plays a role in the integrity of clay barriers used in landfills. The clay barriers are subjected to mechanical and thermal effects coupled with hydraulic behavior, also, if the leachates become in contact with the clay liner, chemical effects may lead to some drastic changes in the properties of the clay. A numerical method to simulate the coupling behavior of soil with chemical pollutant effects is presented. Within the framework of Gens-Alonso model describing the constitutive behavior of unsaturated clay presented in reference[1], basing on the work of Wu[2] and Hueckel[3], a constitutive model describing the chemo-thermo-hydro-mechanical(CTHM) coupling behavior of clays in contact with a single organic contaminant is presented. The thermical softening and chemical softening is considered in the presented model. The strain arising in the material due to chemical and thermical effects can be decomposed into two parts: elastic expansion and plastic compaction. The chemical effects are described in terms of the mass concentration of the contaminant. The increases in temperature and contaminant concentration cause decreases of the pre-consolidation pressure and the cohesion. The mechanisms are called thermical softening and chemical softening. The presented coupled CTHM constitutive model has been integrated into the coupled thermo-hydro-mechanical mathematical model including contaminant transport in porous media. To solve the equilibrium equations, the grogram of finite element methods is developed with a stagger algorithm. The mechanisms taking place due to the coupling behaviour of the clay with a single contaminant solute are analysed with the presented numerical method.

bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport

DOE PAGES

Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.

2015-06-25

We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« less

Benchmarking and Performance Measurement.

ERIC Educational Resources Information Center

Town, J. Stephen

This paper defines benchmarking and its relationship to quality management, describes a project which applied the technique in a library context, and explores the relationship between performance measurement and benchmarking. Numerous benchmarking methods contain similar elements: deciding what to benchmark; identifying partners; gathering…

An overview of methods for comparative effectiveness research.

PubMed

Meyer, Anne-Marie; Wheeler, Stephanie B; Weinberger, Morris; Chen, Ronald C; Carpenter, William R

2014-01-01

Comparative effectiveness research (CER) is a broad category of outcomes research encompassing many different methods employed by researchers and clinicians from numerous disciplines. The goal of cancer-focused CER is to generate new knowledge to assist cancer stakeholders in making informed decisions that will improve health care and outcomes of both individuals and populations. There are numerous CER methods that may be used to examine specific questions, including randomized controlled trials, observational studies, systematic literature reviews, and decision sciences modeling. Each has its strengths and weaknesses. To both inform and serve as a reference for readers of this issue of Seminars in Radiation Oncology as well as the broader oncology community, we describe CER and several of the more commonly used approaches and analytical methods. © 2013 Published by Elsevier Inc.

Application of the CSCM method to the design of wedge cavities. [Conservative Supra Characteristic Method

NASA Technical Reports Server (NTRS)

Venkatapathy, Ethiraj; Nystrom, G. A.; Bardina, J.; Lombard, C. K.

1987-01-01

This paper describes the application of the conservative supra characteristic method (CSCM) to predict the flow around two-dimensional slot injection cooled cavities in hypersonic flow. Seven different numerical solutions are presented that model three different experimental designs. The calculations manifest outer flow conditions including the effects of nozzle/lip geometry, angle of attack, nozzle inlet conditions, boundary and shear layer growth and turbulance on the surrounding flow. The calculations were performed for analysis prior to wind tunnel testing for sensitivity studies early in the design process. Qualitative and quantitative understanding of the flows for each of the cavity designs and design recommendations are provided. The present paper demonstrates the ability of numerical schemes, such as the CSCM method, to play a significant role in the design process.

Rapid calculation method for Frenkel-type two-exciton states in one to three dimensions

NASA Astrophysics Data System (ADS)

Ajiki, Hiroshi

2014-07-01

Biexciton and two-exciton dissociated states of Frenkel-type excitons are well described by a tight-binding model with a nearest-neighbor approximation. Such two-exciton states in a finite-size lattice are usually calculated by numerical diagonalization of the Hamiltonian, which requires an increasing amount of computational time and memory as the lattice size increases. I develop here a rapid, memory-saving method to calculate the energies and wave functions of two-exciton states by employing a bisection method. In addition, an attractive interaction between two excitons in the tight-binding model can be obtained directly so that the biexciton energy agrees with the observed energy, without the need for the trial-and-error procedure implemented in the numerical diagonalization method.

Numerical simulation of Bragg scattering of sound by surface roughness for different values of the Rayleigh parameter

NASA Astrophysics Data System (ADS)

Salin, M. B.; Dosaev, A. S.; Konkov, A. I.; Salin, B. M.

2014-07-01

Numerical simulation methods are described for the spectral characteristics of an acoustic signal scattered by multiscale surface waves. The methods include the algorithms for calculating the scattered field by the Kirchhoff method and with the use of an integral equation, as well as the algorithms of surface waves generation with allowance for nonlinear hydrodynamic effects. The paper focuses on studying the spectrum of Bragg scattering caused by surface waves whose frequency exceeds the fundamental low-frequency component of the surface waves by several octaves. The spectrum broadening of the backscattered signal is estimated. The possibility of extending the range of applicability of the computing method developed under small perturbation conditions to cases characterized by a Rayleigh parameter of ≥1 is estimated.

Modelling of non-equilibrium flow in the branched pipeline systems

NASA Astrophysics Data System (ADS)

Sumskoi, S. I.; Sverchkov, A. M.; Lisanov, M. V.; Egorov, A. F.

2016-09-01

This article presents a mathematical model and a numerical method for solving the task of water hammer in the branched pipeline system. The task is considered in the onedimensional non-stationary formulation taking into account the realities such as the change in the diameter of the pipeline and its branches. By comparison with the existing analytic solution it has been shown that the proposed method possesses good accuracy. With the help of the developed model and numerical method the task has been solved concerning the transmission of the compression waves complex in the branching pipeline system when several shut down valves operate. It should be noted that the offered model and method may be easily introduced to a number of other tasks, for example, to describe the flow of blood in the vessels.

Conservative discretization of the Landau collision integral

DOE PAGES

Hirvijoki, E.; Adams, M. F.

2017-03-28

Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

Dynamic Environmental Qualification Techniques.

DTIC Science & Technology

1981-12-01

environments peculiar to military operations and requirements. numerous dynamic qualification test methods have been established. It was the purpose...requires the achievement of the highest practicable degree in the standard- ization of items, materials and engineering practices within the...standard is described as "A document that established engineering and technical requirements for processes, pro’cedures, practices and methods that have

A Model for Engaging Students in a Research Experience Involving Variational Techniques, Mathematica, and Descent Methods.

ERIC Educational Resources Information Center

Mahavier, W. Ted

2002-01-01

Describes a two-semester numerical methods course that serves as a research experience for undergraduate students without requiring external funding or the modification of current curriculum. Uses an engineering problem to introduce students to constrained optimization via a variation of the traditional isoperimetric problem of finding the curve…

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

NASA Astrophysics Data System (ADS)

Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

NASA Astrophysics Data System (ADS)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Examination of two methods of describing the thermodynamic properties of oxygen near the critical point

NASA Technical Reports Server (NTRS)

Rees, T. H.; Suttles, J. T.

1972-01-01

A computer study was conducted to compare the numerical behavior of two approaches to describing the thermodynamic properties of oxygen near the critical point. Data on the relative differences between values of specific heats at constant pressure (sub p) density, and isotherm and isochor derivatives of the equation of state are presented for selected supercritical pressures at temperatures in the range 100 to 300 K. The results of a more detailed study of the sub p representations afforded by the two methods are also presented.

A new technique of laparoscopic cholangiography.

PubMed

Hagan, K D; Rosemurgy, A S; Albrink, M H; Carey, L C

1992-04-01

With the advent and rapid proliferation of laparoscopic cholecystectomy, numerous techniques and "tips" have been described. Intraoperative cholangiography during laparoscopic cholecystectomy can be tedious, frustrating, and time consuming. Described herein is a technique of intraoperative cholangiography during laparoscopic cholecystectomy which has proven to be easy, fast, and succinct. This method utilizes a rigid cholangiogram catheter which is placed into the peritoneal cavity through a small additional puncture site. This catheter is easily inserted into the cystic duct by extracorporeal manipulation. We suggest this method to surgeons who have shared our prior frustration with intraoperative cholangiography.

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

NASA Astrophysics Data System (ADS)

Abert, Claas; Exl, Lukas; Bruckner, Florian; Drews, André; Suess, Dieter

2013-11-01

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Vimmr, Jan; Bublík, Ondřej; Prausová, Helena; Hála, Jindřich; Pešek, Luděk

2018-06-01

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

TEMPEST: A three-dimensional time-dependent computer program for hydrothermal analysis: Volume 1, Numerical methods and input instructions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trent, D.S.; Eyler, L.L.; Budden, M.J.

This document describes the numerical methods, current capabilities, and the use of the TEMPEST (Version L, MOD 2) computer program. TEMPEST is a transient, three-dimensional, hydrothermal computer program that is designed to analyze a broad range of coupled fluid dynamic and heat transfer systems of particular interest to the Fast Breeder Reactor thermal-hydraulic design community. The full three-dimensional, time-dependent equations of motion, continuity, and heat transport are solved for either laminar or turbulent fluid flow, including heat diffusion and generation in both solid and liquid materials. 10 refs., 22 figs., 2 tabs.

Meta-synthesis of qualitative research: the challenges and opportunities.

PubMed

Mohammed, Mohammed A; Moles, Rebekah J; Chen, Timothy F

2016-06-01

Synthesis of qualitative studies is an emerging area that has been gaining more interest as an important source of evidence for improving health care policy and practice. In the last decade there have been numerous attempts to develop methods of aggregating and synthesizing qualitative data. Although numerous empirical qualitative studies have been published about different aspects of health care research, to date, the aggregation and syntheses of these data has not been commonly reported, particularly in pharmacy practice related research. This paper describes different methods of conducting meta-synthesis and provides an overview of selected common methods. The paper also emphasizes the challenges and opportunities associated with conducting meta-synthesis and highlights the importance of meta-synthesis in informing practice, policy and research.

Extension of transonic flow computational concepts in the analysis of cavitated bearings

NASA Technical Reports Server (NTRS)

Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

1990-01-01

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

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

PubMed

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.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1995-01-01

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

A sophisticated simulation for the fracture behavior of concrete material using XFEM

NASA Astrophysics Data System (ADS)

Zhai, Changhai; Wang, Xiaomin; Kong, Jingchang; Li, Shuang; Xie, Lili

2017-10-01

The development of a powerful numerical model to simulate the fracture behavior of concrete material has long been one of the dominant research areas in earthquake engineering. A reliable model should be able to adequately represent the discontinuous characteristics of cracks and simulate various failure behaviors under complicated loading conditions. In this paper, a numerical formulation, which incorporates a sophisticated rigid-plastic interface constitutive model coupling cohesion softening, contact, friction and shear dilatation into the XFEM, is proposed to describe various crack behaviors of concrete material. An effective numerical integration scheme for accurately assembling the contribution to the weak form on both sides of the discontinuity is introduced. The effectiveness of the proposed method has been assessed by simulating several well-known experimental tests. It is concluded that the numerical method can successfully capture the crack paths and accurately predict the fracture behavior of concrete structures. The influence of mode-II parameters on the mixed-mode fracture behavior is further investigated to better determine these parameters.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

NASA Astrophysics Data System (ADS)

Bartuccelli, Michele; Deane, Jonathan; Gentile, Guido

2017-08-01

We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is C^1 in the velocity. Such an ODE arises as a model of spin-orbit coupling in a star/planet system, and the motivation for devising a fast algorithm for its solution comes from the desire to estimate probability of capture in various solutions, via Monte Carlo simulation: the integration times are very long, since we are interested in phenomena occurring on timescales of the order of 10^6-10^7 years. The proposed algorithm is based on the high-order Euler method which was described in Bartuccelli et al. (Celest Mech Dyn Astron 121(3):233-260, 2015), and it requires computer algebra to set up the code for its implementation. The payoff is an overall increase in speed by a factor of about 7.5 compared to standard numerical methods. Means for accelerating the purely numerical computation are also discussed.

Nonlinear Schrödinger approach to European option pricing

NASA Astrophysics Data System (ADS)

Wróblewski, Marcin

2017-05-01

This paper deals with numerical option pricing methods based on a Schrödinger model rather than the Black-Scholes model. Nonlinear Schrödinger boundary value problems seem to be alternatives to linear models which better reflect the complexity and behavior of real markets. Therefore, based on the nonlinear Schrödinger option pricing model proposed in the literature, in this paper a model augmented by external atomic potentials is proposed and numerically tested. In terms of statistical physics the developed model describes the option in analogy to a pair of two identical quantum particles occupying the same state. The proposed model is used to price European call options on a stock index. the model is calibrated using the Levenberg-Marquardt algorithm based on market data. A Runge-Kutta method is used to solve the discretized boundary value problem numerically. Numerical results are provided and discussed. It seems that our proposal more accurately models phenomena observed in the real market than do linear models.

Numerical investigation of flow motion and performance of a horizontal axis tidal turbine subjected to a steady current

NASA Astrophysics Data System (ADS)

Li, Lin-juan; Zheng, Jin-hai; Peng, Yu-xuan; Zhang, Ji-sheng; Wu, Xiu-guang

2015-04-01

Horizontal axis tidal turbines have attracted more and more attentions nowadays, because of their convenience and low expense in construction and high efficiency in extracting tidal energy. The present study numerically investigates the flow motion and performance of a horizontal axis tidal turbine with a supporting vertical cylinder under steady current. In the numerical model, the continuous equation and incompressible Reynolds-averaged Navier-Stokes equations are solved, and the volume of fluid method is employed to track free surface motion. The RNG k- ɛ model is adopted to calculate turbulence transport while the fractional area/volume obstacle representation method is used to describe turbine characteristics and movement. The effects of installation elevation of tidal turbine and inlet velocity on the water elevation, and current velocity, rotating speed and resultant force on turbine are discussed. Based on the comparison of the numerical results, a better understanding of flow structure around horizontal axis tidal turbine and turbine performance is achieved.

The Better Mousetrap...Can Be Built by Engineers.

ERIC Educational Resources Information Center

McBride, Matthew

2003-01-01

Describes the growth of the INSPEC database developed by the Institution of Electrical Engineers. Highlights include an historical background of its growth from "Science Abstracts"; production methods, including computerization; indexing, including controlled (thesaurus-based), uncontrolled, chemical, and numerical indexing; and the…

A rating system for the esthetics of bridges.

DOT National Transportation Integrated Search

1980-01-01

There is a need for a tangible way to evaluate the esthetic or visual characteristics of bridges. This report describes such a method based on a numerical experiential rating scale of -10 to +10. Negative values represent unpleasurable responses; pos...

Nuclear radiation analysis

NASA Technical Reports Server (NTRS)

Knies, R. J.; Byrn, N. R.; Smith, H. T.

1972-01-01

A study program of radiation shielding against the deleterious effects of nuclear radiation on man and equipment is reported. The methods used to analyze the radiation environment from bremsstrahlung photons are discussed along with the methods employed by transport code users. The theory and numerical methods used to solve transport of neutrons and gammas are described, and the neutron and cosmic fluxes that would be present on the gamma-ray telescope were analyzed.

Structural optimization by multilevel decomposition

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.; James, B.; Dovi, A.

1983-01-01

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Quasi-static image-based immersed boundary-finite element model of left ventricle under diastolic loading

PubMed Central

Gao, Hao; Wang, Huiming; Berry, Colin; Luo, Xiaoyu; Griffith, Boyce E

2014-01-01

Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart. © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons, Ltd. PMID:24799090

Numerical simulation of dark envelope soliton in plasma

NASA Astrophysics Data System (ADS)

Wang, Fang-Ping; Han, Juan-fang; Zhang, Jie; Gao, Dong-Ning; Li, Zhong-Zheng; Duan, Wen-Shan; Zhang, Heng

2018-03-01

One-dimensional (1-D) particle-in-cell simulation is used to study the propagation of dark envelop solitons described by the nonlinear Schrödinger equation (NLSE) in electron-ion plasmas. The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the dark envelope soliton in plasma. It is demonstrated by our numerical simulation that there is dark envelope soliton in electron-ion plasmas. The numerical results are in good agreements with the analytical ones from the NLSE which is obtained from the reductive perturbation method. The limitation of the amplitude of dark envelop solitons in plasma is noticed.

Experimental and numerical study on the strength of all-ceramic crowns

NASA Astrophysics Data System (ADS)

Lu, Chenglin; Zhang, Xiuyin; Zhang, Dongsheng

2008-11-01

Two types of sectioned tooth-like ceramic crowns (IPS Empress 2) were prepared along lingual-facial direction and the fracture process of crowns under contact load was directly monitored with the use of imaging system. The displacement filed resulted from digital image correlation indicate that the fracture mode of real crown is more complicated while the flat crown has the same rupture mode as described by other investigators. Meanwhile numerical simulation was also carried out to support the experiments. Stress distributions in individual layer and interface were presented. Results indicate that the presented experimental and numerical methods are efficient in studying the fracture mechanism of all-ceramic crowns.

An analytical-numerical method for determining the mechanical response of a condenser microphone

PubMed Central

Homentcovschi, Dorel; Miles, Ronald N.

2011-01-01

The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone. PMID:22225026

An analytical-numerical method for determining the mechanical response of a condenser microphone.

PubMed

Homentcovschi, Dorel; Miles, Ronald N

2011-12-01

The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone. © 2011 Acoustical Society of America

Further studies using matched filter theory and stochastic simulation for gust loads prediction

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd Iii

1993-01-01

This paper describes two analysis methods -- one deterministic, the other stochastic -- for computing maximized and time-correlated gust loads for aircraft with nonlinear control systems. The first method is based on matched filter theory; the second is based on stochastic simulation. The paper summarizes the methods, discusses the selection of gust intensity for each method and presents numerical results. A strong similarity between the results from the two methods is seen to exist for both linear and nonlinear configurations.

Reconstructing gravitational wave source parameters via direct comparisons to numerical relativity II: Applications

NASA Astrophysics Data System (ADS)

O'Shaughnessy, Richard; Lange, Jacob; Healy, James; Carlos, Lousto; Shoemaker, Deirdre; Lovelace, Geoffrey; Scheel, Mark

2016-03-01

In this talk, we apply a procedure to reconstruct the parameters of sufficiently massive coalescing compact binaries via direct comparison with numerical relativity simulations. We illustrate how to use only comparisons between synthetic data and these simulations to reconstruct properties of a synthetic candidate source. We demonstrate using selected examples that we can reconstruct posterior distributions obtained by other Bayesian methods with our sparse grid. We describe how followup simulations can corroborate and improve our understanding of a candidate signal.

Numerical analysis of laser ablation using the axisymmetric two-temperature model

NASA Astrophysics Data System (ADS)

Dziatkiewicz, Jolanta; Majchrzak, Ewa

2018-01-01

Laser ablation of the axisymmetric micro-domain is analyzed. To describe the thermal processes occurring in the micro-domain the two-temperature hyperbolic model supplemented by the boundary and initial conditions is used. This model takes into account the phase changes of material (solid-liquid and liquid-vapour) and the ablation process. At the stage of numerical computations the finite difference method with staggered grid is used. In the final part the results of computations are shown.

Numerical Study on Electroosmotic Flow in Trapezoidal Microchannels

NASA Astrophysics Data System (ADS)

Zuo, C. C.; Ji, F.; Wang, L. F.

The analysis of electroosmotic flow mechanism in trapezoidal microchannels is performed in this work. The coupled Poisson-Boltzmann equation, Laplace equation, and modified Navier-Stokes equation are solved by finite volume method to describe distribution of electroosmotic flow. The detailed numerical results show that the salt concentration and applied electrical potential have great effects on the fundamental characteristics of elelctroosmotic flow. The most important finding is that the corner and wall effects in trapezoidal microchannels are stronger than those in rectangular microchannels.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Priimak, Dmitri

2014-12-01

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

Singularity computations

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1976-01-01

An approach is described for singularity computations based on a numerical method for elastoplastic flow to delineate radial and angular distribution of field quantities and measure the intensity of the singularity. The method is applicable to problems in solid mechanics and lends itself to certain types of heat flow and fluid motion studies. Its use is not limited to linear, elastic, small strain, or two-dimensional situations.

Determining the Viscosity of Liquids Using an Extended Falling Ball Method

ERIC Educational Resources Information Center

Houari, Ahmed

2011-01-01

In this article, I will extend the falling ball method to measure the viscosity of liquids regardless of the degree of their viscosity. For this, I will show that one can obtain a measurement of the terminal velocity of a falling spherical ball in a viscous liquid by solving numerically the equation of motion which describes the dynamics of the…

Third-order accurate conservative method on unstructured meshes for gasdynamic simulations

NASA Astrophysics Data System (ADS)

Shirobokov, D. A.

2017-04-01

A third-order accurate finite-volume method on unstructured meshes is proposed for solving viscous gasdynamic problems. The method is described as applied to the advection equation. The accuracy of the method is verified by computing the evolution of a vortex on meshes of various degrees of detail with variously shaped cells. Additionally, unsteady flows around a cylinder and a symmetric airfoil are computed. The numerical results are presented in the form of plots and tables.

Interpolation Method Needed for Numerical Uncertainty

NASA Technical Reports Server (NTRS)

Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

Direct and accelerated parameter mapping using the unscented Kalman filter.

PubMed

Zhao, Li; Feng, Xue; Meyer, Craig H

2016-05-01

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem. In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling. Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies. This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping. © 2015 Wiley Periodicals, Inc.

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

A Numerical Method of Calculating Propeller Noise Including Acoustic Nonlinear Effects

NASA Technical Reports Server (NTRS)

Korkan, K. D.

1985-01-01

Using the transonic flow fields(s) generated by the NASPROP-E computer code for an eight blade SR3-series propeller, a theoretical method is investigated to calculate the total noise values and frequency content in the acoustic near and far field without using the Ffowcs Williams - Hawkings equation. The flow field is numerically generated using an implicit three dimensional Euler equation solver in weak conservation law form. Numerical damping is required by the differencing method for stability in three dimensions, and the influence of the damping on the calculated acoustic values is investigated. The acoustic near field is solved by integrating with respect to time the pressure oscillations induced at a stationary observer location. The acoustic far field is calculated from the near field primitive variables as generated by NASPROP-E computer code using a method involving a perturbation velocity potential as suggested by Hawkings in the calculation of the acoustic pressure time-history at a specified far field observed location. the methodologies described are valid for calculating total noise levels and are applicable to any propeller geometry for which a flow field solution is available.

NMR spectroscopy for assessing lipid oxidation

USDA-ARS?s Scientific Manuscript database

Although lipid oxidation involves a variety of chemical reactions to produce numerous substances, most of traditional methods assessing lipid oxidation measure only one kind of oxidation product. For this reason, in general, one indicator of oxidation is not enough to accurately describe the oxidati...

Numerical Simulation of Delamination Growth in Composite Materials

NASA Technical Reports Server (NTRS)

Camanho, P. P.; Davila, C. G.; Ambur, D. R.

2001-01-01

The use of decohesion elements for the simulation of delamination in composite materials is reviewed. The test methods available to measure the interfacial fracture toughness used in the formulation of decohesion elements are described initially. After a brief presentation of the virtual crack closure technique, the technique most widely used to simulate delamination growth, the formulation of interfacial decohesion elements is described. Problems related with decohesion element constitutive equations, mixed-mode crack growth, element numerical integration and solution procedures are discussed. Based on these investigations, it is concluded that the use of interfacial decohesion elements is a promising technique that avoids the need for a pre-existing crack and pre-defined crack paths, and that these elements can be used to simulate both delamination onset and growth.

Computerized series solution of relativistic equations of motion.

NASA Technical Reports Server (NTRS)

Broucke, R.

1971-01-01

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

Proposal for a quantitative index of flood disasters.

PubMed

Feng, Lihua; Luo, Gaoyuan

2010-07-01

Drawing on calculations of wind scale and earthquake magnitude, this paper develops a new quantitative method for measuring flood magnitude and disaster intensity. Flood magnitude is the quantitative index that describes the scale of a flood; the flood's disaster intensity is the quantitative index describing the losses caused. Both indices have numerous theoretical and practical advantages with definable concepts and simple applications, which lend them key practical significance.

Studies of Low Luminosity Active Galactic Nuclei with Monte Carlo and Magnetohydrodynamic Simulations

NASA Astrophysics Data System (ADS)

Hilburn, Guy Louis

Results from several studies are presented which detail explorations of the physical and spectral properties of low luminosity active galactic nuclei. An initial Sagittarius A* general relativistic magnetohydrodynamic simulation and Monte Carlo radiation transport model suggests accretion rate changes as the dominant flaring method. A similar study on M87 introduces new methods to the Monte Carlo model for increased consistency in highly energetic sources. Again, accretion rate variation seems most appropriate to explain spectral transients. To more closely resolve the methods of particle energization in active galactic nuclei accretion disks, a series of localized shearing box simulations explores the effect of numerical resolution on the development of current sheets. A particular focus on numerically describing converged current sheet formation will provide new methods for consideration of turbulence in accretion disks.

Statistical analysis of loopy belief propagation in random fields

NASA Astrophysics Data System (ADS)

Yasuda, Muneki; Kataoka, Shun; Tanaka, Kazuyuki

2015-10-01

Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pairwise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

Method for taking into account hard-photon emission in four-fermion processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aleksejevs, A. G., E-mail: aaleksejevs@swgc.mun.ca; Barkanova, S. G., E-mail: svetlana.barkanova@acadiau.ca; Zykunov, V. A., E-mail: vladimir.zykunov@cern.ch

2016-01-15

A method for taking into account hard-photon emission in four-fermion processes proceeding in the s channel is described. The application of this method is exemplified by numerically estimating one-loop electroweak corrections to observables (cross sections and asymmetries) of the reaction e{sup −}e{sup +} → μ{sup −}μ{sup +}(γ) involving longitudinally polarized electrons and proceeding at energies below the Z-resonance energy.

Errors incurred in profile reconstruction and methods for increasing inversion accuracies for occultation type measurements

NASA Technical Reports Server (NTRS)

Gross, S. H.; Pirraglia, J. A.

1972-01-01

A method for augmenting the occultation experiment is described for slightly refractive media. This method which permits separation of the components of the gradient of refractivity, appears applicable to most of the planets for a major portion of their atmospheres and ionospheres. The analytic theory is given, and the results of numerical tests with a radially and angularly varying model of an ionosphere are discussed.

Numerical and experimental investigations on cavitation erosion

NASA Astrophysics Data System (ADS)

Fortes Patella, R.; Archer, A.; Flageul, C.

2012-11-01

A method is proposed to predict cavitation damage from cavitating flow simulations. For this purpose, a numerical process coupling cavitating flow simulations and erosion models was developed and applied to a two-dimensional (2D) hydrofoil tested at TUD (Darmstadt University of Technology, Germany) [1] and to a NACA 65012 tested at LMH-EPFL (Lausanne Polytechnic School) [2]. Cavitation erosion tests (pitting tests) were carried out and a 3D laser profilometry was used to analyze surfaces damaged by cavitation [3]. The method allows evaluating the pit characteristics, and mainly the volume damage rates. The paper describes the developed erosion model, the technique of cavitation damage measurement and presents some comparisons between experimental results and numerical damage predictions. The extent of cavitation erosion was correctly estimated in both hydrofoil geometries. The simulated qualitative influence of flow velocity, sigma value and gas content on cavitation damage agreed well with experimental observations.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

Cosmic reionization on computers. I. Design and calibration of simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gnedin, Nickolay Y., E-mail: gnedin@fnal.gov

Cosmic Reionization On Computers is a long-term program of numerical simulations of cosmic reionization. Its goal is to model fully self-consistently (albeit not necessarily from the first principles) all relevant physics, from radiative transfer to gas dynamics and star formation, in simulation volumes of up to 100 comoving Mpc, and with spatial resolution approaching 100 pc in physical units. In this method paper, we describe our numerical method, the design of simulations, and the calibration of numerical parameters. Using several sets (ensembles) of simulations in 20 h {sup –1} Mpc and 40 h {sup –1} Mpc boxes with spatial resolutionmore » reaching 125 pc at z = 6, we are able to match the observed galaxy UV luminosity functions at all redshifts between 6 and 10, as well as obtain reasonable agreement with the observational measurements of the Gunn-Peterson optical depth at z < 6.« less

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

NASA Astrophysics Data System (ADS)

Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

2018-02-01

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

Class and Home Problems. The Lambert W Function in Ultrafiltration and Diafiltration

ERIC Educational Resources Information Center

Foley, Greg

2016-01-01

Novel analytical solutions based on the Lambert W function for two problems in ultrafiltration and diafiltration are described. Example problems, suitable for incorporation into an introductory module in unit operations, membrane processing, or numerical methods are provided in each case.

Wireless Infrared Networking in the Duke Paperless Classroom.

ERIC Educational Resources Information Center

Stetten, George D.; Guthrie, Scott D.

1995-01-01

Discusses wireless (diffuse infrared) networking technology to link laptop computers in a computer programming and numerical methods course at Duke University (North Carolina). Describes products and technologies, and effects on classroom dynamics. Reports on effective instructional strategies for lecture, solving student problems, building shared…

Simulation of quasi-static hydraulic fracture propagation in porous media with XFEM

NASA Astrophysics Data System (ADS)

Juan-Lien Ramirez, Alina; Neuweiler, Insa; Löhnert, Stefan

2015-04-01

Hydraulic fracturing is the injection of a fracking fluid at high pressures into the underground. Its goal is to create and expand fracture networks to increase the rock permeability. It is a technique used, for example, for oil and gas recovery and for geothermal energy extraction, since higher rock permeability improves production. Many physical processes take place when it comes to fracking; rock deformation, fluid flow within the fractures, as well as into and through the porous rock. All these processes are strongly coupled, what makes its numerical simulation rather challenging. We present a 2D numerical model that simulates the hydraulic propagation of an embedded fracture quasi-statically in a poroelastic, fully saturated material. Fluid flow within the porous rock is described by Darcy's law and the flow within the fracture is approximated by a parallel plate model. Additionally, the effect of leak-off is taken into consideration. The solid component of the porous medium is assumed to be linear elastic and the propagation criteria are given by the energy release rate and the stress intensity factors [1]. The used numerical method for the spatial discretization is the eXtended Finite Element Method (XFEM) [2]. It is based on the standard Finite Element Method, but introduces additional degrees of freedom and enrichment functions to describe discontinuities locally in a system. Through them the geometry of the discontinuity (e.g. a fracture) becomes independent of the mesh allowing it to move freely through the domain without a mesh-adapting step. With this numerical model we are able to simulate hydraulic fracture propagation with different initial fracture geometries and material parameters. Results from these simulations will also be presented. References [1] D. Gross and T. Seelig. Fracture Mechanics with an Introduction to Micromechanics. Springer, 2nd edition, (2011) [2] T. Belytschko and T. Black. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Meth. Engng. 45, 601-620, (1999)

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

FASOR - A second generation shell of revolution code

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1978-01-01

An integrated computer program entitled Field Analysis of Shells of Revolution (FASOR) currently under development for NASA is described. When completed, this code will treat prebuckling, buckling, initial postbuckling and vibrations under axisymmetric static loads as well as linear response and bifurcation under asymmetric static loads. Although these modes of response are treated by existing programs, FASOR extends the class of problems treated to include general anisotropy and transverse shear deformations of stiffened laminated shells. At the same time, a primary goal is to develop a program which is free of the usual problems of modeling, numerical convergence and ill-conditioning, laborious problem setup, limitations on problem size and interpretation of output. The field method is briefly described, the shell differential equations are cast in a suitable form for solution by this method and essential aspects of the input format are presented. Numerical results are given for both unstiffened and stiffened anisotropic cylindrical shells and compared with previously published analytical solutions.

Modeling of nonequilibrium space plasma flows

NASA Technical Reports Server (NTRS)

Gombosi, Tamas

1995-01-01

Godunov-type numerical solution of the 20 moment plasma transport equations. One of the centerpieces of our proposal was the development of a higher order Godunov-type numerical scheme to solve the gyration dominated 20 moment transport equations. In the first step we explored some fundamental analytic properties of the 20 moment transport equations for a low b plasma, including the eigenvectors and eigenvalues of propagating disturbances. The eigenvalues correspond to wave speeds, while the eigenvectors characterize the transported physical quantities. In this paper we also explored the physically meaningful parameter range of the normalized heat flow components. In the second step a new Godunov scheme type numerical method was developed to solve the coupled set of 20 moment transport equations for a quasineutral single-ion plasma. The numerical method and the first results were presented at several national and international meetings and a paper describing the method has been published in the Journal of Computational Physics. To our knowledge this is the first numerical method which is capable of producing stable time-dependent solutions to the full 20 (or 16) moment set of transport equations, including the full heat flow equation. Previous attempts resulted in unstable (oscillating) solutions of the heat flow equations. Our group invested over two man-years into the development and implementation of the new method. The present model solves the 20 moment transport equations for an ion species and thermal electrons in 8 domain extending from a collision dominated to a collisionless region (200 km to 12,000 km). This model has been applied to study O+ acceleration due to Joule heating in the lower ionosphere.

A parallelization method for time periodic steady state in simulation of radio frequency sheath dynamics

NASA Astrophysics Data System (ADS)

Kwon, Deuk-Chul; Shin, Sung-Sik; Yu, Dong-Hun

2017-10-01

In order to reduce the computing time in simulation of radio frequency (rf) plasma sources, various numerical schemes were developed. It is well known that the upwind, exponential, and power-law schemes can efficiently overcome the limitation on the grid size for fluid transport simulations of high density plasma discharges. Also, the semi-implicit method is a well-known numerical scheme to overcome on the simulation time step. However, despite remarkable advances in numerical techniques and computing power over the last few decades, efficient multi-dimensional modeling of low temperature plasma discharges has remained a considerable challenge. In particular, there was a difficulty on parallelization in time for the time periodic steady state problems such as capacitively coupled plasma discharges and rf sheath dynamics because values of plasma parameters in previous time step are used to calculate new values each time step. Therefore, we present a parallelization method for the time periodic steady state problems by using period-slices. In order to evaluate the efficiency of the developed method, one-dimensional fluid simulations are conducted for describing rf sheath dynamics. The result shows that speedup can be achieved by using a multithreading method.

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

NASA Technical Reports Server (NTRS)

Pandya, Shishir A.; Venkateswaran, Sankaran; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)

2003-01-01

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Analysis and Correction of Diffraction Effect on the B/A Measurement at High Frequencies

NASA Astrophysics Data System (ADS)

Zhang, Dong; Gong, Xiu-Fen; Liu, Xiao-Zhou; Kushibiki, Jun-ichi; Nishino, Hideo

2004-01-01

A numerical method is developed to analyse and to correct the diffraction effect in the measurement of acoustic nonlinearity parameter B/A at high frequencies. By using the KZK nonlinear equation and the superposition approach of Gaussian beams, an analytical model is derived to describe the second harmonic generation through multi-layer medium SiO2/liquid specimen/SiO2. Frequency dependence of the nonlinear characterization curve for water in 110-155 MHz is numerically and experimentally investigated. With the measured dip position and the new model, values of B/A for water are evaluated. The results show that the present method can effectively correct the diffraction effect in the measurement.

Numerical Simulation of the Detonation of Condensed Explosives

NASA Astrophysics Data System (ADS)

Wang, Cheng; Ye, Ting; Ning, Jianguo

Detonation process of a condensed explosive was simulated using a finite difference method. Euler equations were applied to describe the detonation flow field, an ignition and growth model for the chemical reaction and Jones-Wilkins-Lee (JWL) equations of state for the state of explosives and detonation products. Based on the simple mixture rule that assumes the reacting explosives to be a mixture of the reactant and product components, 1D and 2D codes were developed to simulate the detonation process of high explosive PBX9404. The numerical results are in good agreement with the experimental results, which demonstrates that the finite difference method, mixture rule and chemical reaction proposed in this paper are adequate and feasible.

A 3D staggered-grid finite difference scheme for poroelastic wave equation

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai

2014-10-01

Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.

Predicting chaos in memristive oscillator via harmonic balance method.

PubMed

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Large-scale structural analysis: The structural analyst, the CSM Testbed and the NAS System

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.; Mccleary, Susan L.; Macy, Steven C.; Aminpour, Mohammad A.

1989-01-01

The Computational Structural Mechanics (CSM) activity is developing advanced structural analysis and computational methods that exploit high-performance computers. Methods are developed in the framework of the CSM testbed software system and applied to representative complex structural analysis problems from the aerospace industry. An overview of the CSM testbed methods development environment is presented and some numerical methods developed on a CRAY-2 are described. Selected application studies performed on the NAS CRAY-2 are also summarized.

Some observations on a new numerical method for solving Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Kumar, A.

1981-01-01

An explicit-implicit technique for solving Navier-Stokes equations is described which, is much less complex than other implicit methods. It is used to solve a complex, two-dimensional, steady-state, supersonic-flow problem. The computational efficiency of the method and the quality of the solution obtained from it at high Courant-Friedrich-Lewy (CFL) numbers are discussed. Modifications are discussed and certain observations are made about the method which may be helpful in using it successfully.

Simulating propagation of coherent light in random media using the Fredholm type integral equation

NASA Astrophysics Data System (ADS)

Kraszewski, Maciej; Pluciński, Jerzy

2017-06-01

Studying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g. Radiative Transfer Theory and Monte Carlo methods) but they do not treat coherence properties of light directly. Some variations of these methods allows to predict behavior of coherent light but only for an averaged realization of the scattering medium. This limits their application in studying many physical phenomena connected to a specific distribution of scattering particles (e.g. laser speckle). In general, numerical simulation of coherent light propagation in a specific realization of random medium is a time- and memory-consuming problem. The goal of the presented research was to develop new efficient method for solving this problem. The method, presented in our earlier works, is based on solving the Fredholm type integral equation, which describes multiple light scattering process. This equation can be discretized and solved numerically using various algorithms e.g. by direct solving the corresponding linear equations system, as well as by using iterative or Monte Carlo solvers. Here we present recent development of this method including its comparison with well-known analytical results and a finite-difference type simulations. We also present extension of the method for problems of multiple scattering of a polarized light on large spherical particles that joins presented mathematical formalism with Mie theory.

Resonance ionization for analytical spectroscopy

DOEpatents

Hurst, George S.; Payne, Marvin G.; Wagner, Edward B.

1976-01-01

This invention relates to a method for the sensitive and selective analysis of an atomic or molecular component of a gas. According to this method, the desired neutral component is ionized by one or more resonance photon absorptions, and the resultant ions are measured in a sensitive counter. Numerous energy pathways are described for accomplishing the ionization including the use of one or two tunable pulsed dye lasers.

New variational principles for locating periodic orbits of differential equations.

PubMed

Boghosian, Bruce M; Fazendeiro, Luis M; Lätt, Jonas; Tang, Hui; Coveney, Peter V

2011-06-13

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.

A recurrence matrix method for the analysis of longitudinal and torsional vibrations in non-uniform multibranch beams with variable boundary conditions

NASA Technical Reports Server (NTRS)

Davis, R. B.; Stephens, M. V.

1974-01-01

An approximate method for calculating the longitudinal and torsional natural frequencies and associated modal data of a beamlike, variable cross section multibranch structure is presented. The procedure described is the numerical integration of the first order differential equations that characterize the beam element in longitudinal motion and that satisfy the appropriate boundary conditions.

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2014-08-01

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also themore » stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.« less

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

A mathematical model for describing the mechanical behaviour of root canal instruments.

PubMed

Zhang, E W; Cheung, G S P; Zheng, Y F

2011-01-01

The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

Computer programs to assist in high resolution thermal denaturation and circular dichroism studies on nucleic acids

PubMed Central

Goodman, Thomas C.; Hardies, Stephen C.; Cortez, Carlos; Hillen, Wolfgang

1981-01-01

Computer programs are described that direct the collection, processing, and graphical display of numerical data obtained from high resolution thermal denaturation (1-3) and circular dichroism (4) studies. Besides these specific applications, the programs may also be useful, either directly or as programming models, in other types of spectrophotometric studies employing computers, programming languages, or instruments similar to those described here (see Materials and Methods). PMID:7335498

Implicit level set algorithms for modelling hydraulic fracture propagation.

PubMed

Peirce, A

2016-10-13

Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture 'tip screen-out'; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research. This article is part of the themed issue 'Energy and the subsurface'. © 2016 The Author(s).

Implicit level set algorithms for modelling hydraulic fracture propagation

PubMed Central

2016-01-01

Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture ‘tip screen-out’; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research.  This article is part of the themed issue ‘Energy and the subsurface’. PMID:27597787

A numerical investigation of premixed combustion in wave rotors

NASA Technical Reports Server (NTRS)

Nalim, M. Razi; Paxson, Daniel E.

1996-01-01

Wave rotor cycles which utilize premixed combustion processes within the passages are examined numerically using a one-dimensional CFD-based simulation. Internal-combustion wave rotors are envisioned for use as pressure-gain combustors in gas turbine engines. The simulation methodology is described, including a presentation of the assumed governing equations for the flow and reaction in the channels, the numerical integration method used, and the modeling of external components such as recirculation ducts. A number of cycle simulations are then presented which illustrate both turbulent-deflagration and detonation modes of combustion. Estimates of performance and rotor wall temperatures for the various cycles are made, and the advantages and disadvantages of each are discussed.

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

NASA Technical Reports Server (NTRS)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Colella, Phillip

2007-11-01

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.

Investigation of the feasibility of an analytical method of accounting for the effects of atmospheric drag on satellite motion

NASA Technical Reports Server (NTRS)

Bozeman, Robert E.

1987-01-01

An analytic technique for accounting for the joint effects of Earth oblateness and atmospheric drag on close-Earth satellites is investigated. The technique is analytic in the sense that explicit solutions to the Lagrange planetary equations are given; consequently, no numerical integrations are required in the solution process. The atmospheric density in the technique described is represented by a rotating spherical exponential model with superposed effects of the oblate atmosphere and the diurnal variations. A computer program implementing the process is discussed and sample output is compared with output from program NSEP (Numerical Satellite Ephemeris Program). NSEP uses a numerical integration technique to account for atmospheric drag effects.

A SIMPLE, EFFICIENT SOLUTION OF FLUX-PROFILE RELATIONSHIPS IN THE ATMOSPHERIC SURFACE LAYER

EPA Science Inventory

This note describes a simple scheme for analytical estimation of the surface layer similarity functions from state variables. What distinguishes this note from the many previous papers on this topic is that this method is specifically targeted for numerical models where simplici...

Digital pre-compensation techniques enabling high-capacity bandwidth variable transponders

NASA Astrophysics Data System (ADS)

Napoli, Antonio; Berenguer, Pablo Wilke; Rahman, Talha; Khanna, Ginni; Mezghanni, Mahdi M.; Gardian, Lennart; Riccardi, Emilio; Piat, Anna Chiadò; Calabrò, Stefano; Dris, Stefanos; Richter, André; Fischer, Johannes Karl; Sommerkorn-Krombholz, Bernd; Spinnler, Bernhard

2018-02-01

Digital pre-compensation techniques are among the enablers for cost-efficient high-capacity transponders. In this paper we describe various methods to mitigate the impairments introduced by state-of-the-art components within modern optical transceivers. Numerical and experimental results validate their performance and benefits.

Ultrastructural Study of Some Pollen Grains of Prairie Flowers

ERIC Educational Resources Information Center

Kozar, Frank

1973-01-01

Discusses the importance of the electron microscope, and in particular the scanning electron microscope, in studying the surface topography, sectional substructures, and patterns of development of pollen grains. The production, dispersal methods, and structure of pollen grains are described and illustrated with numerous electron micrographs. (JR)

Literacy Skills among Academically Underprepared Students

ERIC Educational Resources Information Center

Perin, Dolores

2013-01-01

A review of studies published from 2000 to 2012 was conducted to describe the literacy skills of underprepared postsecondary students, identify teaching approaches designed to bring their skills to the college level, and determine methods of embedding developmental instruction in college-level course work. The studies pinpointed numerous weak…

Numerical simulation of the processes in the normal incidence tube for high acoustic pressure levels

NASA Astrophysics Data System (ADS)

Fedotov, E. S.; Khramtsov, I. V.; Kustov, O. Yu.

2016-10-01

Numerical simulation of the acoustic processes in an impedance tube at high levels of acoustic pressure is a way to solve a problem of noise suppressing by liners. These studies used liner specimen that is one cylindrical Helmholtz resonator. The evaluation of the real and imaginary parts of the liner acoustic impedance and sound absorption coefficient was performed for sound pressure levels of 130, 140 and 150 dB. The numerical simulation used experimental data having been obtained on the impedance tube with normal incidence waves. At the first stage of the numerical simulation it was used the linearized Navier-Stokes equations, which describe well the imaginary part of the liner impedance whatever the sound pressure level. These equations were solved by finite element method in COMSOL Multiphysics program in axisymmetric formulation. At the second stage, the complete Navier-Stokes equations were solved by direct numerical simulation in ANSYS CFX in axisymmetric formulation. As the result, the acceptable agreement between numerical simulation and experiment was obtained.

Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling

NASA Astrophysics Data System (ADS)

Katsiolides, Grigoris; Müller, Eike H.; Scheichl, Robert; Shardlow, Tony; Giles, Michael B.; Thomson, David J.

2018-02-01

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations (SDEs). The computational bottleneck is the Monte Carlo algorithm, which simulates the motion of a large number of model particles in a turbulent velocity field; for each particle, a trajectory is calculated with a numerical timestepping method. Choosing an efficient numerical method is particularly important in operational emergency-response applications, such as tracking radioactive clouds from nuclear accidents or predicting the impact of volcanic ash clouds on international aviation, where accurate and timely predictions are essential. In this paper, we investigate the application of the Multilevel Monte Carlo (MLMC) method to simulate the propagation of particles in a representative one-dimensional dispersion scenario in the atmospheric boundary layer. MLMC can be shown to result in asymptotically superior computational complexity and reduced computational cost when compared to the Standard Monte Carlo (StMC) method, which is currently used in atmospheric dispersion modelling. To reduce the absolute cost of the method also in the non-asymptotic regime, it is equally important to choose the best possible numerical timestepping method on each level. To investigate this, we also compare the standard symplectic Euler method, which is used in many operational models, with two improved timestepping algorithms based on SDE splitting methods.

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Piecewise parabolic method for simulating one-dimensional shear shock wave propagation in tissue-mimicking phantoms

NASA Astrophysics Data System (ADS)

Tripathi, B. B.; Espíndola, D.; Pinton, G. F.

2017-11-01

The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.

Evaluation of methods for measuring relative permeability of anhydride from the Salado Formation: Sensitivity analysis and data reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christiansen, R.L.; Kalbus, J.S.; Howarth, S.M.

This report documents, demonstrates, evaluates, and provides theoretical justification for methods used to convert experimental data into relative permeability relationships. The report facilities accurate determination of relative permeabilities of anhydride rock samples from the Salado Formation at the Waste Isolation Pilot Plant (WIPP). Relative permeability characteristic curves are necessary for WIPP Performance Assessment (PA) predictions of the potential for flow of waste-generated gas from the repository and brine flow into repository. This report follows Christiansen and Howarth (1995), a comprehensive literature review of methods for measuring relative permeability. It focuses on unsteady-state experiments and describes five methods for obtaining relativemore » permeability relationships from unsteady-state experiments. Unsteady-state experimental methods were recommended for relative permeability measurements of low-permeability anhydrite rock samples form the Salado Formation because these tests produce accurate relative permeability information and take significantly less time to complete than steady-state tests. Five methods for obtaining relative permeability relationships from unsteady-state experiments are described: the Welge method, the Johnson-Bossler-Naumann method, the Jones-Roszelle method, the Ramakrishnan-Cappiello method, and the Hagoort method. A summary, an example of the calculations, and a theoretical justification are provided for each of the five methods. Displacements in porous media are numerically simulated for the calculation examples. The simulated product data were processed using the methods, and the relative permeabilities obtained were compared with those input to the numerical model. A variety of operating conditions were simulated to show sensitivity of production behavior to rock-fluid properties.« less

Efficient numerical method of freeform lens design for arbitrary irradiance shaping

NASA Astrophysics Data System (ADS)

Wojtanowski, Jacek

2018-05-01

A computational method to design a lens with a flat entrance surface and a freeform exit surface that can transform a collimated, generally non-uniform input beam into a beam with a desired irradiance distribution of arbitrary shape is presented. The methodology is based on non-linear elliptic partial differential equations, known as Monge-Ampère PDEs. This paper describes an original numerical algorithm to solve this problem by applying the Gauss-Seidel method with simplified boundary conditions. A joint MATLAB-ZEMAX environment is used to implement and verify the method. To prove the efficiency of the proposed approach, an exemplary study where the designed lens is faced with the challenging illumination task is shown. An analysis of solution stability, iteration-to-iteration ray mapping evolution (attached in video format), depth of focus and non-zero étendue efficiency is performed.

Optical Sensor/Actuator Locations for Active Structural Acoustic Control

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; Palumbo, Daniel L.; Kincaid, Rex K.

1998-01-01

Researchers at NASA Langley Research Center have extensive experience using active structural acoustic control (ASAC) for aircraft interior noise reduction. One aspect of ASAC involves the selection of optimum locations for microphone sensors and force actuators. This paper explains the importance of sensor/actuator selection, reviews optimization techniques, and summarizes experimental and numerical results. Three combinatorial optimization problems are described. Two involve the determination of the number and position of piezoelectric actuators, and the other involves the determination of the number and location of the sensors. For each case, a solution method is suggested, and typical results are examined. The first case, a simplified problem with simulated data, is used to illustrate the method. The second and third cases are more representative of the potential of the method and use measured data. The three case studies and laboratory test results establish the usefulness of the numerical methods.

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Faegri, Knut, Jr.; Taylor, Peter R.

1990-01-01

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

A Computational Procedure for Identifying Bilinear Representations of Nonlinear Systems Using Volterra Kernels

NASA Technical Reports Server (NTRS)

Kvaternik, Raymond G.; Silva, Walter A.

2008-01-01

A computational procedure for identifying the state-space matrices corresponding to discrete bilinear representations of nonlinear systems is presented. A key feature of the method is the use of first- and second-order Volterra kernels (first- and second-order pulse responses) to characterize the system. The present method is based on an extension of a continuous-time bilinear system identification procedure given in a 1971 paper by Bruni, di Pillo, and Koch. The analytical and computational considerations that underlie the original procedure and its extension to the title problem are presented and described, pertinent numerical considerations associated with the process are discussed, and results obtained from the application of the method to a variety of nonlinear problems from the literature are presented. The results of these exploratory numerical studies are decidedly promising and provide sufficient credibility for further examination of the applicability of the method.

Modeling and simulation of axisymmetric stagnation flames

NASA Astrophysics Data System (ADS)

Sone, Kazuo

Laminar flame modeling is an important element in turbulent combustion research. The accuracy of a turbulent combustion model is highly dependent upon our understanding of laminar flames and their behavior in many situations. How much we understand combustion can only be measured by how well the model describes and predicts combustion phenomena. One of the most commonly used methane combustion models is GRI-Mech 3.0. However, how well the model describes the reacting flow phenomena is still uncertain even after many attempts to validate the model or quantify uncertainties. In the present study, the behavior of laminar flames under different aerodynamic and thermodynamic conditions is studied numerically in a stagnation-flow configuration. In order to make such a numerical study possible, the spectral element method is reformulated to accommodate the large density variations in methane reacting flows. In addition, a new axisymmetric basis function set for the spectral element method that satisfies the correct behavior near the axis is developed, and efficient integration techniques are developed to accurately model axisymmetric reacting flow within a reasonable amount of computational time. The numerical method is implemented using an object-oriented programming technique, and the resulting computer program is verified with several different verification methods. The present study then shows variances with the commonly used GRI-Mech 3.0 chemical kinetics model through a direct simulation of laboratory flames that allows direct comparison to experimental data. It is shown that the methane combustion model based on GRI-Mech 3.0 works well for methane-air mixtures near stoichiometry. However, GRI-Mech 3.0 leads to an overprediction of laminar flame speed for lean mixtures and an underprediction for rich mixtures. This result is slightly different from conclusion drawn in previous work, in which experimental data are compared with a one-dimensional numerical solutions. Detailed analysis reveals that flame speed is sensitive to even slight flame front curvature as well as its finite extension in the radial direction. Neither of these can be incorporated in one-dimensional flow modeli

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohsuga, Ken; Takahashi, Hiroyuki R.

2016-02-20

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitlymore » solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.« less

A Constructive Mean-Field Analysis of Multi-Population Neural Networks with Random Synaptic Weights and Stochastic Inputs

PubMed Central

Faugeras, Olivier; Touboul, Jonathan; Cessac, Bruno

2008-01-01

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean-field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales. PMID:19255631

QED contributions to electron g-2

NASA Astrophysics Data System (ADS)

Laporta, Stefano

2018-05-01

In this paper I briefly describe the results of the numerical evaluation of the mass-independent 4-loop contribution to the electron g-2 in QED with 1100 digits of precision. In particular I also show the semi-analytical fit to the numerical value, which contains harmonic polylogarithms of eiπ/3, e2iπ/3 and eiπ/2 one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I give also some information about the methods and the program used.

Numerical Modeling in Problems of Near-Earth Object Dynamics

NASA Astrophysics Data System (ADS)

Aleksandrova, A. G.; Bordovitsyna, T. V.; Chuvashov, I. N.

2017-05-01

A method of numerical modeling is used to solve three most interesting problems of artificial Earth satellite (AES) dynamics. Orbital evolution of an ensemble of near-Earth objects at altitudes in the range from 1 500 to 60 000 km is considered, chaoticity of motion of objects in the geosynchronous zone is studied by the MEGNOanalysis, the parameters of AES motion are determined, and the models of forces are considered from measurements for GLONASS satellites. The recent versions of algorithms and programs used to perform investigations are briefly described.

Full velocity difference model for a car-following theory.

PubMed

Jiang, R; Wu, Q; Zhu, Z

2001-07-01

In this paper, we present a full velocity difference model for a car-following theory based on the previous models in the literature. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in car-following process than others. This point is verified by numerical simulation. Then we investigate the property of the model using both analytic and numerical methods, and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion.

Numerical simulation of two-dimensional Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Grigoriev, Vasiliy V.; Zakharov, Petr E.

2017-11-01

This paper considered Rayleigh-Benard convection (natural convection). This is a flow, which is formed in a viscous medium when heated from below and cooled from above. As a result, are formed vortices (convective cells). This process is described by a system of nonlinear differential equations in Oberbeck-Boussinesq approximation. As the governing parameters characterizing convection states Rayleigh number, Prandtl number are picked. The problem is solved by using finite element method with computational package FEniCS. Numerical results for different Rayleigh numbers are obtained. Studied integral characteristic (Nusselt number) depending on the Rayleigh number.

Active damping of modal vibrations by force apportioning

NASA Technical Reports Server (NTRS)

Hallauer, W. L., Jr.

1980-01-01

Force apportioning, a method of active structural damping based on that used in modal vibration testing of isolating modes by multiple shaker excitation, was analyzed and numerically simulated. A distribution of as few forces as possible on the structure is chosen so as to maximally affect selected vibration modes while minimally exciting all other modes. The accuracy of numerical simulations of active damping, active damping of higher-frequency modes, and studies of imperfection sensitivity are discussed. The computer programs developed are described and possible refinements of the research are examined.

Computational wave dynamics for innovative design of coastal structures

PubMed Central

GOTOH, Hitoshi; OKAYASU, Akio

2017-01-01

For innovative designs of coastal structures, Numerical Wave Flumes (NWFs), which are solvers of Navier-Stokes equation for free-surface flows, are key tools. In this article, various methods and techniques for NWFs are overviewed. In the former half, key techniques of NWFs, namely the interface capturing (MAC, VOF, C-CUP) and significance of NWFs in comparison with the conventional wave models are described. In the latter part of this article, recent improvements of the particle method are shown as one of cores of NWFs. Methods for attenuating unphysical pressure fluctuation and improving accuracy, such as CMPS method for momentum conservation, Higher-order Source of Poisson Pressure Equation (PPE), Higher-order Laplacian, Error-Compensating Source in PPE, and Gradient Correction for ensuring Taylor-series consistency, are reviewed briefly. Finally, the latest new frontier of the accurate particle method, including Dynamic Stabilization for providing minimum-required artificial repulsive force to improve stability of computation, and Space Potential Particle for describing the exact free-surface boundary condition, is described. PMID:29021506

A plane wave generation method by wave number domain point focusing.

PubMed

Chang, Ji-Ho; Choi, Jung-Woo; Kim, Yang-Hann

2010-11-01

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

NASA Astrophysics Data System (ADS)

Simmons, Daniel; Cools, Kristof; Sewell, Phillip

2016-11-01

Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications.

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simmons, Daniel, E-mail: daniel.simmons@nottingham.ac.uk; Cools, Kristof; Sewell, Phillip

Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removesmore » staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications. - Graphical abstract:.« less

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

NASA Technical Reports Server (NTRS)

Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.

1997-01-01

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Metallography of Aluminum and Its Alloys : Use of Electrolytic Polishing

NASA Technical Reports Server (NTRS)

Jacquet, Pierre A

1955-01-01

Recent methods are described for electropolishing aluminum and aluminum alloys. Numerous references are included of electrolytic micrographic investigations carried out during the period 1948 to 1952. A detailed description of a commercial electrolytic polishing unit, suitable for micrographic examination of aluminum and its alloys, is included.

Optimization of a new mathematical model for bacterial growth

USDA-ARS?s Scientific Manuscript database

The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...

Modeling population response to anthropogenic threats for a long-lived reptile, the desert tortoise

EPA Science Inventory

Background/Question/Methods The decline in desert tortoise population densities and abundances since the 1970s has been attributed to numerous threats, leading scientists, land managers, and conservationists to describe the plight of the species as a “death by a thousand cuts.” ...

Pythagoras' Canvas

ERIC Educational Resources Information Center

Musto, Garrod

2009-01-01

This article seeks to provide an insight into little known numerical methods for deriving meaning from ancient sacred texts to give an understanding of some of the symbolism contained in the wonderful artwork and sculptures of Venetian artist Tobia Rava. The author describes how he used Rava's artwork to inspire a multi-faceted mathematics…

Aerospace Materials and Process Technology Reinvestment Workshop Held in Dayton, Ohio on 18-19 May 1993.

DTIC Science & Technology

1993-05-19

The Laboratories Theory, Modeling and Simulation , • ATP Characterization J Education and Human Resources • MTC Facilities -- NBSR and CNRF MISSION...34 Automiated System for Composite Analysis (ASCA).Y -Basis for usefri(eadly numerical methods to describe composite laminates and predict ?heir response

Cambridge Crystallographic Data Centre. II. Structural Data File

ERIC Educational Resources Information Center

Allen, F. H.; And Others

1973-01-01

The Cambridge Crystallographic Data Centre is concerned with the retrieval, evaluation, synthesis, and dissemination of structural data obtained by diffraction methods. This article (Part I is EJ053033) describes the work of the center and deals with the organization and maintenance of a computerized file of numeric crystallographic structural…

Modeling of shock wave propagation in large amplitude ultrasound.

PubMed

Pinton, Gianmarco F; Trahey, Gregg E

2008-01-01

The Rankine-Hugoniot relation for shock wave propagation describes the shock speed of a nonlinear wave. This paper investigates time-domain numerical methods that solve the nonlinear parabolic wave equation, or the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and the conditions they require to satisfy the Rankine-Hugoniot relation. Two numerical methods commonly used in hyperbolic conservation laws are adapted to solve the KZK equation: Godunov's method and the monotonic upwind scheme for conservation laws (MUSCL). It is shown that they satisfy the Rankine-Hugoniot relation regardless of attenuation. These two methods are compared with the current implicit solution based method. When the attenuation is small, such as in water, the current method requires a degree of grid refinement that is computationally impractical. All three numerical methods are compared in simulations for lithotripters and high intensity focused ultrasound (HIFU) where the attenuation is small compared to the nonlinearity because much of the propagation occurs in water. The simulations are performed on grid sizes that are consistent with present-day computational resources but are not sufficiently refined for the current method to satisfy the Rankine-Hugoniot condition. It is shown that satisfying the Rankine-Hugoniot conditions has a significant impact on metrics relevant to lithotripsy (such as peak pressures) and HIFU (intensity). Because the Godunov and MUSCL schemes satisfy the Rankine-Hugoniot conditions on coarse grids, they are particularly advantageous for three-dimensional simulations.

An efficient numerical solution of the transient storage equations for solute transport in small streams

USGS Publications Warehouse

Runkel, Robert L.; Chapra, Steven C.

1993-01-01

Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.

Numerical heating in Particle-In-Cell simulations with Monte Carlo binary collisions

NASA Astrophysics Data System (ADS)

Alves, E. Paulo; Mori, Warren; Fiuza, Frederico

2017-10-01

The binary Monte Carlo collision (BMCC) algorithm is a robust and popular method to include Coulomb collision effects in Particle-in-Cell (PIC) simulations of plasmas. While a number of works have focused on extending the validity of the model to different physical regimes of temperature and density, little attention has been given to the fundamental coupling between PIC and BMCC algorithms. Here, we show that the coupling between PIC and BMCC algorithms can give rise to (nonphysical) numerical heating of the system, that can be far greater than that observed when these algorithms operate independently. This deleterious numerical heating effect can significantly impact the evolution of the simulated system particularly for long simulation times. In this work, we describe the source of this numerical heating, and derive scaling laws for the numerical heating rates based on the numerical parameters of PIC-BMCC simulations. We compare our theoretical scalings with PIC-BMCC numerical experiments, and discuss strategies to minimize this parasitic effect. This work is supported by DOE FES under FWP 100237 and 100182.

Study on longitudinal force simulation of heavy-haul train

NASA Astrophysics Data System (ADS)

Chang, Chongyi; Guo, Gang; Wang, Junbiao; Ma, Yingming

2017-04-01

The longitudinal dynamics model of heavy-haul trains and air brake model used in the longitudinal train dynamics (LTDs) are established. The dry friction damping hysteretic characteristic of steel friction draft gears is simulated by the equation which describes the suspension forces in truck leaf springs. The model of draft gears introduces dynamic loading force, viscous friction of steel friction and the damping force. Consequently, the numerical model of the draft gears is brought forward. The equation of LTDs is strongly non-linear. In order to solve the response of the strongly non-linear system, the high-precision and equilibrium iteration method based on the Newmark-β method is presented and numerical analysis is made. Longitudinal dynamic forces of the 20,000 tonnes heavy-haul train are tested, and models and solution method provided are verified by the test results.

Integral equation methods for vesicle electrohydrodynamics in three dimensions

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan

2016-12-01

In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor-Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.

An analytic-numerical method for the construction of the reference law of operation for a class of mechanical controlled systems

NASA Astrophysics Data System (ADS)

Mizhidon, A. D.; Mizhidon, K. A.

2017-04-01

An analytic-numerical method for the construction of a reference law of operation for a class of dynamic systems describing vibrations in controlled mechanical systems is proposed. By the reference law of operation of a system, we mean a law of the system motion that satisfies all the requirements for the quality and design features of the system under permanent external disturbances. As disturbances, we consider polyharmonic functions with known amplitudes and frequencies of the harmonics but unknown initial phases. For constructing the reference law of motion, an auxiliary optimal control problem is solved in which the cost function depends on a weighting coefficient. The choice of the weighting coefficient ensures the design of the reference law. Theoretical foundations of the proposed method are given.

Computational methods for yeast prion curing curves.

PubMed

Ridout, Martin S

2008-10-01

If the chemical guanidine hydrochloride is added to a dividing culture of yeast cells in which some of the protein Sup35p is in its prion form, the proportion of cells that carry replicating units of the prion, termed propagons, decreases gradually over time. Stochastic models to describe this process of 'curing' have been developed in earlier work. The present paper investigates the use of numerical methods of Laplace transform inversion to calculate curing curves and contrasts this with an alternative, more direct, approach that involves numerical integration. Transform inversion is found to provide a much more efficient computational approach that allows different models to be investigated with minimal programming effort. The method is used to investigate the robustness of the curing curve to changes in the assumed distribution of cell generation times. Matlab code is available for carrying out the calculations.

Optimization of droplets for UV-NIL using coarse-grain simulation of resist flow

NASA Astrophysics Data System (ADS)

Sirotkin, Vadim; Svintsov, Alexander; Zaitsev, Sergey

2009-03-01

A mathematical model and numerical method are described, which make it possible to simulate ultraviolet ("step and flash") nanoimprint lithography (UV-NIL) process adequately even using standard Personal Computers. The model is derived from 3D Navier-Stokes equations with the understanding that the resist motion is largely directed along the substrate surface and characterized by ultra-low values of the Reynolds number. By the numerical approximation of the model, a special finite difference method is applied (a coarse-grain method). A coarse-grain modeling tool for detailed analysis of resist spreading in UV-NIL at the structure-scale level is tested. The obtained results demonstrate the high ability of the tool to calculate optimal dispensing for given stamp design and process parameters. This dispensing provides uniform filled areas and a homogeneous residual layer thickness in UV-NIL.

Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

NASA Astrophysics Data System (ADS)

Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.

2018-01-01

This study focuses on a numerical investigation of an initial stable jet through the air-sealed electro-centrifugal spinning process, which is known as a viable method for the mass production of nanofibers. A liquid jet undergoing electric and centrifugal forces, as well as other forces, first travels in a stable trajectory and then goes through an unstable curled path to the collector. In numerical modeling, hydrodynamic equations have been solved using the perturbation method—and the boundary integral method has been implemented to efficiently solve the electric potential equation. Hydrodynamic equations have been coupled with the electric field using stress boundary conditions at the fluid-fluid interface. Perturbation equations were discretized by a second order finite difference method, and the Newton method was implemented to solve the discretized non-linear system. Also, the boundary element method was utilized to solve electrostatic equations. In the theoretical study, the fluid was described as a leaky dielectric with charges only on the surface of the jet traveling in dielectric air. The effect of the electric field induced around the nozzle tip on the jet instability and trajectory deviation was also experimentally studied through plate-plate geometry as well as point-plate geometry. It was numerically found that the centrifugal force prevails on electric force by increasing the rotational speed. Therefore, the alteration of the applied voltage does not significantly affect the jet thinning profile or the jet trajectory.

Use of the Fracture Continuum Model for Numerical Modeling of Flow and Transport of Deep Geologic Disposal of Nuclear Waste in Crystalline Rock

NASA Astrophysics Data System (ADS)

Hadgu, T.; Kalinina, E.; Klise, K. A.; Wang, Y.

2015-12-01

Numerical modeling of disposal of nuclear waste in a deep geologic repository in fractured crystalline rock requires robust characterization of fractures. Various methods for fracture representation in granitic rocks exist. In this study we used the fracture continuum model (FCM) to characterize fractured rock for use in the simulation of flow and transport in the far field of a generic nuclear waste repository located at 500 m depth. The FCM approach is a stochastic method that maps the permeability of discrete fractures onto a regular grid. The method generates permeability fields using field observations of fracture sets. The original method described in McKenna and Reeves (2005) was designed for vertical fractures. The method has since then been extended to incorporate fully three-dimensional representations of anisotropic permeability, multiple independent fracture sets, and arbitrary fracture dips and orientations, and spatial correlation (Kalinina et al. 20012, 2014). For this study the numerical code PFLOTRAN (Lichtner et al., 2015) has been used to model flow and transport. PFLOTRAN solves a system of generally nonlinear partial differential equations describing multiphase, multicomponent and multiscale reactive flow and transport in porous materials. The code is designed to run on massively parallel computing architectures as well as workstations and laptops (e.g. Hammond et al., 2011). Benchmark tests were conducted to simulate flow and transport in a specified model domain. Distributions of fracture parameters were used to generate a selected number of realizations. For each realization, the FCM method was used to generate a permeability field of the fractured rock. The PFLOTRAN code was then used to simulate flow and transport in the domain. Simulation results and analysis are presented. The results indicate that the FCM approach is a viable method to model fractured crystalline rocks. The FCM is a computationally efficient way to generate realistic representation of complex fracture systems. This approach is of interest for nuclear waste disposal models applied over large domains.

Steel Fibre Reinforced Concrete Simulation with the SPH Method

NASA Astrophysics Data System (ADS)

Hušek, Martin; Kala, Jiří; Král, Petr; Hokeš, Filip

2017-10-01

Steel fibre reinforced concrete (SFRC) is very popular in many branches of civil engineering. Thanks to its increased ductility, it is able to resist various types of loading. When designing a structure, the mechanical behaviour of SFRC can be described by currently available material models (with equivalent material for example) and therefore no problems arise with numerical simulations. But in many scenarios, e.g. high speed loading, it would be a mistake to use such an equivalent material. Physical modelling of the steel fibres used in concrete is usually problematic, though. It is necessary to consider the fact that mesh-based methods are very unsuitable for high-speed simulations with regard to the issues that occur due to the effect of excessive mesh deformation. So-called meshfree methods are much more suitable for this purpose. The Smoothed Particle Hydrodynamics (SPH) method is currently the best choice, thanks to its advantages. However, a numerical defect known as tensile instability may appear when the SPH method is used. It causes the development of numerical (false) cracks, making simulations of ductile types of failure significantly more difficult to perform. The contribution therefore deals with the description of a procedure for avoiding this defect and successfully simulating the behaviour of SFRC with the SPH method. The essence of the problem lies in the choice of coordinates and the description of the integration domain derived from them - spatial (Eulerian kernel) or material coordinates (Lagrangian kernel). The contribution describes the behaviour of both formulations. Conclusions are drawn from the fundamental tasks, and the contribution additionally demonstrates the functionality of SFRC simulations. The random generation of steel fibres and their inclusion in simulations are also discussed. The functionality of the method is supported by the results of pressure test simulations which compare various levels of fibre reinforcement of SFRC specimens.

An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

NASA Astrophysics Data System (ADS)

Karwas, Alex

Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach is capable of accurately simulating sailcraft motion. Sailcraft and spacecraft simulations are compared to flight data and to other numerical solution techniques. The new formulation shows an increase in accuracy over a widely used trajectory propagation technique. Simulations for two-dimensional, three-dimensional, and variable attitude trajectories are presented to show the multiple capabilities of the new technique. An element of optimal control is also part of the new technique. An additional equation is added to the sailcraft equations of motion that maximizes thrust in a specific direction. A technical description and results of an example optimization problem are presented. The spacecraft attitude dynamics equations take the simulation a step further by providing control torques using the angular rate and acceleration outputs of the numerical formulation.

Pricing index-based catastrophe bonds: Part 1: Formulation and discretization issues using a numerical PDE approach

NASA Astrophysics Data System (ADS)

Unger, André J. A.

2010-02-01

This work is the first installment in a two-part series, and focuses on the development of a numerical PDE approach to price components of a Bermudan-style callable catastrophe (CAT) bond. The bond is based on two underlying stochastic variables; the PCS index which posts quarterly estimates of industry-wide hurricane losses as well as a single-factor CIR interest rate model for the three-month LIBOR. The aggregate PCS index is analogous to losses claimed under traditional reinsurance in that it is used to specify a reinsurance layer. The proposed CAT bond model contains a Bermudan-style call feature designed to allow the reinsurer to minimize their interest rate risk exposure on making substantial fixed coupon payments using capital from the reinsurance premium. Numerical PDE methods are the fundamental strategy for pricing early-exercise constraints, such as the Bermudan-style call feature, into contingent claim models. Therefore, the objective and unique contribution of this first installment in the two-part series is to develop a formulation and discretization strategy for the proposed CAT bond model utilizing a numerical PDE approach. Object-oriented code design is fundamental to the numerical methods used to aggregate the PCS index, and implement the call feature. Therefore, object-oriented design issues that relate specifically to the development of a numerical PDE approach for the component of the proposed CAT bond model that depends on the PCS index and LIBOR are described here. Formulation, numerical methods and code design issues that relate to aggregating the PCS index and introducing the call option are the subject of the companion paper.

Indicators of Arctic Sea Ice Bistability in Climate Model Simulations and Observations

DTIC Science & Technology

2014-09-30

ultimately developed a novel mathematical method to solve the system of equations involving the addition of a numerical “ ghost ” layer, as described in the...balance models ( EBMs ) and (ii) seasonally-varying single-column models (SCMs). As described in Approach item #1, we developed an idealized model that...includes both latitudinal and seasonal variations (Fig. 1). The model reduces to a standard EBM or SCM as limiting cases in the parameter space, thus

Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse

NASA Astrophysics Data System (ADS)

Lusso, Christelle; Ern, Alexandre; Bouchut, François; Mangeney, Anne; Farin, Maxime; Roche, Olivier

2017-03-01

This work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. We consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2D setting with a free surface. We implement a regularization method to deal with the singularity of the rheological law, using a mixed finite element approximation of the momentum and incompressibility equations, and an arbitrary Lagrangian Eulerian (ALE) formulation for the displacement of the domain. The free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. Several tests are performed to assess the efficiency of our method. The first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. On this configuration we setup rules for the choice of the numerical parameters. The second test aims to compare the results of our numerical method to those predicted by an augmented Lagrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. Finally we show the reliability of our method by comparing numerical predictions to data from experiments of granular collapse of both trapezoidal and rectangular columns over horizontal rigid or erodible granular bed made of the same material. We compare the evolution of the free surface, the velocity profiles, and the static-flowing interface. The results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed.

Application of stochastic automata networks for creation of continuous time Markov chain models of voltage gating of gap junction channels.

PubMed

Snipas, Mindaugas; Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Paulauskas, Nerijus; Bukauskas, Feliksas F

2015-01-01

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ~20 times.

Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

NASA Astrophysics Data System (ADS)

Sun, Dihua; Chen, Dong; Zhao, Min; Liu, Weining; Zheng, Linjiang

2018-07-01

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

On approximation of non-Newtonian fluid flow by the finite element method

NASA Astrophysics Data System (ADS)

Svácek, Petr

2008-08-01

In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Semantic Information Processing of Physical Simulation Based on Scientific Concept Vocabulary Model

NASA Astrophysics Data System (ADS)

Kino, Chiaki; Suzuki, Yoshio; Takemiya, Hiroshi

Scientific Concept Vocabulary (SCV) has been developed to actualize Cognitive methodology based Data Analysis System: CDAS which supports researchers to analyze large scale data efficiently and comprehensively. SCV is an information model for processing semantic information for physics and engineering. In the model of SCV, all semantic information is related to substantial data and algorisms. Consequently, SCV enables a data analysis system to recognize the meaning of execution results output from a numerical simulation. This method has allowed a data analysis system to extract important information from a scientific view point. Previous research has shown that SCV is able to describe simple scientific indices and scientific perceptions. However, it is difficult to describe complex scientific perceptions by currently-proposed SCV. In this paper, a new data structure for SCV has been proposed in order to describe scientific perceptions in more detail. Additionally, the prototype of the new model has been constructed and applied to actual data of numerical simulation. The result means that the new SCV is able to describe more complex scientific perceptions.

Harmony search method: theory and applications.

PubMed

Gao, X Z; Govindasamy, V; Xu, H; Wang, X; Zenger, K

2015-01-01

The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem.

On the convergence of a discrete Kirchhoff triangle method valid for shells of arbitrary shape

NASA Astrophysics Data System (ADS)

Bernadou, Michel; Eiroa, Pilar Mato; Trouve, Pascal

1994-10-01

In a recent paper by the same authors, we have thoroughly described how to extend to the case of general shells the well known DKT (discrete Kirchhoff triangle) methods which are now classically used to solve plate problems. In that paper we have also detailed how to realize the implementation and reported some numerical results obtained for classical benchmarks. The aim of this paper is to prove the convergence of a closely related method and to obtain corresponding error estimates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Larsen, E.W.

A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Nonideal isentropic gas flow through converging-diverging nozzles

NASA Technical Reports Server (NTRS)

Bober, W.; Chow, W. L.

1990-01-01

A method for treating nonideal gas flows through converging-diverging nozzles is described. The method incorporates the Redlich-Kwong equation of state. The Runge-Kutta method is used to obtain a solution. Numerical results were obtained for methane gas. Typical plots of pressure, temperature, and area ratios as functions of Mach number are given. From the plots, it can be seen that there exists a range of reservoir conditions that require the gas to be treated as nonideal if an accurate solution is to be obtained.

Dynamic Rod Worth Measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chao, Y.A.; Chapman, D.M.; Hill, D.J.

2000-12-15

The dynamic rod worth measurement (DRWM) technique is a method of quickly validating the predicted bank worth of control rods and shutdown rods. The DRWM analytic method is based on three-dimensional, space-time kinetic simulations of the rapid rod movements. Its measurement data is processed with an advanced digital reactivity computer. DRWM has been used as the method of bank worth validation at numerous plant startups with excellent results. The process and methodology of DRWM are described, and the measurement results of using DRWM are presented.

Prediction of overall and blade-element performance for axial-flow pump configurations

NASA Technical Reports Server (NTRS)

Serovy, G. K.; Kavanagh, P.; Okiishi, T. H.; Miller, M. J.

1973-01-01

A method and a digital computer program for prediction of the distributions of fluid velocity and properties in axial flow pump configurations are described and evaluated. The method uses the blade-element flow model and an iterative numerical solution of the radial equilbrium and continuity conditions. Correlated experimental results are used to generate alternative methods for estimating blade-element turning and loss characteristics. Detailed descriptions of the computer program are included, with example input and typical computed results.

UQTk Version 3.0.3 User Manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sargsyan, Khachik; Safta, Cosmin; Chowdhary, Kamaljit Singh

2017-05-01

The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.3 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sen- sitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

A high-throughput microtiter plate based method for the determination of peracetic acid and hydrogen peroxide.

PubMed

Putt, Karson S; Pugh, Randall B

2013-01-01

Peracetic acid is gaining usage in numerous industries who have found a myriad of uses for its antimicrobial activity. However, rapid high throughput quantitation methods for peracetic acid and hydrogen peroxide are lacking. Herein, we describe the development of a high-throughput microtiter plate based assay based upon the well known and trusted titration chemical reactions. The adaptation of these titration chemistries to rapid plate based absorbance methods for the sequential determination of hydrogen peroxide specifically and the total amount of peroxides present in solution are described. The results of these methods were compared to those of a standard titration and found to be in good agreement. Additionally, the utility of the developed method is demonstrated through the generation of degradation curves of both peracetic acid and hydrogen peroxide in a mixed solution.

A High-Throughput Microtiter Plate Based Method for the Determination of Peracetic Acid and Hydrogen Peroxide

PubMed Central

Putt, Karson S.; Pugh, Randall B.

2013-01-01

Peracetic acid is gaining usage in numerous industries who have found a myriad of uses for its antimicrobial activity. However, rapid high throughput quantitation methods for peracetic acid and hydrogen peroxide are lacking. Herein, we describe the development of a high-throughput microtiter plate based assay based upon the well known and trusted titration chemical reactions. The adaptation of these titration chemistries to rapid plate based absorbance methods for the sequential determination of hydrogen peroxide specifically and the total amount of peroxides present in solution are described. The results of these methods were compared to those of a standard titration and found to be in good agreement. Additionally, the utility of the developed method is demonstrated through the generation of degradation curves of both peracetic acid and hydrogen peroxide in a mixed solution. PMID:24260173

Tradeoff studies in multiobjective insensitive design of airplane control systems

NASA Technical Reports Server (NTRS)

Schy, A. A.; Giesy, D. P.

1983-01-01

A computer aided design method for multiobjective parameter-insensitive design of airplane control systems is described. Methods are presented for trading off nominal values of design objectives against sensitivities of the design objectives to parameter uncertainties, together with guidelines for designer utilization of the methods. The methods are illustrated by application to the design of a lateral stability augmentation system for two supersonic flight conditions of the Shuttle Orbiter. Objective functions are conventional handling quality measures and peak magnitudes of control deflections and rates. The uncertain parameters are assumed Gaussian, and numerical approximations of the stochastic behavior of the objectives are described. Results of applying the tradeoff methods to this example show that stochastic-insensitive designs are distinctly different from deterministic multiobjective designs. The main penalty for achieving significant decrease in sensitivity is decreased speed of response for the nominal system.

A Cartesian Adaptive Level Set Method for Two-Phase Flows

NASA Technical Reports Server (NTRS)

Ham, F.; Young, Y.-N.

2003-01-01

In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.

Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leblond, Herve; Kremer, David; Mihalache, Dumitru

2010-03-15

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.

Where Words Fail, Music Speaks: A Mixed Method Study of an Evidence-Based Music Protocol.

PubMed

Daniels, Ruby A; Torres, David; Reeser, Cathy

2016-01-01

Despite numerous studies documenting the benefits of music, hospice social workers are often unfamiliar with evidence-based music practices that may improve end of life care. This mixed method study tested an intervention to teach hospice social workers and chaplains (N = 10) an evidence-based music protocol. Participants used the evidence-based practice (EBP) for 30 days, recording 226 journal entries that described observations of 84 patients and their families. There was a significant increase in EBP knowledge (35%). Prompting behavioral and emotional responses, music was described frequently as a catalyst that facilitated deeper dialogue between patients, families, social workers, and chaplains.

New Software Developments for Quality Mesh Generation and Optimization from Biomedical Imaging Data

PubMed Central

Yu, Zeyun; Wang, Jun; Gao, Zhanheng; Xu, Ming; Hoshijima, Masahiko

2013-01-01

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit. PMID:24252469

RT DDA: A hybrid method for predicting the scattering properties by densely packed media

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D.

2017-12-01

The most accurate approaches to predicting the scattering properties of particulate media are based on exact solutions of the Maxwell's equations (MEs), such as the T-matrix and discrete dipole methods. Applying these techniques for optically thick targets is challenging problem due to the large-scale computations and are usually substituted by phenomenological radiative transfer (RT) methods. On the other hand, the RT technique is of questionable validity in media with large particle packing densities. In recent works, we used numerically exact ME solvers to examine the effects of particle concentration on the polarized reflection properties of plane parallel random media. The simulations were performed for plane parallel layers of wavelength-sized spherical particles, and results were compared with RT predictions. We have shown that RTE results monotonically converge to the exact solution as the particle volume fraction becomes smaller and one can observe a nearly perfect fit for packing densities of 2%-5%. This study describes the hybrid technique composed of exact and numerical scalar RT methods. The exact methodology in this work is the plane parallel discrete dipole approximation whereas the numerical method is based on the adding and doubling method. This approach not only decreases the computational time owing to the RT method but also includes the interference and multiple scattering effects, so it may be applicable to large particle density conditions.

An exploratory study of a finite difference method for calculating unsteady transonic potential flow

NASA Technical Reports Server (NTRS)

Bennett, R. M.; Bland, S. R.

1979-01-01

A method for calculating transonic flow over steady and oscillating airfoils was developed by Isogai. The full potential equation is solved with a semi-implicit, time-marching, finite difference technique. Steady flow solutions are obtained from time asymptotic solutions for a steady airfoil. Corresponding oscillatory solutions are obtained by initiating an oscillation and marching in time for several cycles until a converged periodic solution is achieved. The method is described in general terms and results for the case of an airfoil with an oscillating flap are presented for Mach numbers 0.500 and 0.875. Although satisfactory results are obtained for some reduced frequencies, it is found that the numerical technique generates spurious oscillations in the indicial response functions and in the variation of the aerodynamic coefficients with reduced frequency. These oscillations are examined with a dynamic data reduction method to evaluate their effects and trends with reduced frequency and Mach number. Further development of the numerical method is needed to eliminate these oscillations.

Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

NASA Astrophysics Data System (ADS)

Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

2016-11-01

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

Continuous spectra of atomic hydrogen in a strong magnetic field

NASA Astrophysics Data System (ADS)

Zhao, L. B.; Zatsarinny, O.; Bartschat, K.

2016-09-01

We describe a theoretical method, developed in the coupled-channel formalism, to study photoionization of H atoms in a strong magnetic field of a size that is typical for magnetic white dwarfs. The coupled Schrödinger equations are solved numerically using the renormalized Numerov method proposed by Johnson [B. R. Johnson, J. Chem. Phys. 67, 4086 (1977), 10.1063/1.435384; B. R. Johnson, J. Chem. Phys. 69, 4678 (1978), 10.1063/1.436421]. The distinct advantage of this method is the fact that no overflow problems are encountered in the classically forbidden region, and hence the method exhibits excellent numerical stability. Photoionization cross sections are presented for magnetized H atoms in the ground and 2 p excited states. The calculated results are compared with those obtained by other theories. The present method is particularly useful for explaining the complex features of continuous spectra in a strong magnetic field and hence provides an efficient tool for modeling photoionization spectra observed in the atmosphere of magnetic white dwarfs.

A Fast and Accurate Method of Radiation Hydrodynamics Calculation in Spherical Symmetry

NASA Astrophysics Data System (ADS)

Stamer, Torsten; Inutsuka, Shu-ichiro

2018-06-01

We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation, and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.

A SCILAB Program for Computing General-Relativistic Models of Rotating Neutron Stars by Implementing Hartle's Perturbation Method

NASA Astrophysics Data System (ADS)

Papasotiriou, P. J.; Geroyannis, V. S.

We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

Interpolation Method Needed for Numerical Uncertainty Analysis of Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Groves, Curtis; Ilie, Marcel; Schallhorn, Paul

2014-01-01

Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors in an unstructured grid, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors. Nomenclature

Hybrid transfer-matrix FDTD method for layered periodic structures.

PubMed

Deinega, Alexei; Belousov, Sergei; Valuev, Ilya

2009-03-15

A hybrid transfer-matrix finite-difference time-domain (FDTD) method is proposed for modeling the optical properties of finite-width planar periodic structures. This method can also be applied for calculation of the photonic bands in infinite photonic crystals. We describe the procedure of evaluating the transfer-matrix elements by a special numerical FDTD simulation. The accuracy of the new method is tested by comparing computed transmission spectra of a 32-layered photonic crystal composed of spherical or ellipsoidal scatterers with the results of direct FDTD and layer-multiple-scattering calculations.

Efficient harvesting methods for early-stage snake and turtle embryos.

PubMed

Matsubara, Yoshiyuki; Kuroiwa, Atsushi; Suzuki, Takayuki

2016-04-01

Reptile development is an intriguing research target for understating the unique morphogenesis of reptiles as well as the evolution of vertebrates. However, there are numerous difficulties associated with studying development in reptiles. The number of available reptile eggs is usually quite limited. In addition, the reptile embryo is tightly adhered to the eggshell, making it a challenge to isolate reptile embryos intact. Furthermore, there have been few reports describing efficient procedures for isolating intact embryos especially prior to pharyngula stage. Thus, the aim of this review is to present efficient procedures for obtaining early-stage reptilian embryos intact. We first describe the method for isolating early-stage embryos of the Japanese striped snake. This is the first detailed method for obtaining embryos prior to oviposition in oviparous snake species. Second, we describe an efficient strategy for isolating early-stage embryos of the soft-shelled turtle. © 2016 Japanese Society of Developmental Biologists.

Reverse Transcription Quantitative Polymerase Chain Reaction for Detection of and Differentiation Between RNA and DNA of HIV-1-Based Lentiviral Vectors.

PubMed

Pavlovic, Melanie; Koehler, Nina; Anton, Martina; Dinkelmeier, Anna; Haase, Maren; Stellberger, Thorsten; Busch, Ulrich; Baiker, Armin E

2017-08-01

The purpose of the described method is the detection of and differentiation between RNA and DNA of human immunodeficiency virus (HIV)-derived lentiviral vectors (LV) in cell culture supernatants and swab samples. For the analytical surveillance of genetic engineering, operations methods for the detection of the HIV-1-based LV generations are required. Furthermore, for research issues, it is important to prove the absence of LV particles for downgrading experimental settings in terms of the biosafety level. Here, a quantitative polymerase chain reaction method targeting the long terminal repeat U5 subunit and the start sequence of the packaging signal ψ is described. Numerous controls are included in order to monitor the technical procedure.

Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kudryashov, Nikolay A.; Shilnikov, Kirill E.

Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumormore » tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.« less

Numerical approach to describe complementary drying of banana slices osmotically dehydrated

NASA Astrophysics Data System (ADS)

da Silva Júnior, Aluízio Freire; da Silva, Wilton Pereira; de Farias Aires, Juarez Everton; Farias Aires, Kalina Lígia C. A.

2018-02-01

In this work, diffusion model was used to describe the water loss in the complementary drying process of cylindrical slices of banana pretreated by osmotic dehydration. A numerical solution has been proposed for the diffusion equation in cylindrical coordinates, which was obtained through the Finite Volume Method. The diffusion equation was discretized assuming that the effective water diffusivity and the dimensions of a finite cylinder may vary; also considering the boundary condition of the third kind. The banana slices were cut in length of about 1.00 cm and average radius 1.70 cm before osmotic pretreatment, and completed the pretreatment with length of about 0.74 cm and average radius 1.40 cm. The complementary drying was carried out in a kiln with circulation and air exchange. Drying temperatures were the same as used in the osmotic pretreatment (40 to 70 °C). The proposed model described well the water loss, with good statistical indicators for all fits.

Determination of the Ephemeris Accuracy for AJISAI, LAGEOS and ETALON Satellites, Obtained with A Simplified Numerical Motion Model Using the ILRS Coordinates

NASA Astrophysics Data System (ADS)

Kara, I. V.

This paper describes a simplified numerical model of passive artificial Earth satellite (AES) motion. The model accuracy is determined using the International Laser Ranging Service (ILRS) highprecision coordinates. Those data are freely available on http://ilrs.gsfc.nasa.gov. The differential equations of the AES motion are solved by the Everhart numerical method of 17th and 19th orders with the integration step automatic correction. The comparison between the AES coordinates computed with the motion model and the ILRS coordinates enabled to determine the accuracy of the ephemerides obtained. As a result, the discrepancy of the computed Etalon-1 ephemerides from the ILRS data is about 10'' for a one-year ephemeris.

The liquid fuel jet in subsonic crossflow

NASA Technical Reports Server (NTRS)

Nguyen, T. T.; Karagozian, A. R.

1990-01-01

An analytical/numerical model is described which predicts the behavior of nonreacting and reacting liquid jets injected transversely into subsonic cross flow. The compressible flowfield about the elliptical jet cross section is solved at various locations along the jet trajectory by analytical means for free-stream local Mach number perpendicular to jet cross section smaller than 0.3 and by numerical means for free-stream local Mach number perpendicular to jet cross section in the range 0.3-1.0. External and internal boundary layers along the jet cross section are solved by integral and numerical methods, and the mass losses due to boundary layer shedding, evaporation, and combustion are calculated and incorporated into the trajectory calculation. Comparison of predicted trajectories is made with limited experimental observations.

The Numerical Technique for the Landslide Tsunami Simulations Based on Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Kozelkov, A. S.

2017-12-01

The paper presents an integral technique simulating all phases of a landslide-driven tsunami. The technique is based on the numerical solution of the system of Navier-Stokes equations for multiphase flows. The numerical algorithm uses a fully implicit approximation method, in which the equations of continuity and momentum conservation are coupled through implicit summands of pressure gradient and mass flow. The method we propose removes severe restrictions on the time step and allows simulation of tsunami propagation to arbitrarily large distances. The landslide origin is simulated as an individual phase being a Newtonian fluid with its own density and viscosity and separated from the water and air phases by an interface. The basic formulas of equation discretization and expressions for coefficients are presented, and the main steps of the computation procedure are described in the paper. To enable simulations of tsunami propagation across wide water areas, we propose a parallel algorithm of the technique implementation, which employs an algebraic multigrid method. The implementation of the multigrid method is based on the global level and cascade collection algorithms that impose no limitations on the paralleling scale and make this technique applicable to petascale systems. We demonstrate the possibility of simulating all phases of a landslide-driven tsunami, including its generation, propagation and uprush. The technique has been verified against the problems supported by experimental data. The paper describes the mechanism of incorporating bathymetric data to simulate tsunamis in real water areas of the world ocean. Results of comparison with the nonlinear dispersion theory, which has demonstrated good agreement, are presented for the case of a historical tsunami of volcanic origin on the Montserrat Island in the Caribbean Sea.

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pelanti, Marica, E-mail: marica.pelanti@ensta-paristech.fr; Shyue, Keh-Ming, E-mail: shyue@ntu.edu.tw

2014-02-15

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxationmore » terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.« less

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

User's Manual for LINER: FORTRAN Code for the Numerical Simulation of Plane Wave Propagation in a Lined Two-Dimensional Channel

NASA Technical Reports Server (NTRS)

Reichert, R, S.; Biringen, S.; Howard, J. E.

1999-01-01

LINER is a system of Fortran 77 codes which performs a 2D analysis of acoustic wave propagation and noise suppression in a rectangular channel with a continuous liner at the top wall. This new implementation is designed to streamline the usage of the several codes making up LINER, resulting in a useful design tool. Major input parameters are placed in two main data files, input.inc and nurn.prm. Output data appear in the form of ASCII files as well as a choice of GNUPLOT graphs. Section 2 briefly describes the physical model. Section 3 discusses the numerical methods; Section 4 gives a detailed account of program usage, including input formats and graphical options. A sample run is also provided. Finally, Section 5 briefly describes the individual program files.

An Investigation of the Tensile Strength of a Composite-To-Metal Adhesive Joint

NASA Astrophysics Data System (ADS)

Tsouvalis, Nicholas G.; Karatzas, Vassilios A.

2011-04-01

The present study examines the feasibility of a simple concept composite-to-metal butt joint through the performance of both numerical and experimental studies. The composite part is made of glass/epoxy unidirectional layers made with the vacuum bag method. The geometry of the joint is typical for marine applications and corresponds to a low stiffness ratio. Two major parameters are investigated, namely the overlap length and the surface preparation of the steel adherent. Manufacturing of specimens and the procedure of the tensile tests are described in detail, giving hints for obtaining a better quality joint. Axial elongation and strains at various places of the joint were monitored and also numerically calculated. The tests revealed that the joint is quite effective, irrespectively of the steel surface preparation method. The failure loads are comparable and in some cases superior to other corresponding values found in the literature. The numerical models proved to adequately predict the structural response of the joint up to the loading where debonding starts.

A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG

NASA Astrophysics Data System (ADS)

Griffiths, M. K.; Fedun, V.; Erdélyi, R.

2015-03-01

Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

NASA Technical Reports Server (NTRS)

Liandrat, J.; Tchamitchian, PH.

1990-01-01

The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Numerical algorithms for computations of feedback laws arising in control of flexible systems

NASA Technical Reports Server (NTRS)

Lasiecka, Irena

1989-01-01

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

NASA Astrophysics Data System (ADS)

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.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

Freak oscillation in a dusty plasma.

PubMed

Zhang, Heng; Yang, Yang; Hong, Xue-Ren; Qi, Xin; Duan, Wen-Shan; Yang, Lei

2017-05-01

The freak oscillation in one-dimensional dusty plasma is studied numerically by particle-in-cell method. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in dusty plasma. Additionally, the application scope of the analytical solution of the rogue wave described by the NLSE is given.

Singularity computations. [finite element methods for elastoplastic flow

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1978-01-01

Direct descriptions of the structure of a singularity would describe the radial and angular distributions of the field quantities as explicitly as practicable along with some measure of the intensity of the singularity. This paper discusses such an approach based on recent development of numerical methods for elastoplastic flow. Attention is restricted to problems where one variable or set of variables is finite at the origin of the singularity but a second set is not.

The kinked interface crack

NASA Astrophysics Data System (ADS)

Heitzer, Joerg

1992-05-01

Two methods for the numerical solution of the integral equation describing the kinked interface crack, one proposed by Erdogan et al. (1973) and the other by Theokaris and Iokimidis (1979), are examined. The method of Erdogan et al. is then used to solve the equation in order to determine the kinking angle of the interface crack. Results are presented for two material combinations, aluminum/epoxy and glass/ceramic, under uniaxial tension in the direction normal to the interface.

Approximate Solutions for Flow with a Stretching Boundary due to Partial Slip

PubMed Central

Filobello-Nino, U.; Vazquez-Leal, H.; Sarmiento-Reyes, A.; Benhammouda, B.; Jimenez-Fernandez, V. M.; Pereyra-Diaz, D.; Perez-Sesma, A.; Cervantes-Perez, J.; Huerta-Chua, J.; Sanchez-Orea, J.; Contreras-Hernandez, A. D.

2014-01-01

The homotopy perturbation method (HPM) is coupled with versions of Laplace-Padé and Padé methods to provide an approximate solution to the nonlinear differential equation that describes the behaviour of a flow with a stretching flat boundary due to partial slip. Comparing results between approximate and numerical solutions, we concluded that our results are capable of providing an accurate solution and are extremely efficient. PMID:27433526

Rare Earth Oxide Fluoride Nanoparticles And Hydrothermal Method For Forming Nanoparticles

DOEpatents

Fulton, John L.; Hoffmann, Markus M.

2003-12-23

A hydrothermal method for forming nanoparticles of a rare earth element, oxygen and fluorine has been discovered. Nanoparticles comprising a rare earth element, oxygen and fluorine are also described. These nanoparticles can exhibit excellent refractory properties as well as remarkable stability in hydrothermal conditions. The nanoparticles can exhibit excellent properties for numerous applications including fiber reinforcement of ceramic composites, catalyst supports, and corrosion resistant coatings for high-temperature aqueous solutions.

Rare earth oxide fluoride nanoparticles and hydrothermal method for forming nanoparticles

DOEpatents

Fulton, John L [Richland, WA; Hoffmann, Markus M [Richland, WA

2001-11-13

A hydrothermal method for forming nanoparticles of a rare earth element, oxygen and fluorine has been discovered. Nanoparticles comprising a rare earth element, oxygen and fluorine are also described. These nanoparticles can exhibit excellent refractory properties as well as remarkable stability in hydrothermal conditions. The nanoparticles can exhibit excellent properties for numerous applications including fiber reinforcement of ceramic composites, catalyst supports, and corrosion resistant coatings for high-temperature aqueous solutions.

Use of various versions of Schwarz method for solving the problem of contact interaction of elastic bodies

NASA Astrophysics Data System (ADS)

Galanin, M. P.; Lukin, V. V.; Rodin, A. S.

2018-04-01

A definition of a sufficiently common problem of mechanical contact interaction in a system of elastic bodies is given. Various versions of realization of the Schwarz method for solving the contact problem numerically are described and the results of solution of a number of problems are presented. Special attention is paid to calculations where the grids in the bodies significantly differ in steps.

A Study of Confined Diffusion Flames

DTIC Science & Technology

1990-09-04

Introduction ............................................................................................... 1 11. Numerical Methods and the Model ...numbers but kept the basic idea of the flame sheet model . This paper describes a time-dependent, axisymmetric, compressible nu- merical model which is...June 5, 1990. first uses of the diffusion flame model , we simulate a Burke-Schumann flame and remove the restrictious individually. We present results

Demographic Accounting and Model-Building. Education and Development Technical Reports.

ERIC Educational Resources Information Center

Stone, Richard

This report describes and develops a model for coordinating a variety of demographic and social statistics within a single framework. The framework proposed, together with its associated methods of analysis, serves both general and specific functions. The general aim of these functions is to give numerical definition to the pattern of society and…

Putting Biology Students Out to Grass: the Nettlecombe Experiment After Thirteen Years.

ERIC Educational Resources Information Center

Crothers, J. H.; Lucas, A. M.

1982-01-01

The importance of examining both the natural history of organisms being investigated and numerical data from long-term field experiments is illustrated by describing a long-running field experiment at an English Field Study Council Centre. Sample results are discussed and alternative methods of using field studies in biology instruction are…

More on Systematic Error in a Boyle's Law Experiment

ERIC Educational Resources Information Center

McCall, Richard P.

2012-01-01

A recent article in "The Physics Teacher" describes a method for analyzing a systematic error in a Boyle's law laboratory activity. Systematic errors are important to consider in physics labs because they tend to bias the results of measurements. There are numerous laboratory examples and resources that discuss this common source of error.

Some Finite Difference Solutions of the Laminar Compressible Boundary Layer Showing the Effects of Upstream Transpiration Cooling

NASA Technical Reports Server (NTRS)

Howe, John T.

1959-01-01

Three numerical solutions of the partial differential equations describing the compressible laminar boundary layer are obtained by the finite difference method described in reports by I. Flugge-Lotz, D.C. Baxter, and this author. The solutions apply to steady-state supersonic flow without pressure gradient, over a cold wall and over an adiabatic wall, both having transpiration cooling upstream, and over an adiabatic wall with upstream cooling but without upstream transpiration. It is shown that for a given upstream wall temperature, upstream transpiration cooling affords much better protection to the adiabatic solid wall than does upstream cooling without transpiration. The results of the numerical solutions are compared with those of approximate solutions. The thermal results of the finite difference solution lie between the results of Rubesin and Inouye, and those of Libby and Pallone. When the skin-friction results of one finite difference solution are used in the thermal analysis of Rubesin and Inouye, improved agreement between the thermal results of the two methods of solution is obtained.

Stationary holographic plasma quenches and numerical methods for non-killing horizons.

PubMed

Figueras, Pau; Wiseman, Toby

2013-04-26

We explore use of the harmonic Einstein equations to numerically find stationary black holes where the problem is posed on an ingoing slice that extends into the interior of the black hole. Requiring no boundary conditions at the horizon beyond smoothness of the metric, this method may be applied for horizons that are not Killing. As a nontrivial illustration we find black holes which, via AdS-CFT, describe a time-independent CFT plasma flowing through a static spacetime which asymptotes to Minkowski in the flow's past and future, with a varying spatial geometry in between. These are the first nonperturbative examples of stationary black holes which do not have Killing horizons. When the CFT spacetime slowly varies, the CFT stress tensor derived from gravity is well described by viscous hydrodynamics. For fast variation it is not, and the solutions are stationary analogs of dynamical quenches, with the plasma being suddenly driven out of equilibrium. We find evidence these flows become unstable for sufficiently strong quenches, and speculate the instability may be turbulent.

Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

NASA Astrophysics Data System (ADS)

Yagasaki, Kazuyuki; Wagenknecht, Thomas

2006-02-01

We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations. We assume that the unperturbed system has primary, symmetric homoclinic orbits, which may be either isolated or appear in a family, and use an idea similar to that of Melnikov’s method to detect homoclinic orbits in their neighbourhood. This technique also allows us to identify bifurcations of unperturbed or perturbed, symmetric homoclinic orbits. Our technique is of importance in applications such as nonlinear optics and water waves since homoclinic orbits to saddle-centre equilibria describe embedded solitons (ESs) in systems of partial differential equations representing physical models, and except for special cases their existence has been previously studied only numerically using shooting methods and continuation techniques. We apply the general theory to two examples, a four-dimensional system describing ESs in nonlinear optical media and a six-dimensional system which can possess a one-parameter family of symmetric homoclinic orbits in the unperturbed case. For these examples, the analysis is compared with numerical computations and an excellent agreement between both results is found.

Advancing Efficient All-Electron Electronic Structure Methods Based on Numeric Atom-Centered Orbitals for Energy Related Materials

NASA Astrophysics Data System (ADS)

Blum, Volker

This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.

Spectral/ hp element methods: Recent developments, applications, and perspectives

NASA Astrophysics Data System (ADS)

Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

2018-02-01

The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

A domain-specific compiler for a parallel multiresolution adaptive numerical simulation environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajbhandari, Samyam; Kim, Jinsung; Krishnamoorthy, Sriram

This paper describes the design and implementation of a layered domain-specific compiler to support MADNESS---Multiresolution ADaptive Numerical Environment for Scientific Simulation. MADNESS is a high-level software environment for the solution of integral and differential equations in many dimensions, using adaptive and fast harmonic analysis methods with guaranteed precision. MADNESS uses k-d trees to represent spatial functions and implements operators like addition, multiplication, differentiation, and integration on the numerical representation of functions. The MADNESS runtime system provides global namespace support and a task-based execution model including futures. MADNESS is currently deployed on massively parallel supercomputers and has enabled many science advances.more » Due to the highly irregular and statically unpredictable structure of the k-d trees representing the spatial functions encountered in MADNESS applications, only purely runtime approaches to optimization have previously been implemented in the MADNESS framework. This paper describes a layered domain-specific compiler developed to address some performance bottlenecks in MADNESS. The newly developed static compile-time optimizations, in conjunction with the MADNESS runtime support, enable significant performance improvement for the MADNESS framework.« less

Experimental Investigations And Numerical Modelling of 210CR12 Steel in Semi-Solid State

NASA Astrophysics Data System (ADS)

Macioł, Piotr; Zalecki, Władysław; Kuziak, Roman; Jakubowicz, Aleksandra; Weglarczyk, Stanisław

2011-05-01

Experimental investigation, including hot compression and simple closed die filling was performed. Temperature range of tests was between 1225 °C and 1320 °C. Temperature selection was adequate with liquid fraction between 20 and 60%, which is typical for thixoforming processes. In the die filling test, steel dies with ceramic layer was used (highly refractory air-setting mortar JM 3300 manufactured by Thermal Ceramics). Experiments were carried out on the Gleeble 3800 physical simulator with MCU unit. In the paper, methodology of experimental investigation is described. Dependency of forming forces on temperature and forming velocities is analysed. Obtained results are discussed. The second part of the paper concerns numerical modelling of semi-solid forming. Numerical models for both sets of test were developed. Structural and Computational Fluid Dynamics models are compared. Initial works in microstructural modelling of 210CR12 steel behaviour are described. Lattice Boltzman Method model for thixotropic flows is introduced. Microscale and macroscale models were integrated into multiscale simulation of semi-solid forming. Some fundamental issues related to multiscale modelling of thixoforming are discussed.

A Numerical Scheme for the Solution of the Space Charge Problem on a Multiply Connected Region

NASA Astrophysics Data System (ADS)

Budd, C. J.; Wheeler, A. A.

1991-11-01

In this paper we extend the work of Budd and Wheeler ( Proc. R. Soc. London A, 417, 389, 1988) , who described a new numerical scheme for the solution of the space charge equation on a simple connected domain, to multiply connected regions. The space charge equation, ▿ · ( Δ overlineϕ ▽ overlineϕ) = 0 , is a third-order nonlinear partial differential equation for the electric potential overlineϕ which models the electric field in the vicinity of a coronating conductor. Budd and Wheeler described a new way of analysing this equation by constructing an orthogonal coordinate system ( overlineϕ, overlineψ) and recasting the equation in terms of x, y, and ▽ overlineϕ as functions of ( overlineϕ, overlineψ). This transformation is singular on multiply connected regions and in this paper we show how this may be overcome to provide an efficient numerical scheme for the solution of the space charge equation. This scheme also provides a new method for the solution of Laplaces equation and the calculation of orthogonal meshes on multiply connected regions.

A gradient enhanced plasticity-damage microplane model for concrete

NASA Astrophysics Data System (ADS)

Zreid, Imadeddin; Kaliske, Michael

2018-03-01

Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Digital database architecture and delineation methodology for deriving drainage basins, and a comparison of digitally and non-digitally derived numeric drainage areas

USGS Publications Warehouse

Dupree, Jean A.; Crowfoot, Richard M.

2012-01-01

The drainage basin is a fundamental hydrologic entity used for studies of surface-water resources and during planning of water-related projects. Numeric drainage areas published by the U.S. Geological Survey water science centers in Annual Water Data Reports and on the National Water Information Systems (NWIS) Web site are still primarily derived from hard-copy sources and by manual delineation of polygonal basin areas on paper topographic map sheets. To expedite numeric drainage area determinations, the Colorado Water Science Center developed a digital database structure and a delineation methodology based on the hydrologic unit boundaries in the National Watershed Boundary Dataset. This report describes the digital database architecture and delineation methodology and also presents the results of a comparison of the numeric drainage areas derived using this digital methodology with those derived using traditional, non-digital methods. (Please see report for full Abstract)

Numerical Simulation of Black Holes

NASA Astrophysics Data System (ADS)

Teukolsky, Saul

2003-04-01

Einstein's equations of general relativity are prime candidates for numerical solution on supercomputers. There is some urgency in being able to carry out such simulations: Large-scale gravitational wave detectors are now coming on line, and the most important expected signals cannot be predicted except numerically. Problems involving black holes are perhaps the most interesting, yet also particularly challenging computationally. One difficulty is that inside a black hole there is a physical singularity that cannot be part of the computational domain. A second difficulty is the disparity in length scales between the size of the black hole and the wavelength of the gravitational radiation emitted. A third difficulty is that all existing methods of evolving black holes in three spatial dimensions are plagued by instabilities that prohibit long-term evolution. I will describe the ideas that are being introduced in numerical relativity to deal with these problems, and discuss the results of recent calculations of black hole collisions.

Calculation of three dimensional viscous flows in annular cascades using parabolized Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Lawerenz, M.

Numerical algorithms for describing the endwall boundary layers and secondary flows in high turning turbine cascades are described. Partially-parabolic methods which cover three-dimensional viscous flow effects are outlined. Introduction of tip-clearance models and modifications of no-slip conditions without the use of wall functions expand the range of application and improve accuracy. Simultaneous computation of the profile boundary layers by refinement of the mesh size in the circumferential direction makes it possible to describe the boundary layer interaction in the corners formed by the bladings and the endwalls. The partially-parabolic method means that the streamwise elliptic coupling is well represented by the given pressure field and that separation does not occur, but it is not possible to describe the separation of the endwall boundary layer near the leading edge and the horse-shoe vortex there properly.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

NASA Technical Reports Server (NTRS)

Gallardo, V. C.; Storace, A. S.; Gaffney, E. F.; Bach, L. J.; Stallone, M. J.

1981-01-01

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described.

On importance assessment of aging multi-state system

NASA Astrophysics Data System (ADS)

Frenkel, Ilia; Khvatskin, Lev; Lisnianski, Anatoly

2017-01-01

Modern high-tech equipment requires precise temperature control and effective cooling below the ambient temperature. Greater cooling efficiencies will allow equipment to be operated for longer periods without overheating, providing a greater return on investment and increased in availability of the equipment. This paper presents application of the Lz-transform method to importance assessment of aging multi-state water-cooling system used in one of Israeli hospitals. The water cooling system consists of 3 principal sub-systems: chillers, heat exchanger and pumps. The performance of the system and the sub-systems is measured by their produced cooling capacity. Heat exchanger is an aging component. Straightforward Markov method applied to solve this problem will require building of a system model with numerous numbers of states and solving a corresponding system of multiple differential equations. Lz-transform method, which is used for calculation of the system elements importance, drastically simplified the solution. Numerical example is presented to illustrate the described approach.

Simulation of two-dimensional turbulent flows in a rotating annulus

NASA Astrophysics Data System (ADS)

Storey, Brian D.

2004-05-01

Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments.

Numerical solutions of anharmonic vibration of BaO and SrO molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pramudito, Sidikrubadi; Sanjaya, Nugraha Wanda; Sumaryada, Tony, E-mail: tsumaryada@ipb.ac.id

2016-03-11

The Morse potential is a potential model that is used to describe the anharmonic behavior of molecular vibration between atoms. The BaO and SrO molecules, which are two almost similar diatomic molecules, were investigated in this research. Some of their properties like the value of the dissociation energy, the energy eigenvalues of each energy level, and the profile of the wavefunctions in their correspondence vibrational states were presented in this paper. Calculation of the energy eigenvalues and plotting the wave function’s profiles were performed using Numerov method combined with the shooting method. In general we concluded that the Morse potentialmore » solved with numerical methods could accurately produce the vibrational properties and the wavefunction behavior of BaO and SrO molecules from the ground state to the higher states close to the dissociation level.« less

Numerical Calculation Method for Prediction of Ground-borne Vibration near Subway Tunnel

NASA Astrophysics Data System (ADS)

Tsuno, Kiwamu; Furuta, Masaru; Abe, Kazuhisa

This paper describes the development of prediction method for ground-borne vibration from railway tunnels. Field measurement was carried out both in a subway shield tunnel, in the ground and on the ground surface. The generated vibration in the tunnel was calculated by means of the train/track/tunnel interaction model and was compared with the measurement results. On the other hand, wave propagation in the ground was calculated utilizing the empirical model, which was proposed based on the relationship between frequency and material damping coefficient α in order to predict the attenuation in the ground in consideration of frequency characteristics. Numerical calculation using 2-dimensinal FE analysis was also carried out in this research. The comparison between calculated and measured results shows that the prediction method including the model for train/track/tunnel interaction and that for wave propagation is applicable to the prediction of train-induced vibration propagated from railway tunnel.

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

NASA Technical Reports Server (NTRS)

Solakiewicz, Richard; Attele, Rohan; Koshak, William

2011-01-01

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Development of Extended Ray-tracing method including diffraction, polarization and wave decay effects

NASA Astrophysics Data System (ADS)

Yanagihara, Kota; Kubo, Shin; Dodin, Ilya; Nakamura, Hiroaki; Tsujimura, Toru

2017-10-01

Geometrical Optics Ray-tracing is a reasonable numerical analytic approach for describing the Electron Cyclotron resonance Wave (ECW) in slowly varying spatially inhomogeneous plasma. It is well known that the result with this conventional method is adequate in most cases. However, in the case of Helical fusion plasma which has complicated magnetic structure, strong magnetic shear with a large scale length of density can cause a mode coupling of waves outside the last closed flux surface, and complicated absorption structure requires a strong focused wave for ECH. Since conventional Ray Equations to describe ECW do not have any terms to describe the diffraction, polarization and wave decay effects, we can not describe accurately a mode coupling of waves, strong focus waves, behavior of waves in inhomogeneous absorption region and so on. For fundamental solution of these problems, we consider the extension of the Ray-tracing method. Specific process is planned as follows. First, calculate the reference ray by conventional method, and define the local ray-base coordinate system along the reference ray. Then, calculate the evolution of the distributions of amplitude and phase on ray-base coordinate step by step. The progress of our extended method will be presented.

Numerical Solution of a 3-D Advection-Dispersion Model for Dissolved Oxygen Distribution in Facultative Ponds

NASA Astrophysics Data System (ADS)

Sunarsih; Sasongko, Dwi P.; Sutrisno

2018-02-01

This paper describes a mathematical model for the dissolved oxygen distribution in the plane of a facultative pond with a certain depth. The purpose of this paper is to determine the variation of dissolved oxygen concentration in facultative ponds. The 3-dimensional advection-diffusion equation is solved using the finite difference method Forward Time Central Space (FTCS). Numerical results show that the aerator greatly affects the occurrence of oxygen concentration variations in the facultative pond in the certain depth. The concentration of dissolved oxygen decreases as the depth of the pond increases.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

A numerical study of electromagnetic scattering from ocean like surfaces

NASA Technical Reports Server (NTRS)

Lentz, R. R.

1972-01-01

The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.; Tang, Harry (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think of a mechanism that activates the split form of the equations only at some parts of the domain. Another issue is how to define good sensors for determining in which parts of the computational domain a certain feature should be filtered by the appropriate numerical dissipation. For the present study we employ a wavelet technique introduced in as sensors. Here, the method is briefly described with selected numerical experiments.

Numerical simulation of wave-induced fluid flow seismic attenuation based on the Cole-Cole model.

PubMed

Picotti, Stefano; Carcione, José M

2017-07-01

The acoustic behavior of porous media can be simulated more realistically using a stress-strain relation based on the Cole-Cole model. In particular, seismic velocity dispersion and attenuation in porous rocks is well described by mesoscopic-loss models. Using the Zener model to simulate wave propagation is a rough approximation, while the Cole-Cole model provides an optimal description of the physics. Here, a time-domain algorithm is proposed based on the Grünwald-Letnikov numerical approximation of the fractional derivative involved in the time-domain representation of the Cole-Cole model, while the spatial derivatives are computed with the Fourier pseudospectral method. The numerical solution is successfully tested against an analytical solution. The methodology is applied to a model of saline aquifer, where carbon dioxide (CO 2 ) is injected. To follow the migration of the gas and detect possible leakages, seismic monitoring surveys should be carried out periodically. To this aim, the sensitivity of the seismic method must be carefully assessed for the specific case. The simulated test considers a possible leakage in the overburden, above the caprock, where the sandstone is partially saturated with gas and brine. The numerical examples illustrate the implementation of the theory.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

Electron-phonon scattering rates in complex polar crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prange, M. P.; Campbell, L. W.; Kerisit, S.

2017-09-01

The thermalization of fast electrons by phonons is studied in CsI, NaI, SrI2, and YAP. This numerical study uses an improvement to a recently developed ab initio method based on a density functional perturbation theoretical description of the phonon modes that provides a way to go beyond widely used phonon models based on binary crystals. Improvements to this method are described, and scattering rates are presented and discussed. The results here treat polar and nonpolar scattering on equal footing and allow an assessment of the relative importance of the two types of scattering. The relative activity of the numerous phononmore » modes in materials with complicated structures is discussed, and a simple criterion for finding the modes that scatter strongly is presented.« less

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

A one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer 3. Numerical methods and comparisons with exact solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gelbard, F.; Fitzgerald, J.W.; Hoppel, W.A.

1998-07-01

We present the theoretical framework and computational methods that were used by {ital Fitzgerald} {ital et al.} [this issue (a), (b)] describing a one-dimensional sectional model to simulate multicomponent aerosol dynamics in the marine boundary layer. The concepts and limitations of modeling spatially varying multicomponent aerosols are elucidated. New numerical sectional techniques are presented for simulating multicomponent aerosol growth, settling, and eddy transport, coupled to time-dependent and spatially varying condensing vapor concentrations. Comparisons are presented with new exact solutions for settling and particle growth by simultaneous dynamic condensation of one vapor and by instantaneous equilibration with a spatially varying secondmore » vapor. {copyright} 1998 American Geophysical Union« less

General Potential Theory of Arbitrary Wing Sections

NASA Technical Reports Server (NTRS)

Theodorsen, T.; Garrick, I. E.

1979-01-01

The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

Application of Stochastic Automata Networks for Creation of Continuous Time Markov Chain Models of Voltage Gating of Gap Junction Channels

PubMed Central

Pranevicius, Henrikas; Pranevicius, Mindaugas; Pranevicius, Osvaldas; Bukauskas, Feliksas F.

2015-01-01

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ∼20 times. PMID:25705700

Development of an integrated BEM for hot fluid-structure interaction

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Dargush, G. F.

1989-01-01

The Boundary Element Method (BEM) is chosen as a basic analysis tool principally because the definition of quantities like fluxes, temperature, displacements, and velocities is very precise on a boundary base discretization scheme. One fundamental difficulty is, of course, that the entire analysis requires a very considerable amount of analytical work which is not present in other numerical methods. During the last 18 months all of this analytical work was completed and a two-dimensional, general purpose code was written. Some of the early results are described. It is anticipated that within the next two to three months almost all two-dimensional idealizations will be examined. It should be noted that the analytical work for the three-dimensional case has also been done and numerical implementation will begin next year.

Modified Newton-Raphson GRAPE methods for optimal control of spin systems

NASA Astrophysics Data System (ADS)

Goodwin, D. L.; Kuprov, Ilya

2016-05-01

Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.

Sparsity based terahertz reflective off-axis digital holography

NASA Astrophysics Data System (ADS)

Wan, Min; Muniraj, Inbarasan; Malallah, Ra'ed; Zhao, Liang; Ryle, James P.; Rong, Lu; Healy, John J.; Wang, Dayong; Sheridan, John T.

2017-05-01

Terahertz radiation lies between the microwave and infrared regions in the electromagnetic spectrum. Emitted frequencies range from 0.1 to 10 THz with corresponding wavelengths ranging from 30 μm to 3 mm. In this paper, a continuous-wave Terahertz off-axis digital holographic system is described. A Gaussian fitting method and image normalisation techniques were employed on the recorded hologram to improve the image resolution. A synthesised contrast enhanced hologram is then digitally constructed. Numerical reconstruction is achieved using the angular spectrum method of the filtered off-axis hologram. A sparsity based compression technique is introduced before numerical data reconstruction in order to reduce the dataset required for hologram reconstruction. Results prove that a tiny amount of sparse dataset is sufficient in order to reconstruct the hologram with good image quality.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Fabrication of ultrathin and highly uniform silicon on insulator by numerically controlled plasma chemical vaporization machining.

PubMed

Sano, Yasuhisa; Yamamura, Kazuya; Mimura, Hidekazu; Yamauchi, Kazuto; Mori, Yuzo

2007-08-01

Metal-oxide semiconductor field-effect transistors fabricated on a silicon-on-insulator (SOI) wafer operate faster and at a lower power than those fabricated on a bulk silicon wafer. Scaling down, which improves their performances, demands thinner SOI wafers. In this article, improvement on the thinning of SOI wafers by numerically controlled plasma chemical vaporization machining (PCVM) is described. PCVM is a gas-phase chemical etching method in which reactive species generated in atmospheric-pressure plasma are used. Some factors affecting uniformity are investigated and methods for improvements are presented. As a result of thinning a commercial 8 in. SOI wafer, the initial SOI layer thickness of 97.5+/-4.7 nm was successfully thinned and made uniform at 7.5+/-1.5 nm.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build

NASA Astrophysics Data System (ADS)

Schwegler, Eric; Challacombe, Matt; Head-Gordon, Martin

1997-06-01

A new linear scaling method for computation of the Cartesian Gaussian-based Hartree-Fock exchange matrix is described, which employs a method numerically equivalent to standard direct SCF, and which does not enforce locality of the density matrix. With a previously described method for computing the Coulomb matrix [J. Chem. Phys. 106, 5526 (1997)], linear scaling incremental Fock builds are demonstrated for the first time. Microhartree accuracy and linear scaling are achieved for restricted Hartree-Fock calculations on sequences of water clusters and polyglycine α-helices with the 3-21G and 6-31G basis sets. Eightfold speedups are found relative to our previous method. For systems with a small ionization potential, such as graphitic sheets, the method naturally reverts to the expected quadratic behavior. Also, benchmark 3-21G calculations attaining microhartree accuracy are reported for the P53 tetramerization monomer involving 698 atoms and 3836 basis functions.

Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow

NASA Astrophysics Data System (ADS)

Henshaw, William D.; Schwendeman, Donald W.

2006-08-01

We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows that demonstrate the use and accuracy of the numerical approach.

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

PubMed Central

Zhou, Shenggao; Sun, Hui; Cheng, Li-Tien; Dzubiella, Joachim; McCammon, J. Andrew

2016-01-01

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach. PMID:27497546

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Shenggao, E-mail: sgzhou@suda.edu.cn, E-mail: bli@math.ucsd.edu; Sun, Hui; Cheng, Li-Tien

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. Wemore » also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.« less

CSR Fields: Direct Numerical Solution of the Maxwell___s Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novokhatski, A.; /SLAC

2011-06-22

We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particlemore » accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in [1]. Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in [2]. We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields [3].« less

Multiphysics phase field modeling of hydrogen diffusion and delta-hydride precipitation in alpha-zirconium

NASA Astrophysics Data System (ADS)

Jokisaari, Andrea M.

Hydride precipitation in zirconium is a significant factor limiting the lifetime of nuclear fuel cladding, because hydride microstructures play a key role in the degradation of fuel cladding. However, the behavior of hydrogen in zirconium has typically been modeled using mean field approaches, which do not consider microstructural evolution. This thesis describes a quantitative microstructural evolution model for the alpha-zirconium/delta-hydride system and the associated numerical methods and algorithms that were developed. The multiphysics, phase field-based model incorporates CALPHAD free energy descriptions, linear elastic solid mechanics, and classical nucleation theory. A flexible simulation software implementing the model, Hyrax, is built on the Multiphysics Object Oriented Simulation Environment (MOOSE) finite element framework. Hyrax is open-source and freely available; moreover, the numerical methods and algorithms that have been developed are generalizable to other systems. The algorithms are described in detail, and verification studies for each are discussed. In addition, analyses of the sensitivity of the simulation results to the choice of numerical parameters are presented. For example, threshold values for the CALPHAD free energy algorithm and the use of mesh and time adaptivity when employing the nucleation algorithm are studied. Furthermore, preliminary insights into the nucleation behavior of delta-hydrides are described. These include a) the sensitivities of the nucleation rate to temperature, interfacial energy, composition and elastic energy, b) the spatial variation of the nucleation rate around a single precipitate, and c) the effect of interfacial energy and nucleation rate on the precipitate microstructure. Finally, several avenues for future work are discussed. Topics encompass the terminal solid solubility hysteresis of hydrogen in zirconium and the effects of the alpha/delta interfacial energy, as well as thermodiffusion, plasticity, and irradiation, which are not yet accounted for in the model.

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing; Walker, Paul D.

2017-02-01

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

A numerical method for computing unsteady 2-D boundary layer flows

NASA Technical Reports Server (NTRS)

Krainer, Andreas

1988-01-01

A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Improvements to Level Set, Immersed Boundary methods for Interface Tracking

NASA Astrophysics Data System (ADS)

Vogl, Chris; Leveque, Randy

2014-11-01

It is not uncommon to find oneself solving a moving boundary problem under flow in the context of some application. Of particular interest is when the moving boundary exerts a curvature-dependent force on the liquid. Such a force arises when observing a boundary that is resistant to bending or has surface tension. Numerically speaking, stable numerical computation of the curvature can be difficult as it is often described in terms of high-order derivatives of either marker particle positions or of a level set function. To address this issue, the level set method is modified to track not only the position of the boundary, but the curvature as well. The definition of the signed-distance function that is used to modify the level set method is also used to develop an interpolation-free, closest-point method. These improvements are used to simulate a bending-resistant, inextensible boundary under shear flow to highlight area and volume conservation, as well as stable curvature calculation. Funded by a NSF MSPRF grant.

An engineering study of hybrid adaptation of wind tunnel walls for three-dimensional testing

NASA Technical Reports Server (NTRS)

Brown, Clinton; Kalumuck, Kenneth; Waxman, David

1987-01-01

Solid wall tunnels having only upper and lower walls flexing are described. An algorithm for selecting the wall contours for both 2 and 3 dimensional wall flexure is presented and numerical experiments are used to validate its applicability to the general test case of 3 dimensional lifting aircraft models in rectangular cross section wind tunnels. The method requires an initial approximate representation of the model flow field at a given lift with wallls absent. The numerical methods utilized are derived by use of Green's source solutions obtained using the method of images; first order linearized flow theory is employed with Prandtl-Glauert compressibility transformations. Equations are derived for the flexed shape of a simple constant thickness plate wall under the influence of a finite number of jacks in an axial row along the plate centerline. The Green's source methods are developed to provide estimations of residual flow distortion (interferences) with measured wall pressures and wall flow inclinations as inputs.

Ray Tracing Methods in Seismic Emission Tomography

NASA Astrophysics Data System (ADS)

Chebotareva, I. Ya.

2018-03-01

Highly efficient approximate ray tracing techniques which can be used in seismic emission tomography and in other methods requiring a large number of raypaths are described. The techniques are applicable for the gradient and plane-layered velocity sections of the medium and for the models with a complicated geometry of contrasting boundaries. The empirical results obtained with the use of the discussed ray tracing technologies and seismic emission tomography results, as well as the results of numerical modeling, are presented.

Tutorial: Measuring Stellar Atmospheric Parameters with ARES+MOOG

NASA Astrophysics Data System (ADS)

Sousa, Sérgio G.; Andreasen, Daniel T.

The technical aspects of using an Equivalent Width (EW) method for the derivation of spectroscopic stellar parameters with ares+ moog are described herein. While the science background to this method can be found in numerous references, the goal here is to provide a user-friendly guide to the several codes and scripts used in the tutorial presented at the School. All the required data have been made available online at the following repository: https://github.com/sousasag/school_codes.

Mean-Field Description of Ionic Size Effects with Non-Uniform Ionic Sizes: A Numerical Approach

PubMed Central

Zhou, Shenggao; Wang, Zhongming; Li, Bo

2013-01-01

Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, i.e., there is no explicit, Boltzmann type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such non-uniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with non-uniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson–Boltzmann theory, or the generalized Poisson–Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed. PMID:21929014

Microplasma fabrication: from semiconductor technology for 2D-chips and microfluidic channels to rapid prototyping and 3D-printing of microplasma devices

NASA Astrophysics Data System (ADS)

Shatford, R.; Karanassios, Vassili

2014-05-01

Microplasmas are receiving attention in recent conferences and current scientific literature. In our laboratory, microplasmas-on-chips proved to be particularly attractive. The 2D- and 3D-chips we developed became hybrid because they were fitted with a quartz plate (quartz was used due to its transparency to UV). Fabrication of 2D- and 3D-chips for microplasma research is described. The fabrication methods described ranged from semiconductor fabrication technology, to Computer Numerical Control (CNC) machining, to 3D-printing. These methods may prove to be useful for those contemplating in entering microplasma research but have no access to expensive semiconductor fabrication equipment.

A boundary element method for Stokes flows with interfaces

NASA Astrophysics Data System (ADS)

Alinovi, Edoardo; Bottaro, Alessandro

2018-03-01

The boundary element method is a widely used and powerful technique to numerically describe multiphase flows with interfaces, satisfying Stokes' approximation. However, low viscosity ratios between immiscible fluids in contact at an interface and large surface tensions may lead to consistency issues as far as mass conservation is concerned. A simple and effective approach is described to ensure mass conservation at all viscosity ratios and capillary numbers within a standard boundary element framework. Benchmark cases are initially considered demonstrating the efficacy of the proposed technique in satisfying mass conservation, comparing with approaches and other solutions present in the literature. The methodology developed is finally applied to the problem of slippage over superhydrophobic surfaces.

A computer program for calculating laminar and turbulent boundary layers for two-dimensional time-dependent flows

NASA Technical Reports Server (NTRS)

Cebeci, T.; Carr, L. W.

1978-01-01

A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.

New software developments for quality mesh generation and optimization from biomedical imaging data.

PubMed

Yu, Zeyun; Wang, Jun; Gao, Zhanheng; Xu, Ming; Hoshijima, Masahiko

2014-01-01

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

On numerical model of time-dependent processes in three-dimensional porous heat-releasing objects

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2016-10-01

The gas flows in the gravity field through porous objects with heat-releasing sources are investigated when the self-regulation of the flow rate of the gas passing through the porous object takes place. Such objects can appear after various natural or man-made disasters (like the exploded unit of the Chernobyl NPP). The mathematical model and the original numerical method, based on a combination of explicit and implicit finite difference schemes, are developed for investigating the time-dependent processes in 3D porous energy-releasing objects. The advantage of the numerical model is its ability to describe unsteady processes under both natural convection and forced filtration. The gas cooling of 3D porous objects with different distribution of heat sources is studied using computational experiment.

seismo-live: Training in Computational Seismology using Jupyter Notebooks

NASA Astrophysics Data System (ADS)

Igel, H.; Krischer, L.; van Driel, M.; Tape, C.

2016-12-01

Practical training in computational methodologies is still underrepresented in Earth science curriculae despite the increasing use of sometimes highly sophisticated simulation technologies in research projects. At the same time well-engineered community codes make it easy to return simulation-based results yet with the danger that the inherent traps of numerical solutions are not well understood. It is our belief that training with highly simplified numerical solutions (here to the equations describing elastic wave propagation) with carefully chosen elementary ingredients of simulation technologies (e.g., finite-differencing, function interpolation, spectral derivatives, numerical integration) could substantially improve this situation. For this purpose we have initiated a community platform (www.seismo-live.org) where Python-based Jupyter notebooks can be accessed and run without and necessary downloads or local software installations. The increasingly popular Jupyter notebooks allow combining markup language, graphics, equations with interactive, executable python codes. We demonstrate the potential with training notebooks for the finite-difference method, pseudospectral methods, finite/spectral element methods, the finite-volume and the discontinuous Galerkin method. The platform already includes general Python training, introduction to the ObsPy library for seismology as well as seismic data processing and noise analysis. Submission of Jupyter notebooks for general seismology are encouraged. The platform can be used for complementary teaching in Earth Science courses on compute-intensive research areas.

Consensus methods: review of original methods and their main alternatives used in public health

PubMed Central

Bourrée, Fanny; Michel, Philippe; Salmi, Louis Rachid

2008-01-01

Summary Background Consensus-based studies are increasingly used as decision-making methods, for they have lower production cost than other methods (observation, experimentation, modelling) and provide results more rapidly. The objective of this paper is to describe the principles and methods of the four main methods, Delphi, nominal group, consensus development conference and RAND/UCLA, their use as it appears in peer-reviewed publications and validation studies published in the healthcare literature. Methods A bibliographic search was performed in Pubmed/MEDLINE, Banque de Données Santé Publique (BDSP), The Cochrane Library, Pascal and Francis. Keywords, headings and qualifiers corresponding to a list of terms and expressions related to the consensus methods were searched in the thesauri, and used in the literature search. A search with the same terms and expressions was performed on Internet using the website Google Scholar. Results All methods, precisely described in the literature, are based on common basic principles such as definition of subject, selection of experts, and direct or remote interaction processes. They sometimes use quantitative assessment for ranking items. Numerous variants of these methods have been described. Few validation studies have been implemented. Not implementing these basic principles and failing to describe the methods used to reach the consensus were both frequent reasons contributing to raise suspicion regarding the validity of consensus methods. Conclusion When it is applied to a new domain with important consequences in terms of decision making, a consensus method should be first validated. PMID:19013039

Harmony Search Method: Theory and Applications

PubMed Central

Gao, X. Z.; Govindasamy, V.; Xu, H.; Wang, X.; Zenger, K.

2015-01-01

The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem. PMID:25945083

Electrostatic similarity of proteins: Application of three dimensional spherical harmonic decomposition

PubMed Central

Długosz, Maciej; Trylska, Joanna

2008-01-01

We present a method for describing and comparing global electrostatic properties of biomolecules based on the spherical harmonic decomposition of electrostatic potential data. Unlike other approaches our method does not require any prior three dimensional structural alignment. The electrostatic potential, given as a volumetric data set from a numerical solution of the Poisson or Poisson–Boltzmann equation, is represented with descriptors that are rotation invariant. The method can be applied to large and structurally diverse sets of biomolecules enabling to cluster them according to their electrostatic features. PMID:18624502

An Eulerian/Lagrangian method for computing blade/vortex impingement

NASA Technical Reports Server (NTRS)

Steinhoff, John; Senge, Heinrich; Yonghu, Wenren

1991-01-01

A combined Eulerian/Lagrangian approach to calculating helicopter rotor flows with concentrated vortices is described. The method computes a general evolving vorticity distribution without any significant numerical diffusion. Concentrated vortices can be accurately propagated over long distances on relatively coarse grids with cores only several grid cells wide. The method is demonstrated for a blade/vortex impingement case in 2D and 3D where a vortex is cut by a rotor blade, and the results are compared to previous 2D calculations involving a fifth-order Navier-Stokes solver on a finer grid.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents.

PubMed

Bürger, Raimund; Chowell, Gerardo; Gavilán, Elvis; Mulet, Pep; Villada, Luis M

2018-02-01

In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.

A Textbook for a First Course in Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Zingg, D. W.; Pulliam, T. H.; Nixon, David (Technical Monitor)

1999-01-01

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Localized Scale Coupling and New Educational Paradigms in Multiscale Mathematics and Science

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ingber, Marc; Vorobieff, Peter

2014-03-14

We have experimentally demonstrated how microscale phenomena affect suspended particle behavior on the mesoscale, and how particle group behavior on the mesoscale influences the macroscale suspension behavior. Semi-analytical and numerical methods to treat flows on different scales have been developed, and a framework to combine these scale-dependent treatment has been described.

The laser lightning rod system: thunderstorm domestication.

PubMed

Ball, L M

1974-10-01

An unusual application of the laser, namely protection of life and property from lightning, is described. The device relies on multiphoton ionization in mode-locked beams, rather than on collisional (avalanche) electron production. Feasibility is demonstrated numerically, and relevant principles explained. A method of mobile deployment is mentioned, by which economic (as opposed to scientific) feasibility might be achieved.

Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

DTIC Science & Technology

2006-12-01

Specifi- cation described by Scilab [19], a MATLAB-like software, into HDL code. The Design Specification consists of a func- tion f (x), a domain over x...In- ter. Conf. on Field Programmable Logic and Applications (FPL’05), pp.118–123, Tampere, Finland, Aug. 2005. [19] Scilab 3.0, INRIA-ENPC, France

Programmable Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

DTIC Science & Technology

2006-01-01

experts. Fig. 1 shows the synthesis flow for the NFG. It converts the Design Specification described by Scilab [18], a MATLAB-like software, into HDL...Tam- pare, Finland, pp. 118–123, Aug. 2005. [18] Scilab 3.0, INRIA-ENPC, France, http://scilabsoft.inria.fr/ [19] M. J. Schulte and J. E. Stine

Procedures for numerical analysis of circadian rhythms

PubMed Central

REFINETTI, ROBERTO; LISSEN, GERMAINE CORNÉ; HALBERG, FRANZ

2010-01-01

This article reviews various procedures used in the analysis of circadian rhythms at the populational, organismal, cellular and molecular levels. The procedures range from visual inspection of time plots and actograms to several mathematical methods of time series analysis. Computational steps are described in some detail, and additional bibliographic resources and computer programs are listed. PMID:23710111

Approximate analysis of thermal convection in a crystal-growth cell for Spacelab 3

NASA Technical Reports Server (NTRS)

Dressler, R. F.

1982-01-01

The transient and steady thermal convection in microgravity is described. The approach is applicable to many three dimensional flows in containers of various shapes with various thermal gradients imposed. The method employs known analytical solutions to two dimensional thermal flows in simpler geometries, and does not require recourse to numerical calculations by computer.

Conformal anomaly of some 2-d Z (n) models

NASA Astrophysics Data System (ADS)

William, Peter

1991-01-01

We describe a numerical calculation of the conformal anomaly in the case of some two-dimensional statistical models undergoing a second-order phase transition, utilizing a recently developed method to compute the partition function exactly. This computation is carried out on a massively parallel CM2 machine, using the finite size scaling behaviour of the free energy.

Monotonicity based imaging method for time-domain eddy current problems

NASA Astrophysics Data System (ADS)

Su, Z.; Ventre, S.; Udpa, L.; Tamburrino, A.

2017-12-01

Eddy current imaging is an example of inverse problem in nondestructive evaluation for detecting anomalies in conducting materials. This paper introduces the concept of time constants and associated natural modes in eddy current imaging. The monotonicity of time constants is then described and applied to develop a non-iterative imaging method. The proposed imaging method has a low computational cost which makes it suitable for real-time operations. Full 3D numerical examples prove the effectiveness of the method in realistic scenarios. This paper is dedicated to Professor Guglielmo Rubinacci on the occasion of his 65th Birthday.

Noise stochastic corrected maximum a posteriori estimator for birefringence imaging using polarization-sensitive optical coherence tomography

PubMed Central

Kasaragod, Deepa; Makita, Shuichi; Hong, Young-Joo; Yasuno, Yoshiaki

2017-01-01

This paper presents a noise-stochastic corrected maximum a posteriori estimator for birefringence imaging using Jones matrix optical coherence tomography. The estimator described in this paper is based on the relationship between probability distribution functions of the measured birefringence and the effective signal to noise ratio (ESNR) as well as the true birefringence and the true ESNR. The Monte Carlo method is used to numerically describe this relationship and adaptive 2D kernel density estimation provides the likelihood for a posteriori estimation of the true birefringence. Improved estimation is shown for the new estimator with stochastic model of ESNR in comparison to the old estimator, both based on the Jones matrix noise model. A comparison with the mean estimator is also done. Numerical simulation validates the superiority of the new estimator. The superior performance of the new estimator was also shown by in vivo measurement of optic nerve head. PMID:28270974

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

NASA Astrophysics Data System (ADS)

Li, Xiaomin; Guo, Xueli; Guo, Haiyan

2018-06-01

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

On the generalized VIP time integral methodology for transient thermal problems

NASA Technical Reports Server (NTRS)

Mei, Youping; Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The paper describes the development and applicability of a generalized VIrtual-Pulse (VIP) time integral method of computation for thermal problems. Unlike past approaches for general heat transfer computations, and with the advent of high speed computing technology and the importance of parallel computations for efficient use of computing environments, a major motivation via the developments described in this paper is the need for developing explicit computational procedures with improved accuracy and stability characteristics. As a consequence, a new and effective VIP methodology is described which inherits these improved characteristics. Numerical illustrative examples are provided to demonstrate the developments and validate the results obtained for thermal problems.

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

High-resolution modeling of a marine ecosystem using the FRESCO hydroecological model

NASA Astrophysics Data System (ADS)

Zalesny, V. B.; Tamsalu, R.

2009-02-01

The FRESCO (Finnish Russian Estonian Cooperation) mathematical model describing a marine hydroecosystem is presented. The methodology of the numerical solution is based on the method of multicomponent splitting into physical and biological processes, spatial coordinates, etc. The model is used for the reproduction of physical and biological processes proceeding in the Baltic Sea. Numerical experiments are performed with different spatial resolutions for four marine basins that are enclosed into one another: the Baltic Sea, the Gulf of Finland, the Tallinn-Helsinki water area, and Tallinn Bay. Physical processes are described by the equations of nonhydrostatic dynamics, including the k-ω parametrization of turbulence. Biological processes are described by the three-dimensional equations of an aquatic ecosystem with the use of a size-dependent parametrization of biochemical reactions. The main goal of this study is to illustrate the efficiency of the developed numerical technique and to demonstrate the importance of a high spatial resolution for water basins that have complex bottom topography, such as the Baltic Sea. Detailed information about the atmospheric forcing, bottom topography, and coastline is very important for the description of coastal dynamics and specific features of a marine ecosystem. Experiments show that the spatial inhomogeneity of hydroecosystem fields is caused by the combined effect of upwelling, turbulent mixing, surface-wave breaking, and temperature variations, which affect biochemical reactions.